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Sample records for noncommutative causal network

  1. Space/time non-commutative field theories and causality

    International Nuclear Information System (INIS)

    Bozkaya, H.; Fischer, P.; Pitschmann, M.; Schweda, M.; Grosse, H.; Putz, V.; Wulkenhaar, R.

    2003-01-01

    As argued previously, amplitudes of quantum field theories on non-commutative space and time cannot be computed using naive path integral Feynman rules. One of the proposals is to use the Gell-Mann-Low formula with time-ordering applied before performing the integrations. We point out that the previously given prescription should rather be regarded as an interaction-point time-ordering. Causality is explicitly violated inside the region of interaction. It is nevertheless a consistent procedure, which seems to be related to the interaction picture of quantum mechanics. In this framework we compute the one-loop self-energy for a space/time non-commutative φ 4 theory. Although in all intermediate steps only three-momenta play a role, the final result is manifestly Lorentz covariant and agrees with the naive calculation. Deriving the Feynman rules for general graphs, we show, however, that such a picture holds for tadpole lines only. (orig.)

  2. Bayesian networks improve causal environmental ...

    Science.gov (United States)

    Rule-based weight of evidence approaches to ecological risk assessment may not account for uncertainties and generally lack probabilistic integration of lines of evidence. Bayesian networks allow causal inferences to be made from evidence by including causal knowledge about the problem, using this knowledge with probabilistic calculus to combine multiple lines of evidence, and minimizing biases in predicting or diagnosing causal relationships. Too often, sources of uncertainty in conventional weight of evidence approaches are ignored that can be accounted for with Bayesian networks. Specifying and propagating uncertainties improve the ability of models to incorporate strength of the evidence in the risk management phase of an assessment. Probabilistic inference from a Bayesian network allows evaluation of changes in uncertainty for variables from the evidence. The network structure and probabilistic framework of a Bayesian approach provide advantages over qualitative approaches in weight of evidence for capturing the impacts of multiple sources of quantifiable uncertainty on predictions of ecological risk. Bayesian networks can facilitate the development of evidence-based policy under conditions of uncertainty by incorporating analytical inaccuracies or the implications of imperfect information, structuring and communicating causal issues through qualitative directed graph formulations, and quantitatively comparing the causal power of multiple stressors on value

  3. Encoding dependence in Bayesian causal networks

    Science.gov (United States)

    Bayesian networks (BNs) represent complex, uncertain spatio-temporal dynamics by propagation of conditional probabilities between identifiable states with a testable causal interaction model. Typically, they assume random variables are discrete in time and space with a static network structure that ...

  4. Reconstructing Causal Biological Networks through Active Learning.

    Directory of Open Access Journals (Sweden)

    Hyunghoon Cho

    Full Text Available Reverse-engineering of biological networks is a central problem in systems biology. The use of intervention data, such as gene knockouts or knockdowns, is typically used for teasing apart causal relationships among genes. Under time or resource constraints, one needs to carefully choose which intervention experiments to carry out. Previous approaches for selecting most informative interventions have largely been focused on discrete Bayesian networks. However, continuous Bayesian networks are of great practical interest, especially in the study of complex biological systems and their quantitative properties. In this work, we present an efficient, information-theoretic active learning algorithm for Gaussian Bayesian networks (GBNs, which serve as important models for gene regulatory networks. In addition to providing linear-algebraic insights unique to GBNs, leading to significant runtime improvements, we demonstrate the effectiveness of our method on data simulated with GBNs and the DREAM4 network inference challenge data sets. Our method generally leads to faster recovery of underlying network structure and faster convergence to final distribution of confidence scores over candidate graph structures using the full data, in comparison to random selection of intervention experiments.

  5. Foundational perspectives on causality in large-scale brain networks

    Science.gov (United States)

    Mannino, Michael; Bressler, Steven L.

    2015-12-01

    A profusion of recent work in cognitive neuroscience has been concerned with the endeavor to uncover causal influences in large-scale brain networks. However, despite the fact that many papers give a nod to the important theoretical challenges posed by the concept of causality, this explosion of research has generally not been accompanied by a rigorous conceptual analysis of the nature of causality in the brain. This review provides both a descriptive and prescriptive account of the nature of causality as found within and between large-scale brain networks. In short, it seeks to clarify the concept of causality in large-scale brain networks both philosophically and scientifically. This is accomplished by briefly reviewing the rich philosophical history of work on causality, especially focusing on contributions by David Hume, Immanuel Kant, Bertrand Russell, and Christopher Hitchcock. We go on to discuss the impact that various interpretations of modern physics have had on our understanding of causality. Throughout all this, a central focus is the distinction between theories of deterministic causality (DC), whereby causes uniquely determine their effects, and probabilistic causality (PC), whereby causes change the probability of occurrence of their effects. We argue that, given the topological complexity of its large-scale connectivity, the brain should be considered as a complex system and its causal influences treated as probabilistic in nature. We conclude that PC is well suited for explaining causality in the brain for three reasons: (1) brain causality is often mutual; (2) connectional convergence dictates that only rarely is the activity of one neuronal population uniquely determined by another one; and (3) the causal influences exerted between neuronal populations may not have observable effects. A number of different techniques are currently available to characterize causal influence in the brain. Typically, these techniques quantify the statistical

  6. Noncommutative time in quantum field theory

    International Nuclear Information System (INIS)

    Salminen, Tapio; Tureanu, Anca

    2011-01-01

    We analyze, starting from first principles, the quantization of field theories, in order to find out to which problems a noncommutative time would possibly lead. We examine the problem in the interaction picture (Tomonaga-Schwinger equation), the Heisenberg picture (Yang-Feldman-Kaellen equation), and the path integral approach. They all indicate inconsistency when time is taken as a noncommutative coordinate. The causality issue appears as the key aspect, while the unitarity problem is subsidiary. These results are consistent with string theory, which does not admit a time-space noncommutative quantum field theory as its low-energy limit, with the exception of lightlike noncommutativity.

  7. Noncommutative gravity

    International Nuclear Information System (INIS)

    Schupp, P.

    2007-01-01

    Heuristic arguments suggest that the classical picture of smooth commutative spacetime should be replaced by some kind of quantum / noncommutative geometry at length scales and energies where quantum as well as gravitational effects are important. Motivated by this idea much research has been devoted to the study of quantum field theory on noncommutative spacetimes. More recently the focus has started to shift back to gravity in this context. We give an introductory overview to the formulation of general relativity in a noncommutative spacetime background and discuss the possibility of exact solutions. (author)

  8. Causal inference in biology networks with integrated belief propagation.

    Science.gov (United States)

    Chang, Rui; Karr, Jonathan R; Schadt, Eric E

    2015-01-01

    Inferring causal relationships among molecular and higher order phenotypes is a critical step in elucidating the complexity of living systems. Here we propose a novel method for inferring causality that is no longer constrained by the conditional dependency arguments that limit the ability of statistical causal inference methods to resolve causal relationships within sets of graphical models that are Markov equivalent. Our method utilizes Bayesian belief propagation to infer the responses of perturbation events on molecular traits given a hypothesized graph structure. A distance measure between the inferred response distribution and the observed data is defined to assess the 'fitness' of the hypothesized causal relationships. To test our algorithm, we infer causal relationships within equivalence classes of gene networks in which the form of the functional interactions that are possible are assumed to be nonlinear, given synthetic microarray and RNA sequencing data. We also apply our method to infer causality in real metabolic network with v-structure and feedback loop. We show that our method can recapitulate the causal structure and recover the feedback loop only from steady-state data which conventional method cannot.

  9. Quantum Steering Beyond Instrumental Causal Networks

    Science.gov (United States)

    Nery, R. V.; Taddei, M. M.; Chaves, R.; Aolita, L.

    2018-04-01

    We theoretically predict, and experimentally verify with entangled photons, that outcome communication is not enough for hidden-state models to reproduce quantum steering. Hidden-state models with outcome communication correspond, in turn, to the well-known instrumental processes of causal inference but in the one-sided device-independent scenario of one black-box measurement device and one well-characterized quantum apparatus. We introduce one-sided device-independent instrumental inequalities to test against these models, with the appealing feature of detecting entanglement even when communication of the black box's measurement outcome is allowed. We find that, remarkably, these inequalities can also be violated solely with steering, i.e., without outcome communication. In fact, an efficiently computable formal quantifier—the robustness of noninstrumentality—naturally arises, and we prove that steering alone is enough to maximize it. Our findings imply that quantum theory admits a stronger form of steering than known until now, with fundamental as well as practical potential implications.

  10. Interdependencies and Causalities in Coupled Financial Networks.

    Science.gov (United States)

    Vodenska, Irena; Aoyama, Hideaki; Fujiwara, Yoshi; Iyetomi, Hiroshi; Arai, Yuta

    2016-01-01

    We explore the foreign exchange and stock market networks for 48 countries from 1999 to 2012 and propose a model, based on complex Hilbert principal component analysis, for extracting significant lead-lag relationships between these markets. The global set of countries, including large and small countries in Europe, the Americas, Asia, and the Middle East, is contrasted with the limited scopes of targets, e.g., G5, G7 or the emerging Asian countries, adopted by previous works. We construct a coupled synchronization network, perform community analysis, and identify formation of four distinct network communities that are relatively stable over time. In addition to investigating the entire period, we divide the time period into into "mild crisis," (1999-2002), "calm," (2003-2006) and "severe crisis" (2007-2012) sub-periods and find that the severe crisis period behavior dominates the dynamics in the foreign exchange-equity synchronization network. We observe that in general the foreign exchange market has predictive power for the global stock market performances. In addition, the United States, German and Mexican markets have forecasting power for the performances of other global equity markets.

  11. Financial networks based on Granger causality: A case study

    Science.gov (United States)

    Papana, Angeliki; Kyrtsou, Catherine; Kugiumtzis, Dimitris; Diks, Cees

    2017-09-01

    Connectivity analysis is performed on a long financial record of 21 international stock indices employing a linear and a nonlinear causality measure, the conditional Granger causality index (CGCI) and the partial mutual information on mixed embedding (PMIME), respectively. Both measures aim to specify the direction of the interrelationships among the international stock indexes and portray the links of the resulting networks, by the presence of direct couplings between variables exploiting all available information. However, their differences are assessed due to the presence of nonlinearity. The weighted networks formed with respect to the causality measures are transformed to binary ones using a significance test. The financial networks are formed on sliding windows in order to examine the network characteristics and trace changes in the connectivity structure. Subsequently, two statistical network quantities are calculated; the average degree and the average shortest path length. The empirical findings reveal interesting time-varying properties of the constructed network, which are clearly dependent on the nature of the financial cycle.

  12. Immediate causality network of stock markets

    Science.gov (United States)

    Zhou, Li; Qiu, Lu; Gu, Changgui; Yang, Huijie

    2018-02-01

    Extensive works show that a network of stocks within a single stock market stores rich information on evolutionary behaviors of the system, such as collapses and/or crises. But a financial event covers usually several markets or even the global financial system. This mismatch of scale leads to lack of concise information to coordinate the event. In this work by using the transfer entropy we reconstruct the influential network between ten typical stock markets distributed in the world. Interesting findings include, before a financial crisis the connection strength reaches a maximum, which can act as an early warning signal of financial crises. The markets in America are monodirectionally and strongly influenced by that in Europe and act as the center. Some strongly linked pairs have also close correlations. The findings are helpful in understanding the evolution and modelling the dynamical process of the global financial system. This method can be extended straightly to find early warning signals for physiological and ecological systems, etc.

  13. Noncommutative solitons

    International Nuclear Information System (INIS)

    Gopakumar, R.

    2002-01-01

    Though noncommutative field theories have been explored for several years, a resurgence of interest in it was sparked off after it was realised that they arise very naturally as limits of string theory in certain background fields. It became more plausible (at least to string theorists) that these nonlocal deformations of usual quantum field theories are consistent theories in themselves. This led to a detailed exploration of many of their classical and quantum properties. I will elaborate further on the string theory context in the next section. One of the consequences of this exploration was the discovery of novel classical solutions in noncommutative field theories. Since then much work has been done in exploring many of their novel properties. My lectures focussed on some specific aspects of these noncommutative solitons. They primarily reflect the topics that I have worked on and are not intended to be a survey of the large amount of work on this topic. We have tried to give a flavour of the physics that can be captured by the relatively elementary classical solutions of noncommutative field theories. We have seen in different contexts how these solitons are really simple manifestations of D-branes, possessing many of their important features. Though they have been primarily studied in the context of tachyon condensation, we saw that they can also shed some light on the resolution of singularities in spacetime by D-brane probes. In addition to other applications in string theory it is important at this stage to explore their presence in other systems with a strong magnetic field like the quantum hall effect

  14. Noncommutative solitons

    Energy Technology Data Exchange (ETDEWEB)

    Gopakumar, R [Harish-Chandra Research Institute, Jhusi, Allahabad (India)

    2002-05-15

    Though noncommutative field theories have been explored for several years, a resurgence of interest in it was sparked off after it was realised that they arise very naturally as limits of string theory in certain background fields. It became more plausible (at least to string theorists) that these nonlocal deformations of usual quantum field theories are consistent theories in themselves. This led to a detailed exploration of many of their classical and quantum properties. I will elaborate further on the string theory context in the next section. One of the consequences of this exploration was the discovery of novel classical solutions in noncommutative field theories. Since then much work has been done in exploring many of their novel properties. My lectures focussed on some specific aspects of these noncommutative solitons. They primarily reflect the topics that I have worked on and are not intended to be a survey of the large amount of work on this topic. We have tried to give a flavour of the physics that can be captured by the relatively elementary classical solutions of noncommutative field theories. We have seen in different contexts how these solitons are really simple manifestations of D-branes, possessing many of their important features. Though they have been primarily studied in the context of tachyon condensation, we saw that they can also shed some light on the resolution of singularities in spacetime by D-brane probes. In addition to other applications in string theory it is important at this stage to explore their presence in other systems with a strong magnetic field like the quantum hall effect.

  15. Characterizing time series: when Granger causality triggers complex networks

    International Nuclear Information System (INIS)

    Ge Tian; Cui Yindong; Lin Wei; Liu Chong; Kurths, Jürgen

    2012-01-01

    In this paper, we propose a new approach to characterize time series with noise perturbations in both the time and frequency domains by combining Granger causality and complex networks. We construct directed and weighted complex networks from time series and use representative network measures to describe their physical and topological properties. Through analyzing the typical dynamical behaviors of some physical models and the MIT-BIH human electrocardiogram data sets, we show that the proposed approach is able to capture and characterize various dynamics and has much potential for analyzing real-world time series of rather short length. (paper)

  16. Characterizing time series: when Granger causality triggers complex networks

    Science.gov (United States)

    Ge, Tian; Cui, Yindong; Lin, Wei; Kurths, Jürgen; Liu, Chong

    2012-08-01

    In this paper, we propose a new approach to characterize time series with noise perturbations in both the time and frequency domains by combining Granger causality and complex networks. We construct directed and weighted complex networks from time series and use representative network measures to describe their physical and topological properties. Through analyzing the typical dynamical behaviors of some physical models and the MIT-BIHMassachusetts Institute of Technology-Beth Israel Hospital. human electrocardiogram data sets, we show that the proposed approach is able to capture and characterize various dynamics and has much potential for analyzing real-world time series of rather short length.

  17. Causal biological network database: a comprehensive platform of causal biological network models focused on the pulmonary and vascular systems.

    Science.gov (United States)

    Boué, Stéphanie; Talikka, Marja; Westra, Jurjen Willem; Hayes, William; Di Fabio, Anselmo; Park, Jennifer; Schlage, Walter K; Sewer, Alain; Fields, Brett; Ansari, Sam; Martin, Florian; Veljkovic, Emilija; Kenney, Renee; Peitsch, Manuel C; Hoeng, Julia

    2015-01-01

    With the wealth of publications and data available, powerful and transparent computational approaches are required to represent measured data and scientific knowledge in a computable and searchable format. We developed a set of biological network models, scripted in the Biological Expression Language, that reflect causal signaling pathways across a wide range of biological processes, including cell fate, cell stress, cell proliferation, inflammation, tissue repair and angiogenesis in the pulmonary and cardiovascular context. This comprehensive collection of networks is now freely available to the scientific community in a centralized web-based repository, the Causal Biological Network database, which is composed of over 120 manually curated and well annotated biological network models and can be accessed at http://causalbionet.com. The website accesses a MongoDB, which stores all versions of the networks as JSON objects and allows users to search for genes, proteins, biological processes, small molecules and keywords in the network descriptions to retrieve biological networks of interest. The content of the networks can be visualized and browsed. Nodes and edges can be filtered and all supporting evidence for the edges can be browsed and is linked to the original articles in PubMed. Moreover, networks may be downloaded for further visualization and evaluation. Database URL: http://causalbionet.com © The Author(s) 2015. Published by Oxford University Press.

  18. Inferring the conservative causal core of gene regulatory networks

    Directory of Open Access Journals (Sweden)

    Emmert-Streib Frank

    2010-09-01

    Full Text Available Abstract Background Inferring gene regulatory networks from large-scale expression data is an important problem that received much attention in recent years. These networks have the potential to gain insights into causal molecular interactions of biological processes. Hence, from a methodological point of view, reliable estimation methods based on observational data are needed to approach this problem practically. Results In this paper, we introduce a novel gene regulatory network inference (GRNI algorithm, called C3NET. We compare C3NET with four well known methods, ARACNE, CLR, MRNET and RN, conducting in-depth numerical ensemble simulations and demonstrate also for biological expression data from E. coli that C3NET performs consistently better than the best known GRNI methods in the literature. In addition, it has also a low computational complexity. Since C3NET is based on estimates of mutual information values in conjunction with a maximization step, our numerical investigations demonstrate that our inference algorithm exploits causal structural information in the data efficiently. Conclusions For systems biology to succeed in the long run, it is of crucial importance to establish methods that extract large-scale gene networks from high-throughput data that reflect the underlying causal interactions among genes or gene products. Our method can contribute to this endeavor by demonstrating that an inference algorithm with a neat design permits not only a more intuitive and possibly biological interpretation of its working mechanism but can also result in superior results.

  19. Inferring the conservative causal core of gene regulatory networks.

    Science.gov (United States)

    Altay, Gökmen; Emmert-Streib, Frank

    2010-09-28

    Inferring gene regulatory networks from large-scale expression data is an important problem that received much attention in recent years. These networks have the potential to gain insights into causal molecular interactions of biological processes. Hence, from a methodological point of view, reliable estimation methods based on observational data are needed to approach this problem practically. In this paper, we introduce a novel gene regulatory network inference (GRNI) algorithm, called C3NET. We compare C3NET with four well known methods, ARACNE, CLR, MRNET and RN, conducting in-depth numerical ensemble simulations and demonstrate also for biological expression data from E. coli that C3NET performs consistently better than the best known GRNI methods in the literature. In addition, it has also a low computational complexity. Since C3NET is based on estimates of mutual information values in conjunction with a maximization step, our numerical investigations demonstrate that our inference algorithm exploits causal structural information in the data efficiently. For systems biology to succeed in the long run, it is of crucial importance to establish methods that extract large-scale gene networks from high-throughput data that reflect the underlying causal interactions among genes or gene products. Our method can contribute to this endeavor by demonstrating that an inference algorithm with a neat design permits not only a more intuitive and possibly biological interpretation of its working mechanism but can also result in superior results.

  20. Investigating Driver Fatigue versus Alertness Using the Granger Causality Network

    Directory of Open Access Journals (Sweden)

    Wanzeng Kong

    2015-08-01

    Full Text Available Driving fatigue has been identified as one of the main factors affecting drivers’ safety. The aim of this study was to analyze drivers’ different mental states, such as alertness and drowsiness, and find out a neurometric indicator able to detect drivers’ fatigue level in terms of brain networks. Twelve young, healthy subjects were recruited to take part in a driver fatigue experiment under different simulated driving conditions. The Electroencephalogram (EEG signals of the subjects were recorded during the whole experiment and analyzed by using Granger-Causality-based brain effective networks. It was that the topology of the brain networks and the brain’s ability to integrate information changed when subjects shifted from the alert to the drowsy stage. In particular, there was a significant difference in terms of strength of Granger causality (GC in the frequency domain and the properties of the brain effective network i.e., causal flow, global efficiency and characteristic path length between such conditions. Also, some changes were more significant over the frontal brain lobes for the alpha frequency band. These findings might be used to detect drivers’ fatigue levels, and as reference work for future studies.

  1. Causality

    Science.gov (United States)

    Pearl, Judea

    2000-03-01

    Written by one of the pre-eminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, philosophy, cognitive science, and the health and social sciences. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artifical intelligence, business, epidemiology, social science and economics. Students in these areas will find natural models, simple identification procedures, and precise mathematical definitions of causal concepts that traditional texts have tended to evade or make unduly complicated. This book will be of interest to professionals and students in a wide variety of fields. Anyone who wishes to elucidate meaningful relationships from data, predict effects of actions and policies, assess explanations of reported events, or form theories of causal understanding and causal speech will find this book stimulating and invaluable.

  2. Causal Inference and Explaining Away in a Spiking Network

    Science.gov (United States)

    Moreno-Bote, Rubén; Drugowitsch, Jan

    2015-01-01

    While the brain uses spiking neurons for communication, theoretical research on brain computations has mostly focused on non-spiking networks. The nature of spike-based algorithms that achieve complex computations, such as object probabilistic inference, is largely unknown. Here we demonstrate that a family of high-dimensional quadratic optimization problems with non-negativity constraints can be solved exactly and efficiently by a network of spiking neurons. The network naturally imposes the non-negativity of causal contributions that is fundamental to causal inference, and uses simple operations, such as linear synapses with realistic time constants, and neural spike generation and reset non-linearities. The network infers the set of most likely causes from an observation using explaining away, which is dynamically implemented by spike-based, tuned inhibition. The algorithm performs remarkably well even when the network intrinsically generates variable spike trains, the timing of spikes is scrambled by external sources of noise, or the network is mistuned. This type of network might underlie tasks such as odor identification and classification. PMID:26621426

  3. Dynamics and causalities of atmospheric and oceanic data identified by complex networks and Granger causality analysis

    Science.gov (United States)

    Charakopoulos, A. K.; Katsouli, G. A.; Karakasidis, T. E.

    2018-04-01

    Understanding the underlying processes and extracting detailed characteristics of spatiotemporal dynamics of ocean and atmosphere as well as their interaction is of significant interest and has not been well thoroughly established. The purpose of this study was to examine the performance of two main additional methodologies for the identification of spatiotemporal underlying dynamic characteristics and patterns among atmospheric and oceanic variables from Seawatch buoys from Aegean and Ionian Sea, provided by the Hellenic Center for Marine Research (HCMR). The first approach involves the estimation of cross correlation analysis in an attempt to investigate time-lagged relationships, and further in order to identify the direction of interactions between the variables we performed the Granger causality method. According to the second approach the time series are converted into complex networks and then the main topological network properties such as degree distribution, average path length, diameter, modularity and clustering coefficient are evaluated. Our results show that the proposed analysis of complex network analysis of time series can lead to the extraction of hidden spatiotemporal characteristics. Also our findings indicate high level of positive and negative correlations and causalities among variables, both from the same buoy and also between buoys from different stations, which cannot be determined from the use of simple statistical measures.

  4. Noncommutative geometry

    CERN Document Server

    Connes, Alain

    1994-01-01

    This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat

  5. Causality in Psychiatry: A Hybrid Symptom Network Construct Model

    Directory of Open Access Journals (Sweden)

    Gerald eYoung

    2015-11-01

    Full Text Available Causality or etiology in psychiatry is marked by standard biomedical, reductionistic models (symptoms reflect the construct involved that inform approaches to nosology, or classification, such as in the DSM-5 (Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition; American Psychiatric Association, 2013. However, network approaches to symptom interaction (i.e., symptoms are formative of the construct; e.g., McNally, Robinaugh, Wu, Wang, Deserno, & Borsboom, 2014, for PTSD (posttraumatic stress disorder are being developed that speak to bottom-up processes in mental disorder, in contrast to the typical top-down psychological construct approach. The present article presents a hybrid top-down, bottom-up model of the relationship between symptoms and mental disorder, viewing symptom expression and their causal complex as a reciprocally dynamic system with multiple levels, from lower-order symptoms in interaction to higher-order constructs affecting them. The hybrid model hinges on good understanding of systems theory in which it is embedded, so that the article reviews in depth nonlinear dynamical systems theory (NLDST. The article applies the concept of emergent circular causality (Young, 2011 to symptom development, as well. Conclusions consider that symptoms vary over several dimensions, including: subjectivity; objectivity; conscious motivation effort; and unconscious influences, and the degree to which individual (e.g., meaning and universal (e.g., causal processes are involved. The opposition between science and skepticism is a complex one that the article addresses in final comments.

  6. Pair production by a constant external field in noncommutative QED

    International Nuclear Information System (INIS)

    Chair, N.; Sheikh-Jabbari, M.M.

    2000-09-01

    In this paper we study QED on the noncommutative space in the constant electro-magnetic field background. Using the explicit solutions of the noncommutative version of Dirac equation in such background, we show that there are well-defined in and out-going asymptotic states and also there is a causal Green's function. We calculate the pair production rate in this case. We show that at tree level noncommutativity will not change the pair production and the threshold electric field. We also calculate the pair production rate considering the first loop corrections. In this case we show that the threshold electric field is decreased by the noncommutativity effects. (author)

  7. Unitary quantum physics with time-space non-commutativity

    International Nuclear Information System (INIS)

    Balachandran, A P; Govindarajan, T R; Martins, A G; Molina, C; Teotonio-Sobrinho, P

    2005-01-01

    In these lectures 4 quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. In the context of noncommutative quantum mechanics, some important points are explored, such as the formal construction of the theory, symmetries, causality, simultaneity and observables. The dynamics generated by a noncommutative Schroedinger equation is studied. The theory is further extended to certain noncommutative versions of the cylinder, R 3 and R x S 3 . In all these models, only discrete time translations are possible. One striking consequence of quantised time translations is that even though a time independent Hamiltonian is an observable, in scattering processes, it is conserved only modulo 2π/θ, where θ is the noncommutative parameter. Scattering theory is formulated and an approach to quantumfield theory is outlined

  8. The causal inference of cortical neural networks during music improvisations.

    Science.gov (United States)

    Wan, Xiaogeng; Crüts, Björn; Jensen, Henrik Jeldtoft

    2014-01-01

    We present an EEG study of two music improvisation experiments. Professional musicians with high level of improvisation skills were asked to perform music either according to notes (composed music) or in improvisation. Each piece of music was performed in two different modes: strict mode and "let-go" mode. Synchronized EEG data was measured from both musicians and listeners. We used one of the most reliable causality measures: conditional Mutual Information from Mixed Embedding (MIME), to analyze directed correlations between different EEG channels, which was combined with network theory to construct both intra-brain and cross-brain networks. Differences were identified in intra-brain neural networks between composed music and improvisation and between strict mode and "let-go" mode. Particular brain regions such as frontal, parietal and temporal regions were found to play a key role in differentiating the brain activities between different playing conditions. By comparing the level of degree centralities in intra-brain neural networks, we found a difference between the response of musicians and the listeners when comparing the different playing conditions.

  9. The Causal Inference of Cortical Neural Networks during Music Improvisations

    Science.gov (United States)

    Wan, Xiaogeng; Crüts, Björn; Jensen, Henrik Jeldtoft

    2014-01-01

    We present an EEG study of two music improvisation experiments. Professional musicians with high level of improvisation skills were asked to perform music either according to notes (composed music) or in improvisation. Each piece of music was performed in two different modes: strict mode and “let-go” mode. Synchronized EEG data was measured from both musicians and listeners. We used one of the most reliable causality measures: conditional Mutual Information from Mixed Embedding (MIME), to analyze directed correlations between different EEG channels, which was combined with network theory to construct both intra-brain and cross-brain networks. Differences were identified in intra-brain neural networks between composed music and improvisation and between strict mode and “let-go” mode. Particular brain regions such as frontal, parietal and temporal regions were found to play a key role in differentiating the brain activities between different playing conditions. By comparing the level of degree centralities in intra-brain neural networks, we found a difference between the response of musicians and the listeners when comparing the different playing conditions. PMID:25489852

  10. The causal inference of cortical neural networks during music improvisations.

    Directory of Open Access Journals (Sweden)

    Xiaogeng Wan

    Full Text Available We present an EEG study of two music improvisation experiments. Professional musicians with high level of improvisation skills were asked to perform music either according to notes (composed music or in improvisation. Each piece of music was performed in two different modes: strict mode and "let-go" mode. Synchronized EEG data was measured from both musicians and listeners. We used one of the most reliable causality measures: conditional Mutual Information from Mixed Embedding (MIME, to analyze directed correlations between different EEG channels, which was combined with network theory to construct both intra-brain and cross-brain networks. Differences were identified in intra-brain neural networks between composed music and improvisation and between strict mode and "let-go" mode. Particular brain regions such as frontal, parietal and temporal regions were found to play a key role in differentiating the brain activities between different playing conditions. By comparing the level of degree centralities in intra-brain neural networks, we found a difference between the response of musicians and the listeners when comparing the different playing conditions.

  11. Inferring causal molecular networks: empirical assessment through a community-based effort.

    Science.gov (United States)

    Hill, Steven M; Heiser, Laura M; Cokelaer, Thomas; Unger, Michael; Nesser, Nicole K; Carlin, Daniel E; Zhang, Yang; Sokolov, Artem; Paull, Evan O; Wong, Chris K; Graim, Kiley; Bivol, Adrian; Wang, Haizhou; Zhu, Fan; Afsari, Bahman; Danilova, Ludmila V; Favorov, Alexander V; Lee, Wai Shing; Taylor, Dane; Hu, Chenyue W; Long, Byron L; Noren, David P; Bisberg, Alexander J; Mills, Gordon B; Gray, Joe W; Kellen, Michael; Norman, Thea; Friend, Stephen; Qutub, Amina A; Fertig, Elana J; Guan, Yuanfang; Song, Mingzhou; Stuart, Joshua M; Spellman, Paul T; Koeppl, Heinz; Stolovitzky, Gustavo; Saez-Rodriguez, Julio; Mukherjee, Sach

    2016-04-01

    It remains unclear whether causal, rather than merely correlational, relationships in molecular networks can be inferred in complex biological settings. Here we describe the HPN-DREAM network inference challenge, which focused on learning causal influences in signaling networks. We used phosphoprotein data from cancer cell lines as well as in silico data from a nonlinear dynamical model. Using the phosphoprotein data, we scored more than 2,000 networks submitted by challenge participants. The networks spanned 32 biological contexts and were scored in terms of causal validity with respect to unseen interventional data. A number of approaches were effective, and incorporating known biology was generally advantageous. Additional sub-challenges considered time-course prediction and visualization. Our results suggest that learning causal relationships may be feasible in complex settings such as disease states. Furthermore, our scoring approach provides a practical way to empirically assess inferred molecular networks in a causal sense.

  12. A Temporal-Causal Modelling Approach to Integrated Contagion and Network Change in Social Networks

    NARCIS (Netherlands)

    Blankendaal, Romy; Parinussa, Sarah; Treur, Jan

    2016-01-01

    This paper introduces an integrated temporal-causal model for dynamics in social networks addressing the contagion principle by which states are affected mutually, and both the homophily principle and the more-becomes-more principle by which connections are adapted over time. The integrated model

  13. Noncommutative baby Skyrmions

    International Nuclear Information System (INIS)

    Ioannidou, Theodora; Lechtenfeld, Olaf

    2009-01-01

    We subject the baby Skyrme model to a Moyal deformation, for unitary or Grassmannian target spaces and without a potential term. In the Abelian case, the radial BPS configurations of the ordinary noncommutative sigma model also solve the baby Skyrme equation of motion. This gives a class of exact analytic noncommutative baby Skyrmions, which have a singular commutative limit but are stable against scaling due to the noncommutativity. We compute their energies, investigate their stability and determine the asymptotic two-Skyrmion interaction.

  14. Noncommutative black holes

    Energy Technology Data Exchange (ETDEWEB)

    Lopez-DomInguez, J C [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico); Obregon, O [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico); RamIrez, C [Facultad de Ciencias FIsico Matematicas, Universidad Autonoma de Puebla, PO Box 1364, 72000 Puebla (Mexico); Sabido, M [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico)

    2007-11-15

    We study noncommutative black holes, by using a diffeomorphism between the Schwarzschild black hole and the Kantowski-Sachs cosmological model, which is generalized to noncommutative minisuperspace. Through the use of the Feynman-Hibbs procedure we are able to study the thermodynamics of the black hole, in particular, we calculate Hawking's temperature and entropy for the 'noncommutative' Schwarzschild black hole.

  15. Noncommutative Valuation of Options

    Science.gov (United States)

    Herscovich, Estanislao

    2016-12-01

    The aim of this note is to show that the classical results in finance theory for pricing of derivatives, given by making use of the replication principle, can be extended to the noncommutative world. We believe that this could be of interest in quantum probability. The main result called the First fundamental theorem of asset pricing, states that a noncommutative stock market admits no-arbitrage if and only if it admits a noncommutative equivalent martingale probability.

  16. Exploring causal networks of bovine milk fatty acids in a multivariate mixed model context

    DEFF Research Database (Denmark)

    Bouwman, Aniek C; Valente, Bruno D; Janss, Luc L G

    2014-01-01

    Knowledge regarding causal relationships among traits is important to understand complex biological systems. Structural equation models (SEM) can be used to quantify the causal relations between traits, which allow prediction of outcomes to interventions applied to such a network. Such models...... are fitted conditionally on a causal structure among traits, represented by a directed acyclic graph and an Inductive Causation (IC) algorithm can be used to search for causal structures. The aim of this study was to explore the space of causal structures involving bovine milk fatty acids and to select...

  17. Financial networks based on Granger causality: A case study

    NARCIS (Netherlands)

    Papana, A.; Kyrtsou, C.; Kugiumtzis, D.; Diks, C.

    Connectivity analysis is performed on a long financial record of 21 international stock indices employing a linear and a nonlinear causality measure, the conditional Granger causality index (CGCI) and the partial mutual information on mixed embedding (PMIME), respectively. Both measures aim to

  18. Perturbed nonlinear models from noncommutativity

    International Nuclear Information System (INIS)

    Cabrera-Carnero, I.; Correa-Borbonet, Luis Alejandro; Valadares, G.C.S.

    2007-01-01

    By means of the Ehrenfest's Theorem inside the context of a noncommutative Quantum Mechanics it is obtained the Newton's Second Law in noncommutative space. Considering discrete systems with infinite degrees of freedom whose dynamical evolutions are governed by the noncommutative Newton's Second Law we have constructed some alternative noncommutative generalizations of two-dimensional field theories. (author)

  19. Providing probability distributions for the causal pathogen of clinical mastitis using naive Bayesian networks

    NARCIS (Netherlands)

    Steeneveld, W.; Gaag, van der L.C.; Barkema, H.W.; Hogeveen, H.

    2009-01-01

    Clinical mastitis (CM) can be caused by a wide variety of pathogens and farmers must start treatment before the actual causal pathogen is known. By providing a probability distribution for the causal pathogen, naive Bayesian networks (NBN) can serve as a management tool for farmers to decide which

  20. Characterization of physiological networks in sleep apnea patients using artificial neural networks for Granger causality computation

    Science.gov (United States)

    Cárdenas, Jhon; Orjuela-Cañón, Alvaro D.; Cerquera, Alexander; Ravelo, Antonio

    2017-11-01

    Different studies have used Transfer Entropy (TE) and Granger Causality (GC) computation to quantify interconnection between physiological systems. These methods have disadvantages in parametrization and availability in analytic formulas to evaluate the significance of the results. Other inconvenience is related with the assumptions in the distribution of the models generated from the data. In this document, the authors present a way to measure the causality that connect the Central Nervous System (CNS) and the Cardiac System (CS) in people diagnosed with obstructive sleep apnea syndrome (OSA) before and during treatment with continuous positive air pressure (CPAP). For this purpose, artificial neural networks were used to obtain models for GC computation, based on time series of normalized powers calculated from electrocardiography (EKG) and electroencephalography (EEG) signals recorded in polysomnography (PSG) studies.

  1. Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

    Energy Technology Data Exchange (ETDEWEB)

    Gitman, D.M. [Universidade de Sao Paulo, Instituto de Fisica, Sao Paulo, SP (Brazil); Kupriyanov, V.G. [Universidade de Sao Paulo, Instituto de Fisica, Sao Paulo, SP (Brazil); Tomsk State University, Physics Department, Tomsk (Russian Federation)

    2008-03-15

    It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them {theta}-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing {theta}-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract {theta}-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as {theta}-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The {theta}-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case. (orig.)

  2. The topology of a causal network for the Chinese financial system

    Science.gov (United States)

    Gao, Bo; Ren, Ruo-en

    2013-07-01

    The paper builds a causal network for the Chinese financial system based on the Granger causality of company risks, studies its different topologies in crisis and bull period, and applies the centrality to explain individual risk and prevent systemic risk. The results show that this causal network possesses both small-world phenomenon and scale-free property, and has a little different average distance, clustering coefficient, and degree distribution in different periods, and financial institutions with high centrality not only have large individual risk, but also are important for systemic risk immunization.

  3. Causality and Information Dynamics in Networked Systems with Many Agents

    Science.gov (United States)

    2017-05-11

    algorithms. 6 Future Perspectives Causal graph reconstruction from noisy data is a problem of central importance. In our research we have shown how the idea ...thrust of the research was to develop methods for GCG sparsification using ideas from Tikhonov regularization and ADMM based proximal algorithms...not vary with time. The notion of Granger-causality is captured in the following definition . Definition 2.1 If ξ̂[xi(t) |Ht] < ξ̂[xi(t) |H−jt ] , (2.2

  4. Covariant Noncommutative Field Theory

    Energy Technology Data Exchange (ETDEWEB)

    Estrada-Jimenez, S [Licenciaturas en Fisica y en Matematicas, Facultad de Ingenieria, Universidad Autonoma de Chiapas Calle 4a Ote. Nte. 1428, Tuxtla Gutierrez, Chiapas (Mexico); Garcia-Compean, H [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN P.O. Box 14-740, 07000 Mexico D.F., Mexico and Centro de Investigacion y de Estudios Avanzados del IPN, Unidad Monterrey Via del Conocimiento 201, Parque de Investigacion e Innovacion Tecnologica (PIIT) Autopista nueva al Aeropuerto km 9.5, Lote 1, Manzana 29, cp. 66600 Apodaca Nuevo Leon (Mexico); Obregon, O [Instituto de Fisica de la Universidad de Guanajuato P.O. Box E-143, 37150 Leon Gto. (Mexico); Ramirez, C [Facultad de Ciencias Fisico Matematicas, Universidad Autonoma de Puebla, P.O. Box 1364, 72000 Puebla (Mexico)

    2008-07-02

    The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced.

  5. Noncommutative calculi of probabilty

    Directory of Open Access Journals (Sweden)

    Michał Heller

    2010-12-01

    Full Text Available The paper can be regarded as a short and informal introduction to noncommutative calculi of probability. The standard theory of probability is reformulated in the algebraic language. In this form it is readily generalized to that its version which is virtually present in quantum mechanics, and then generalized to the so-called free theory of probability. Noncommutative theory of probability is a pair (M, φ where M is a von Neumann algebra, and φ a normal state on M which plays the role of a noncommutative probability measure. In the standard (commutative theory of probability, there is, in principle, one mathematically interesting probability measure, namely the Lebesgue measure, whereas in the noncommutative theories there are many nonequivalent probability measures. Philosophical implications of this fact are briefly discussed.

  6. Covariant Noncommutative Field Theory

    International Nuclear Information System (INIS)

    Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.

    2008-01-01

    The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced

  7. Inferring hidden causal relations between pathway members using reduced Google matrix of directed biological networks

    Science.gov (United States)

    2018-01-01

    Signaling pathways represent parts of the global biological molecular network which connects them into a seamless whole through complex direct and indirect (hidden) crosstalk whose structure can change during development or in pathological conditions. We suggest a novel methodology, called Googlomics, for the structural analysis of directed biological networks using spectral analysis of their Google matrices, using parallels with quantum scattering theory, developed for nuclear and mesoscopic physics and quantum chaos. We introduce analytical “reduced Google matrix” method for the analysis of biological network structure. The method allows inferring hidden causal relations between the members of a signaling pathway or a functionally related group of genes. We investigate how the structure of hidden causal relations can be reprogrammed as a result of changes in the transcriptional network layer during cancerogenesis. The suggested Googlomics approach rigorously characterizes complex systemic changes in the wiring of large causal biological networks in a computationally efficient way. PMID:29370181

  8. Noncommutative Lagrange Mechanics

    Directory of Open Access Journals (Sweden)

    Denis Kochan

    2008-02-01

    Full Text Available It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy, which are extensively applied within noncommutative quantum theories. Newton-Lagrange noncommutative equations of motion are formulated and their properties are analyzed from the pure geometrical point of view. It is argued that the dynamical quintessence of the system consists in its kinetic energy (Riemannian metric specifying Riemann-Levi-Civita connection and thus the inertia geodesics of the free motion. Throughout the paper, ''noncommutativity'' is considered as an internal geometric structure of the configuration space, which can not be ''observed'' per se. Manifestation of the noncommutative phenomena is mediated by the interaction of the system with noncommutative background under the consideration. The simplest model of the interaction (minimal coupling is proposed and it is shown that guiding affine connection is modified by the quadratic analog of the Lorentz electromagnetic force (contortion term.

  9. Causal Learning and Explanation of Deep Neural Networks via Autoencoded Activations

    OpenAIRE

    Harradon, Michael; Druce, Jeff; Ruttenberg, Brian

    2018-01-01

    Deep neural networks are complex and opaque. As they enter application in a variety of important and safety critical domains, users seek methods to explain their output predictions. We develop an approach to explaining deep neural networks by constructing causal models on salient concepts contained in a CNN. We develop methods to extract salient concepts throughout a target network by using autoencoders trained to extract human-understandable representations of network activations. We then bu...

  10. Network and system diagrams revisited: Satisfying CEA requirements for causality analysis

    International Nuclear Information System (INIS)

    Perdicoulis, Anastassios; Piper, Jake

    2008-01-01

    Published guidelines for Cumulative Effects Assessment (CEA) have called for the identification of cause-and-effect relationships, or causality, challenging researchers to identify methods that can possibly meet CEA's specific requirements. Together with an outline of these requirements from CEA key literature, the various definitions of cumulative effects point to the direction of a method for causality analysis that is visually-oriented and qualitative. This article consequently revisits network and system diagrams, resolves their reported shortcomings, and extends their capabilities with causal loop diagramming methodology. The application of the resulting composite causality analysis method to three Environmental Impact Assessment (EIA) case studies appears to satisfy the specific requirements of CEA regarding causality. Three 'moments' are envisaged for the use of the proposed method: during the scoping stage, during the assessment process, and during the stakeholder participation process

  11. Arithmetic noncommutative geometry

    CERN Document Server

    Marcolli, Matilde

    2005-01-01

    Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...

  12. Altered causal connectivity of resting state brain networks in amnesic MCI.

    Directory of Open Access Journals (Sweden)

    Peipeng Liang

    Full Text Available Most neuroimaging studies of resting state networks in amnesic mild cognitive impairment (aMCI have concentrated on functional connectivity (FC based on instantaneous correlation in a single network. The purpose of the current study was to investigate effective connectivity in aMCI patients based on Granger causality of four important networks at resting state derived from functional magnetic resonance imaging data--default mode network (DMN, hippocampal cortical memory network (HCMN, dorsal attention network (DAN and fronto-parietal control network (FPCN. Structural and functional MRI data were collected from 16 aMCI patients and 16 age, gender-matched healthy controls. Correlation-purged Granger causality analysis was used, taking gray matter atrophy as covariates, to compare the group difference between aMCI patients and healthy controls. We found that the causal connectivity between networks in aMCI patients was significantly altered with both increases and decreases in the aMCI group as compared to healthy controls. Some alterations were significantly correlated with the disease severity as measured by mini-mental state examination (MMSE, and California verbal learning test (CVLT scores. When the whole-brain signal averaged over the entire brain was used as a nuisance co-variate, the within-group maps were significantly altered while the between-group difference maps did not. These results suggest that the alterations in causal influences may be one of the possible underlying substrates of cognitive impairments in aMCI. The present study extends and complements previous FC studies and demonstrates the coexistence of causal disconnection and compensation in aMCI patients, and thus might provide insights into biological mechanism of the disease.

  13. A noncommutative catenoid

    Science.gov (United States)

    Arnlind, Joakim; Holm, Christoffer

    2018-01-01

    A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex structure, and the curvature is explicitly calculated. A noncommutative analogue of the fact that the catenoid is a minimal surface is studied by constructing a Laplace operator from the connection and showing that the embedding coordinates are harmonic. Furthermore, an integral is defined and the total curvature is computed. Finally, classes of left and right modules are introduced together with constant curvature connections, and bimodule compatibility conditions are discussed in detail.

  14. Extracting neuronal functional network dynamics via adaptive Granger causality analysis.

    Science.gov (United States)

    Sheikhattar, Alireza; Miran, Sina; Liu, Ji; Fritz, Jonathan B; Shamma, Shihab A; Kanold, Patrick O; Babadi, Behtash

    2018-04-24

    Quantifying the functional relations between the nodes in a network based on local observations is a key challenge in studying complex systems. Most existing time series analysis techniques for this purpose provide static estimates of the network properties, pertain to stationary Gaussian data, or do not take into account the ubiquitous sparsity in the underlying functional networks. When applied to spike recordings from neuronal ensembles undergoing rapid task-dependent dynamics, they thus hinder a precise statistical characterization of the dynamic neuronal functional networks underlying adaptive behavior. We develop a dynamic estimation and inference paradigm for extracting functional neuronal network dynamics in the sense of Granger, by integrating techniques from adaptive filtering, compressed sensing, point process theory, and high-dimensional statistics. We demonstrate the utility of our proposed paradigm through theoretical analysis, algorithm development, and application to synthetic and real data. Application of our techniques to two-photon Ca 2+ imaging experiments from the mouse auditory cortex reveals unique features of the functional neuronal network structures underlying spontaneous activity at unprecedented spatiotemporal resolution. Our analysis of simultaneous recordings from the ferret auditory and prefrontal cortical areas suggests evidence for the role of rapid top-down and bottom-up functional dynamics across these areas involved in robust attentive behavior.

  15. Structure and Connectivity Analysis of Financial Complex System Based on G-Causality Network

    International Nuclear Information System (INIS)

    Xu Chuan-Ming; Yan Yan; Zhu Xiao-Wu; Li Xiao-Teng; Chen Xiao-Song

    2013-01-01

    The recent financial crisis highlights the inherent weaknesses of the financial market. To explore the mechanism that maintains the financial market as a system, we study the interactions of U.S. financial market from the network perspective. Applied with conditional Granger causality network analysis, network density, in-degree and out-degree rankings are important indicators to analyze the conditional causal relationships among financial agents, and further to assess the stability of U.S. financial systems. It is found that the topological structure of G-causality network in U.S. financial market changed in different stages over the last decade, especially during the recent global financial crisis. Network density of the G-causality model is much higher during the period of 2007–2009 crisis stage, and it reaches the peak value in 2008, the most turbulent time in the crisis. Ranked by in-degrees and out-degrees, insurance companies are listed in the top of 68 financial institutions during the crisis. They act as the hubs which are more easily influenced by other financial institutions and simultaneously influence others during the global financial disturbance. (interdisciplinary physics and related areas of science and technology)

  16. Structure and Connectivity Analysis of Financial Complex System Based on G-Causality Network

    Science.gov (United States)

    Xu, Chuan-Ming; Yan, Yan; Zhu, Xiao-Wu; Li, Xiao-Teng; Chen, Xiao-Song

    2013-11-01

    The recent financial crisis highlights the inherent weaknesses of the financial market. To explore the mechanism that maintains the financial market as a system, we study the interactions of U.S. financial market from the network perspective. Applied with conditional Granger causality network analysis, network density, in-degree and out-degree rankings are important indicators to analyze the conditional causal relationships among financial agents, and further to assess the stability of U.S. financial systems. It is found that the topological structure of G-causality network in U.S. financial market changed in different stages over the last decade, especially during the recent global financial crisis. Network density of the G-causality model is much higher during the period of 2007-2009 crisis stage, and it reaches the peak value in 2008, the most turbulent time in the crisis. Ranked by in-degrees and out-degrees, insurance companies are listed in the top of 68 financial institutions during the crisis. They act as the hubs which are more easily influenced by other financial institutions and simultaneously influence others during the global financial disturbance.

  17. Experimental violation of local causality in a quantum network

    Science.gov (United States)

    Carvacho, Gonzalo; Andreoli, Francesco; Santodonato, Luca; Bentivegna, Marco; Chaves, Rafael; Sciarrino, Fabio

    2017-03-01

    Bell's theorem plays a crucial role in quantum information processing and thus several experimental investigations of Bell inequalities violations have been carried out over the years. Despite their fundamental relevance, however, previous experiments did not consider an ingredient of relevance for quantum networks: the fact that correlations between distant parties are mediated by several, typically independent sources. Here, using a photonic setup, we investigate a quantum network consisting of three spatially separated nodes whose correlations are mediated by two distinct sources. This scenario allows for the emergence of the so-called non-bilocal correlations, incompatible with any local model involving two independent hidden variables. We experimentally witness the emergence of this kind of quantum correlations by violating a Bell-like inequality under the fair-sampling assumption. Our results provide a proof-of-principle experiment of generalizations of Bell's theorem for networks, which could represent a potential resource for quantum communication protocols.

  18. Resting-state brain networks revealed by granger causal connectivity in frogs.

    Science.gov (United States)

    Xue, Fei; Fang, Guangzhan; Yue, Xizi; Zhao, Ermi; Brauth, Steven E; Tang, Yezhong

    2016-10-15

    Resting-state networks (RSNs) refer to the spontaneous brain activity generated under resting conditions, which maintain the dynamic connectivity of functional brain networks for automatic perception or higher order cognitive functions. Here, Granger causal connectivity analysis (GCCA) was used to explore brain RSNs in the music frog (Babina daunchina) during different behavioral activity phases. The results reveal that a causal network in the frog brain can be identified during the resting state which reflects both brain lateralization and sexual dimorphism. Specifically (1) ascending causal connections from the left mesencephalon to both sides of the telencephalon are significantly higher than those from the right mesencephalon, while the right telencephalon gives rise to the strongest efferent projections among all brain regions; (2) causal connections from the left mesencephalon in females are significantly higher than those in males and (3) these connections are similar during both the high and low behavioral activity phases in this species although almost all electroencephalograph (EEG) spectral bands showed higher power in the high activity phase for all nodes. The functional features of this network match important characteristics of auditory perception in this species. Thus we propose that this causal network maintains auditory perception during the resting state for unexpected auditory inputs as resting-state networks do in other species. These results are also consistent with the idea that females are more sensitive to auditory stimuli than males during the reproductive season. In addition, these results imply that even when not behaviorally active, the frogs remain vigilant for detecting external stimuli. Copyright © 2016 IBRO. Published by Elsevier Ltd. All rights reserved.

  19. Inference of directed climate networks: role of instability of causality estimation methods

    Czech Academy of Sciences Publication Activity Database

    Hlinka, Jaroslav; Hartman, David; Vejmelka, Martin; Paluš, Milan

    2013-01-01

    Roč. 15, - (2013), s. 12987 ISSN 1607-7962. [European Geosciences Union General Assembly 2013. 07.04.2013-12.04.2013, Vienna] R&D Projects: GA ČR GCP103/11/J068 Institutional support: RVO:67985807 Keywords : causality analysis * climate networks Subject RIV: BB - Applied Statistics, Operational Research

  20. Principal noncommutative torus bundles

    DEFF Research Database (Denmark)

    Echterhoff, Siegfried; Nest, Ryszard; Oyono-Oyono, Herve

    2008-01-01

    of bivariant K-theory (denoted RKK-theory) due to Kasparov. Using earlier results of Echterhoff and Williams, we shall give a complete classification of principal non-commutative torus bundles up to equivariant Morita equivalence. We then study these bundles as topological fibrations (forgetting the group...

  1. Noncommutative field gas driven inflation

    Energy Technology Data Exchange (ETDEWEB)

    Barosi, Luciano; Brito, Francisco A [Departamento de Fisica, Universidade Federal de Campina Grande, Caixa Postal 10071, 58109-970 Campina Grande, Paraiba (Brazil); Queiroz, Amilcar R, E-mail: lbarosi@ufcg.edu.br, E-mail: fabrito@df.ufcg.edu.br, E-mail: amilcarq@gmail.com [Centro Internacional de Fisica da Materia Condensada, Universidade de Brasilia, Caixa Postal 04667, Brasilia, DF (Brazil)

    2008-04-15

    We investigate early time inflationary scenarios in a Universe filled with a dilute noncommutative bosonic gas at high temperature. A noncommutative bosonic gas is a gas composed of a bosonic scalar field with noncommutative field space on a commutative spacetime. Such noncommutative field theories were recently introduced as a generalization of quantum mechanics on a noncommutative spacetime. Key features of these theories are Lorentz invariance violation and CPT violation. In the present study we use a noncommutative bosonic field theory that, besides the noncommutative parameter {theta}, shows up a further parameter {sigma}. This parameter {sigma} controls the range of the noncommutativity and acts as a regulator for the theory. Both parameters play a key role in the modified dispersion relations of the noncommutative bosonic field, leading to possible striking consequences for phenomenology. In this work we obtain an equation of state p = {omega}({sigma},{theta};{beta}){rho} for the noncommutative bosonic gas relating pressure p and energy density {rho}, in the limit of high temperature. We analyse possible behaviours for these gas parameters {sigma}, {theta} and {beta}, so that -1{<=}{omega}<-1/3, which is the region where the Universe enters an accelerated phase.

  2. Developmental maturation of dynamic causal control signals in higher-order cognition: a neurocognitive network model.

    Directory of Open Access Journals (Sweden)

    Kaustubh Supekar

    2012-02-01

    Full Text Available Cognitive skills undergo protracted developmental changes resulting in proficiencies that are a hallmark of human cognition. One skill that develops over time is the ability to problem solve, which in turn relies on cognitive control and attention abilities. Here we use a novel multimodal neurocognitive network-based approach combining task-related fMRI, resting-state fMRI and diffusion tensor imaging (DTI to investigate the maturation of control processes underlying problem solving skills in 7-9 year-old children. Our analysis focused on two key neurocognitive networks implicated in a wide range of cognitive tasks including control: the insula-cingulate salience network, anchored in anterior insula (AI, ventrolateral prefrontal cortex and anterior cingulate cortex, and the fronto-parietal central executive network, anchored in dorsolateral prefrontal cortex and posterior parietal cortex (PPC. We found that, by age 9, the AI node of the salience network is a major causal hub initiating control signals during problem solving. Critically, despite stronger AI activation, the strength of causal regulatory influences from AI to the PPC node of the central executive network was significantly weaker and contributed to lower levels of behavioral performance in children compared to adults. These results were validated using two different analytic methods for estimating causal interactions in fMRI data. In parallel, DTI-based tractography revealed weaker AI-PPC structural connectivity in children. Our findings point to a crucial role of AI connectivity, and its causal cross-network influences, in the maturation of dynamic top-down control signals underlying cognitive development. Overall, our study demonstrates how a unified neurocognitive network model when combined with multimodal imaging enhances our ability to generalize beyond individual task-activated foci and provides a common framework for elucidating key features of brain and cognitive

  3. Quantum mechanics on noncommutative spacetime

    International Nuclear Information System (INIS)

    Calmet, Xavier; Selvaggi, Michele

    2006-01-01

    We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a nonrelativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical noncommutative spacetime. An interesting new feature of quantum mechanics formulated on a noncommutative spacetime is an intrinsic electric dipole moment. We note, however, that noncommutative intrinsic dipole moments are not observable in present experiments searching for an electric dipole moment of leptons or nuclei such as the neutron since they are spin independent. These experiments are sensitive to the energy difference between two states and the noncommutative effect thus cancels out. Bounds on the noncommutative scale found in the literature relying on such intrinsic electric dipole moments are thus incorrect

  4. Vacuum energy from noncommutative models

    Science.gov (United States)

    Mignemi, S.; Samsarov, A.

    2018-04-01

    The vacuum energy is computed for a scalar field in a noncommutative background in several models of noncommutative geometry. One may expect that the noncommutativity introduces a natural cutoff on the ultraviolet divergences of field theory. Our calculations show however that this depends on the particular model considered: in some cases the divergences are suppressed and the vacuum energy is only logarithmically divergent, in other cases they are stronger than in the commutative theory.

  5. An invitation to noncommutative geometry

    CERN Document Server

    Marcolli, Matilde

    2008-01-01

    This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory. Sample Chapter(s). A Walk in the Noncommutative Garden (1,639 KB). Contents: A Walk in the Noncommutative Garden (A Connes & M Marcolli); Renormalization of Noncommutative Quantum Field Theory (H Grosse & R Wulke

  6. Phenomenology of noncommutative field theories

    International Nuclear Information System (INIS)

    Carone, C D

    2006-01-01

    Experimental limits on the violation of four-dimensional Lorentz invariance imply that noncommutativity among ordinary spacetime dimensions must be small. In this talk, I review the most stringent bounds on noncommutative field theories and suggest a possible means of evading them: noncommutativity may be restricted to extra, compactified spatial dimensions. Such theories have a number of interesting features, including Abelian gauge fields whose Kaluza-Klein excitations have self couplings. We consider six-dimensional QED in a noncommutative bulk, and discuss the collider signatures of the model

  7. Capturing cognitive causal paths in human reliability analysis with Bayesian network models

    International Nuclear Information System (INIS)

    Zwirglmaier, Kilian; Straub, Daniel; Groth, Katrina M.

    2017-01-01

    reIn the last decade, Bayesian networks (BNs) have been identified as a powerful tool for human reliability analysis (HRA), with multiple advantages over traditional HRA methods. In this paper we illustrate how BNs can be used to include additional, qualitative causal paths to provide traceability. The proposed framework provides the foundation to resolve several needs frequently expressed by the HRA community. First, the developed extended BN structure reflects the causal paths found in cognitive psychology literature, thereby addressing the need for causal traceability and strong scientific basis in HRA. Secondly, the use of node reduction algorithms allows the BN to be condensed to a level of detail at which quantification is as straightforward as the techniques used in existing HRA. We illustrate the framework by developing a BN version of the critical data misperceived crew failure mode in the IDHEAS HRA method, which is currently under development at the US NRC . We illustrate how the model could be quantified with a combination of expert-probabilities and information from operator performance databases such as SACADA. This paper lays the foundations necessary to expand the cognitive and quantitative foundations of HRA. - Highlights: • A framework for building traceable BNs for HRA, based on cognitive causal paths. • A qualitative BN structure, directly showing these causal paths is developed. • Node reduction algorithms are used for making the BN structure quantifiable. • BN quantified through expert estimates and observed data (Bayesian updating). • The framework is illustrated for a crew failure mode of IDHEAS.

  8. Perceived causal relations between anxiety, posttraumatic stress and depression: extension to moderation, mediation, and network analysis.

    Science.gov (United States)

    Frewen, Paul A; Schmittmann, Verena D; Bringmann, Laura F; Borsboom, Denny

    2013-01-01

    Previous research demonstrates that posttraumatic memory reexperiencing, depression, anxiety, and guilt-shame are frequently co-occurring problems that may be causally related. The present study utilized Perceived Causal Relations (PCR) scaling in order to assess participants' own attributions concerning whether and to what degree these co-occurring problems may be causally interrelated. 288 young adults rated the frequency and respective PCR scores associating their symptoms of posttraumatic reexperiencing, depression, anxiety, and guilt-shame. PCR scores were found to moderate associations between the frequency of posttraumatic memory reexperiencing, depression, anxiety, and guilt-shame. Network analyses showed that the number of feedback loops between PCR scores was positively associated with symptom frequencies. Results tentatively support the interpretation of PCR scores as moderators of the association between different psychological problems, and lend support to the hypothesis that increased symptom frequencies are observed in the presence of an increased number of causal feedback loops between symptoms. Additionally, a perceived causal role for the reexperiencing of traumatic memories in exacerbating emotional disturbance was identified.

  9. Perceived causal relations between anxiety, posttraumatic stress and depression: extension to moderation, mediation, and network analysis

    Directory of Open Access Journals (Sweden)

    Paul A. Frewen

    2013-08-01

    Full Text Available Background: Previous research demonstrates that posttraumatic memory reexperiencing, depression, anxiety, and guilt-shame are frequently co-occurring problems that may be causally related. Objectives: The present study utilized Perceived Causal Relations (PCR scaling in order to assess participants’ own attributions concerning whether and to what degree these co-occurring problems may be causally interrelated. Methods: 288 young adults rated the frequency and respective PCR scores associating their symptoms of posttraumatic reexperiencing, depression, anxiety, and guilt-shame. Results: PCR scores were found to moderate associations between the frequency of posttraumatic memory reexperiencing, depression, anxiety, and guilt-shame. Network analyses showed that the number of feedback loops between PCR scores was positively associated with symptom frequencies. Conclusion: Results tentatively support the interpretation of PCR scores as moderators of the association between different psychological problems, and lend support to the hypothesis that increased symptom frequencies are observed in the presence of an increased number of causal feedback loops between symptoms. Additionally, a perceived causal role for the reexperiencing of traumatic memories in exacerbating emotional disturbance was identified.

  10. Verification of temporal-causal network models by mathematical analysis

    Directory of Open Access Journals (Sweden)

    Jan Treur

    2016-04-01

    Full Text Available Abstract Usually dynamic properties of models can be analysed by conducting simulation experiments. But sometimes, as a kind of prediction properties can also be found by calculations in a mathematical manner, without performing simulations. Examples of properties that can be explored in such a manner are: whether some values for the variables exist for which no change occurs (stationary points or equilibria, and how such values may depend on the values of the parameters of the model and/or the initial values for the variables whether certain variables in the model converge to some limit value (equilibria and how this may depend on the values of the parameters of the model and/or the initial values for the variables whether or not certain variables will show monotonically increasing or decreasing values over time (monotonicity how fast a convergence to a limit value takes place (convergence speed whether situations occur in which no convergence takes place but in the end a specific sequence of values is repeated all the time (limit cycle Such properties found in an analytic mathematical manner can be used for verification of the model by checking them for the values observed in simulation experiments. If one of these properties is not fulfilled, then there will be some error in the implementation of the model. In this paper some methods to analyse such properties of dynamical models will be described and illustrated for the Hebbian learning model, and for dynamic connection strengths in social networks. The properties analysed by the methods discussed cover equilibria, increasing or decreasing trends, recurring patterns (limit cycles, and speed of convergence to equilibria.

  11. Non-commutative analysis

    CERN Document Server

    Jorgensen, Palle

    2017-01-01

    The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret 'non-commutative analysis' broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.)A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras.The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.

  12. An Efficient Causal Group Communication Protocol for Free Scale Peer-to-Peer Networks

    Directory of Open Access Journals (Sweden)

    Grigory Evropeytsev

    2016-08-01

    Full Text Available In peer-to-peer (P2P overlay networks, a group of n (≥2 peer processes have to cooperate with each other. Each peer sends messages to every peer and receives messages from every peer in a group. In group communications, each message sent by a peer is required to be causally delivered to every peer. Most of the protocols designed to ensure causal message order are designed for networks with a plain architecture. These protocols can be adapted to use in free scale and hierarchical topologies; however, the amount of control information is O(n, where n is the number of peers in the system. Some protocols are designed for a free scale or hierarchical networks, but in general they force the whole system to accomplish the same order viewed by a super peer. In this paper, we present a protocol that is specifically designed to work with a free scale peer-to-peer network. By using the information about the network’s architecture and by representing message dependencies on a bit level, the proposed protocol ensures causal message ordering without enforcing super peers order. The designed protocol is simulated and compared with the Immediate Dependency Relation and the Dependency Sequences protocols to show its lower overhead.

  13. Noncommutative field theory

    International Nuclear Information System (INIS)

    Douglas, Michael R.; Nekrasov, Nikita A.

    2001-01-01

    This article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, on both the classical and the quantum level

  14. Noncommutativity from spectral flow

    Energy Technology Data Exchange (ETDEWEB)

    Heinzl, Thomas; Ilderton, Anton [School of Mathematics and Statistics, University of Plymouth, Drake Circus, Plymouth PL4 8AA (United Kingdom)

    2007-07-27

    We investigate the transition from second- to first-order systems. Quantum mechanically, this transforms configuration space into phase space and hence introduces noncommutativity in the former. This transition may be described in terms of spectral flow. Gaps in the energy or mass spectrum may become large which effectively truncates the available state space. Using both operator and path integral languages we explicitly discuss examples in quantum mechanics (light-front) quantum field theory and string theory.

  15. Modelling cointegration and Granger causality network to detect long-term equilibrium and diffusion paths in the financial system.

    Science.gov (United States)

    Gao, Xiangyun; Huang, Shupei; Sun, Xiaoqi; Hao, Xiaoqing; An, Feng

    2018-03-01

    Microscopic factors are the basis of macroscopic phenomena. We proposed a network analysis paradigm to study the macroscopic financial system from a microstructure perspective. We built the cointegration network model and the Granger causality network model based on econometrics and complex network theory and chose stock price time series of the real estate industry and its upstream and downstream industries as empirical sample data. Then, we analysed the cointegration network for understanding the steady long-term equilibrium relationships and analysed the Granger causality network for identifying the diffusion paths of the potential risks in the system. The results showed that the influence from a few key stocks can spread conveniently in the system. The cointegration network and Granger causality network are helpful to detect the diffusion path between the industries. We can also identify and intervene in the transmission medium to curb risk diffusion.

  16. Calculating the Prior Probability Distribution for a Causal Network Using Maximum Entropy: Alternative Approaches

    Directory of Open Access Journals (Sweden)

    Michael J. Markham

    2011-07-01

    Full Text Available Some problems occurring in Expert Systems can be resolved by employing a causal (Bayesian network and methodologies exist for this purpose. These require data in a specific form and make assumptions about the independence relationships involved. Methodologies using Maximum Entropy (ME are free from these conditions and have the potential to be used in a wider context including systems consisting of given sets of linear and independence constraints, subject to consistency and convergence. ME can also be used to validate results from the causal network methodologies. Three ME methods for determining the prior probability distribution of causal network systems are considered. The first method is Sequential Maximum Entropy in which the computation of a progression of local distributions leads to the over-all distribution. This is followed by development of the Method of Tribus. The development takes the form of an algorithm that includes the handling of explicit independence constraints. These fall into two groups those relating parents of vertices, and those deduced from triangulation of the remaining graph. The third method involves a variation in the part of that algorithm which handles independence constraints. Evidence is presented that this adaptation only requires the linear constraints and the parental independence constraints to emulate the second method in a substantial class of examples.

  17. Quantum theory of noncommutative fields

    International Nuclear Information System (INIS)

    Carmona, J.M.; Cortes, J.L.; Gamboa, J.; Mendez, F.

    2003-01-01

    Generalizing the noncommutative harmonic oscillator construction, we propose a new extension of quantum field theory based on the concept of 'noncommutative fields'. Our description permits to break the usual particle-antiparticle degeneracy at the dispersion relation level and introduces naturally an ultraviolet and an infrared cutoff. Phenomenological bounds for these new energy scales are given. (author)

  18. The Gribov problem in noncommutative QED

    Energy Technology Data Exchange (ETDEWEB)

    Canfora, Fabrizio [Centro de Estudios Científicos (CECS),Casilla 1469, Valdivia (Chile); Kurkov, Maxim A. [Dipartimento di Matematica, Università di Napoli Federico II,Monte S. Angelo, Via Cintia, 80126 Napoli (Italy); CMCC-Universidade Federal do ABC,Santo André, S.P. (Brazil); INFN, Sezione di Napoli,Monte S. Angelo, Via Cintia, 80126 Napoli (Italy); Rosa, Luigi; Vitale, Patrizia [Dipartimento di Fisica, Università di Napoli Federico II,Monte S. Angelo, Via Cintia, 80126 Napoli (Italy); INFN, Sezione di Napoli,Monte S. Angelo, Via Cintia, 80126 Napoli (Italy)

    2016-01-04

    It is shown that in the noncommutative version of QED (NCQED) Gribov copies induced by the noncommutativity of space-time appear in the Landau gauge. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes.

  19. Hall effect in noncommutative coordinates

    International Nuclear Information System (INIS)

    Dayi, Oemer F.; Jellal, Ahmed

    2002-01-01

    We consider electrons in uniform external magnetic and electric fields which move on a plane whose coordinates are noncommuting. Spectrum and eigenfunctions of the related Hamiltonian are obtained. We derive the electric current whose expectation value gives the Hall effect in terms of an effective magnetic field. We present a receipt to find the action which can be utilized in path integrals for noncommuting coordinates. In terms of this action we calculate the related Aharonov-Bohm phase and show that it also yields the same effective magnetic field. When magnetic field is strong enough this phase becomes independent of magnetic field. Measurement of it may give some hints on spatial noncommutativity. The noncommutativity parameter θ can be tuned such that electrons moving in noncommutative coordinates are interpreted as either leading to the fractional quantum Hall effect or composite fermions in the usual coordinates

  20. Causal mapping of emotion networks in the human brain: Framework and initial findings.

    Science.gov (United States)

    Dubois, Julien; Oya, Hiroyuki; Tyszka, J Michael; Howard, Matthew; Eberhardt, Frederick; Adolphs, Ralph

    2017-11-13

    Emotions involve many cortical and subcortical regions, prominently including the amygdala. It remains unknown how these multiple network components interact, and it remains unknown how they cause the behavioral, autonomic, and experiential effects of emotions. Here we describe a framework for combining a novel technique, concurrent electrical stimulation with fMRI (es-fMRI), together with a novel analysis, inferring causal structure from fMRI data (causal discovery). We outline a research program for investigating human emotion with these new tools, and provide initial findings from two large resting-state datasets as well as case studies in neurosurgical patients with electrical stimulation of the amygdala. The overarching goal is to use causal discovery methods on fMRI data to infer causal graphical models of how brain regions interact, and then to further constrain these models with direct stimulation of specific brain regions and concurrent fMRI. We conclude by discussing limitations and future extensions. The approach could yield anatomical hypotheses about brain connectivity, motivate rational strategies for treating mood disorders with deep brain stimulation, and could be extended to animal studies that use combined optogenetic fMRI. Copyright © 2017 Elsevier Ltd. All rights reserved.

  1. Identifying interactions in the time and frequency domains in local and global networks - A Granger Causality Approach.

    Science.gov (United States)

    Zou, Cunlu; Ladroue, Christophe; Guo, Shuixia; Feng, Jianfeng

    2010-06-21

    Reverse-engineering approaches such as Bayesian network inference, ordinary differential equations (ODEs) and information theory are widely applied to deriving causal relationships among different elements such as genes, proteins, metabolites, neurons, brain areas and so on, based upon multi-dimensional spatial and temporal data. There are several well-established reverse-engineering approaches to explore causal relationships in a dynamic network, such as ordinary differential equations (ODE), Bayesian networks, information theory and Granger Causality. Here we focused on Granger causality both in the time and frequency domain and in local and global networks, and applied our approach to experimental data (genes and proteins). For a small gene network, Granger causality outperformed all the other three approaches mentioned above. A global protein network of 812 proteins was reconstructed, using a novel approach. The obtained results fitted well with known experimental findings and predicted many experimentally testable results. In addition to interactions in the time domain, interactions in the frequency domain were also recovered. The results on the proteomic data and gene data confirm that Granger causality is a simple and accurate approach to recover the network structure. Our approach is general and can be easily applied to other types of temporal data.

  2. Identifying interactions in the time and frequency domains in local and global networks - A Granger Causality Approach

    Directory of Open Access Journals (Sweden)

    Guo Shuixia

    2010-06-01

    Full Text Available Abstract Background Reverse-engineering approaches such as Bayesian network inference, ordinary differential equations (ODEs and information theory are widely applied to deriving causal relationships among different elements such as genes, proteins, metabolites, neurons, brain areas and so on, based upon multi-dimensional spatial and temporal data. There are several well-established reverse-engineering approaches to explore causal relationships in a dynamic network, such as ordinary differential equations (ODE, Bayesian networks, information theory and Granger Causality. Results Here we focused on Granger causality both in the time and frequency domain and in local and global networks, and applied our approach to experimental data (genes and proteins. For a small gene network, Granger causality outperformed all the other three approaches mentioned above. A global protein network of 812 proteins was reconstructed, using a novel approach. The obtained results fitted well with known experimental findings and predicted many experimentally testable results. In addition to interactions in the time domain, interactions in the frequency domain were also recovered. Conclusions The results on the proteomic data and gene data confirm that Granger causality is a simple and accurate approach to recover the network structure. Our approach is general and can be easily applied to other types of temporal data.

  3. Challenges to inferring causality from viral information dispersion in dynamic social networks

    Science.gov (United States)

    Ternovski, John

    2014-06-01

    Understanding the mechanism behind large-scale information dispersion through complex networks has important implications for a variety of industries ranging from cyber-security to public health. With the unprecedented availability of public data from online social networks (OSNs) and the low cost nature of most OSN outreach, randomized controlled experiments, the "gold standard" of causal inference methodologies, have been used with increasing regularity to study viral information dispersion. And while these studies have dramatically furthered our understanding of how information disseminates through social networks by isolating causal mechanisms, there are still major methodological concerns that need to be addressed in future research. This paper delineates why modern OSNs are markedly different from traditional sociological social networks and why these differences present unique challenges to experimentalists and data scientists. The dynamic nature of OSNs is particularly troublesome for researchers implementing experimental designs, so this paper identifies major sources of bias arising from network mutability and suggests strategies to circumvent and adjust for these biases. This paper also discusses the practical considerations of data quality and collection, which may adversely impact the efficiency of the estimator. The major experimental methodologies used in the current literature on virality are assessed at length, and their strengths and limits identified. Other, as-yetunsolved threats to the efficiency and unbiasedness of causal estimators--such as missing data--are also discussed. This paper integrates methodologies and learnings from a variety of fields under an experimental and data science framework in order to systematically consolidate and identify current methodological limitations of randomized controlled experiments conducted in OSNs.

  4. A Temporal-Causal Network Model for the Internal Processes of a Person with a Borderline Personality Disorder

    NARCIS (Netherlands)

    Hoțoiu, Maria; Tavella, Federico; Treur, Jan

    2018-01-01

    This paper presents a computational network model for a person with a Borderline Personality Disorder. It was designed according to a Network-Oriented Modeling approach as a temporal-causal network based on neuropsychological background knowledge. Some example simulations are discussed. The model

  5. Noncommutative quantum mechanics

    Science.gov (United States)

    Gamboa, J.; Loewe, M.; Rojas, J. C.

    2001-09-01

    A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter θ, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of θ the model can be solved by using perturbation theory.

  6. Toward a formalized account of attitudes: The Causal Attitude Network (CAN) model.

    Science.gov (United States)

    Dalege, Jonas; Borsboom, Denny; van Harreveld, Frenk; van den Berg, Helma; Conner, Mark; van der Maas, Han L J

    2016-01-01

    This article introduces the Causal Attitude Network (CAN) model, which conceptualizes attitudes as networks consisting of evaluative reactions and interactions between these reactions. Relevant evaluative reactions include beliefs, feelings, and behaviors toward the attitude object. Interactions between these reactions arise through direct causal influences (e.g., the belief that snakes are dangerous causes fear of snakes) and mechanisms that support evaluative consistency between related contents of evaluative reactions (e.g., people tend to align their belief that snakes are useful with their belief that snakes help maintain ecological balance). In the CAN model, the structure of attitude networks conforms to a small-world structure: evaluative reactions that are similar to each other form tight clusters, which are connected by a sparser set of "shortcuts" between them. We argue that the CAN model provides a realistic formalized measurement model of attitudes and therefore fills a crucial gap in the attitude literature. Furthermore, the CAN model provides testable predictions for the structure of attitudes and how they develop, remain stable, and change over time. Attitude strength is conceptualized in terms of the connectivity of attitude networks and we show that this provides a parsimonious account of the differences between strong and weak attitudes. We discuss the CAN model in relation to possible extensions, implication for the assessment of attitudes, and possibilities for further study. (c) 2015 APA, all rights reserved).

  7. Supersymmetry on the noncommutative lattice

    International Nuclear Information System (INIS)

    Nishimura, Jun; Rey, Soo-Jong; Sugino, Fumihiko

    2003-01-01

    Built upon the proposal of Kaplan et al. (heplat{0206109}), we construct noncommutative lattice gauge theory with manifest supersymmetry. We show that such theory is naturally implementable via orbifold conditions generalizing those used by Kaplan et al. We present the prescription in detail and illustrate it for noncommutative gauge theories latticized partially in two dimensions. We point out a deformation freedom in the defining theory by a complex-parameter, reminiscent of discrete torsion in string theory. We show that, in the continuum limit, the supersymmetry is enhanced only at a particular value of the deformation parameter, determined solely by the size of the noncommutativity. (author)

  8. Causal Interrogation of Neuronal Networks and Behavior through Virally Transduced Ivermectin Receptors.

    Science.gov (United States)

    Obenhaus, Horst A; Rozov, Andrei; Bertocchi, Ilaria; Tang, Wannan; Kirsch, Joachim; Betz, Heinrich; Sprengel, Rolf

    2016-01-01

    The causal interrogation of neuronal networks involved in specific behaviors requires the spatially and temporally controlled modulation of neuronal activity. For long-term manipulation of neuronal activity, chemogenetic tools provide a reasonable alternative to short-term optogenetic approaches. Here we show that virus mediated gene transfer of the ivermectin (IVM) activated glycine receptor mutant GlyRα1 (AG) can be used for the selective and reversible silencing of specific neuronal networks in mice. In the striatum, dorsal hippocampus, and olfactory bulb, GlyRα1 (AG) promoted IVM dependent effects in representative behavioral assays. Moreover, GlyRα1 (AG) mediated silencing had a strong and reversible impact on neuronal ensemble activity and c-Fos activation in the olfactory bulb. Together our results demonstrate that long-term, reversible and re-inducible neuronal silencing via GlyRα1 (AG) is a promising tool for the interrogation of network mechanisms underlying the control of behavior and memory formation.

  9. Testing Non-commutative QED, Constructing Non-commutative MHD

    OpenAIRE

    Guralnik, Z.; Jackiw, R.; Pi, S. Y.; Polychronakos, A. P.

    2001-01-01

    The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the presence of a background magnetic induction field b, the velocity for propagation transverse to b differs from c, while propagation along b is unchanged. In principle, this allows a test by the Michelson-Morley interference method. We also study non-commutativity in another context, by constructing the theory describing a charged fluid in a strong magnetic field, which forces the fluid particles into ...

  10. Granger causal connectivity dissociates navigation networks that subserve allocentric and egocentric path integration.

    Science.gov (United States)

    Lin, Chin-Teng; Chiu, Te-Cheng; Wang, Yu-Kai; Chuang, Chun-Hsiang; Gramann, Klaus

    2018-01-15

    Studies on spatial navigation demonstrate a significant role of the retrosplenial complex (RSC) in the transformation of egocentric and allocentric information into complementary spatial reference frames (SRFs). The tight anatomical connections of the RSC with a wide range of other cortical regions processing spatial information support its vital role within the human navigation network. To better understand how different areas of the navigational network interact, we investigated the dynamic causal interactions of brain regions involved in solving a virtual navigation task. EEG signals were decomposed by independent component analysis (ICA) and subsequently examined for information flow between clusters of independent components (ICs) using direct short-time directed transfer function (sdDTF). The results revealed information flow between the anterior cingulate cortex and the left prefrontal cortex in the theta (4-7 Hz) frequency band and between the prefrontal, motor, parietal, and occipital cortices as well as the RSC in the alpha (8-13 Hz) frequency band. When participants prefered to use distinct reference frames (egocentric vs. allocentric) during navigation was considered, a dominant occipito-parieto-RSC network was identified in allocentric navigators. These results are in line with the assumption that the RSC, parietal, and occipital cortices are involved in transforming egocentric visual-spatial information into an allocentric reference frame. Moreover, the RSC demonstrated the strongest causal flow during changes in orientation, suggesting that this structure directly provides information on heading changes in humans. Copyright © 2017 Elsevier B.V. All rights reserved.

  11. Inference of directed climate networks: role of instability of causality estimation methods

    Science.gov (United States)

    Hlinka, Jaroslav; Hartman, David; Vejmelka, Martin; Paluš, Milan

    2013-04-01

    Climate data are increasingly analyzed by complex network analysis methods, including graph-theoretical approaches [1]. For such analysis, links between localized nodes of climate network are typically quantified by some statistical measures of dependence (connectivity) between measured variables of interest. To obtain information on the directionality of the interactions in the networks, a wide range of methods exists. These can be broadly divided into linear and nonlinear methods, with some of the latter having the theoretical advantage of being model-free, and principally a generalization of the former [2]. However, as a trade-off, this generality comes together with lower accuracy - in particular if the system was close to linear. In an overall stationary system, this may potentially lead to higher variability in the nonlinear network estimates. Therefore, with the same control of false alarms, this may lead to lower sensitivity for detection of real changes in the network structure. These problems are discussed on the example of daily SAT and SLP data from the NCEP/NCAR reanalysis dataset. We first reduce the dimensionality of data using PCA with VARIMAX rotation to detect several dozens of components that together explain most of the data variability. We further construct directed climate networks applying a selection of most widely used methods - variants of linear Granger causality and conditional mutual information. Finally, we assess the stability of the detected directed climate networks by computing them in sliding time windows. To understand the origin of the observed instabilities and their range, we also apply the same procedure to two types of surrogate data: either with non-stationarity in network structure removed, or imposed in a controlled way. In general, the linear methods show stable results in terms of overall similarity of directed climate networks inferred. For instance, for different decades of SAT data, the Spearman correlation of edge

  12. Nonabelian noncommutative gauge theory via noncommutative extra dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, Branislav E-mail: jurco@theorie.physik.uni-muenchen.de; Schupp, Peter E-mail: schupp@theorie.physik.uni-muenchen.de; Wess, Julius E-mail: wess@theorie.physik.uni-muenchen.de

    2001-06-18

    The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arises in string theory with background B-fields. The theory is naturally expressed in terms of cochains in an appropriate cohomology; we discuss how it fits into the framework of projective modules. The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map). As application we show the exact equality of the Dirac-Born-Infeld action with B-field in the commutative setting and its semi-noncommutative cousin in the intermediate picture. Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; an explicit map between abelian and nonabelian gauge fields is given. All constructions are also valid for non-constant B-field, Poisson structure and metric.

  13. Nonabelian noncommutative gauge theory via noncommutative extra dimensions

    International Nuclear Information System (INIS)

    Jurco, Branislav; Schupp, Peter; Wess, Julius

    2001-01-01

    The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arises in string theory with background B-fields. The theory is naturally expressed in terms of cochains in an appropriate cohomology; we discuss how it fits into the framework of projective modules. The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map). As application we show the exact equality of the Dirac-Born-Infeld action with B-field in the commutative setting and its semi-noncommutative cousin in the intermediate picture. Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; an explicit map between abelian and nonabelian gauge fields is given. All constructions are also valid for non-constant B-field, Poisson structure and metric

  14. Duality and noncommutative planes

    DEFF Research Database (Denmark)

    Jøndrup, Søren

    2015-01-01

    We study extensions of simple modules over an associative ring A   and we prove that for twosided ideals mm and nn with artinian factors the condition ExtA1(A/m,A/n)≠0 holds for the left A  -modules A/mA/m and A/nA/n if and only if it holds for the right modules A/nA/n and A/mA/m. The methods pro...... proving this are applied to show that noncommutative models of the plane, i.e. algebras of the form k〈x,y〉/(f)k〈x,y〉/(f), where f∈([x,y])f∈([x,y]) are noetherian only in case (f)=([x,y])...

  15. Ab initio Algorithmic Causal Deconvolution of Intertwined Programs and Networks by Generative Mechanism

    KAUST Repository

    Zenil, Hector

    2018-02-18

    To extract and learn representations leading to generative mechanisms from data, especially without making arbitrary decisions and biased assumptions, is a central challenge in most areas of scientific research particularly in connection to current major limitations of influential topics and methods of machine and deep learning as they have often lost sight of the model component. Complex data is usually produced by interacting sources with different mechanisms. Here we introduce a parameter-free model-based approach, based upon the seminal concept of Algorithmic Probability, that decomposes an observation and signal into its most likely algorithmic generative mechanisms. Our methods use a causal calculus to infer model representations. We demonstrate the method ability to distinguish interacting mechanisms and deconvolve them, regardless of whether the objects produce strings, space-time evolution diagrams, images or networks. We numerically test and evaluate our method and find that it can disentangle observations from discrete dynamic systems, random and complex networks. We think that these causal inference techniques can contribute as key pieces of information for estimations of probability distributions complementing other more statistical-oriented techniques that otherwise lack model inference capabilities.

  16. Students Mental Representation of Biology Diagrams/Pictures Conventions Based on Formation of Causal Network

    Science.gov (United States)

    Sampurno, A. W.; Rahmat, A.; Diana, S.

    2017-09-01

    Diagrams/pictures conventions is one form of visual media that often used to assist students in understanding the biological concepts. The effectiveness of use diagrams/pictures in biology learning at school level has also been mostly reported. This study examines the ability of high school students in reading diagrams/pictures biological convention which is described by Mental Representation based on formation of causal networks. The study involved 30 students 11th grade MIA senior high school Banten Indonesia who are studying the excretory system. MR data obtained by Instrument worksheet, developed based on CNET-protocol, in which there are diagrams/drawings of nephron structure and urinary mechanism. Three patterns formed MR, namely Markov chain, feedback control with a single measurement, and repeated feedback control with multiple measurement. The third pattern is the most dominating pattern, differences in the pattern of MR reveal the difference in how and from which point the students begin to uncover important information contained in the diagram to establish a causal networks. Further analysis shows that a difference in the pattern of MR relate to how complex the students process the information contained in the diagrams/pictures.

  17. Time-varying causal network of the Korean financial system based on firm-specific risk premiums

    Science.gov (United States)

    Song, Jae Wook; Ko, Bonggyun; Cho, Poongjin; Chang, Woojin

    2016-09-01

    The aim of this paper is to investigate the Korean financial system based on time-varying causal network. We discover many stylized facts by utilizing the firm-specific risk premiums for measuring the causality direction from a firm to firm. At first, we discover that the interconnectedness of causal network is affected by the outbreak of financial events; the co-movement of firm-specific risk premium is strengthened after each positive event, and vice versa. Secondly, we find that the major sector of the Korean financial system is the Depositories, and the financial reform in June-2011 achieves its purpose by weakening the power of risk-spillovers of Broker-Dealers. Thirdly, we identify that the causal network is a small-world network with scale-free topology where the power-law exponents of out-Degree and negative event are more significant than those of in-Degree and positive event. Lastly, we discuss that the current aspects of causal network are closely related to the long-term future scenario of the KOSPI Composite index where the direction and stability are significantly affected by the power of risk-spillovers and the power-law exponents of degree distributions, respectively.

  18. Noncommuting fields and non-Abelian fluids

    International Nuclear Information System (INIS)

    Jackiw, R.

    2004-01-01

    The original ideas about noncommuting coordinates are recalled. The connection between U(1) gauge fields defined on noncommuting coordinates and fluid mechanics is explained. Non-Abelian fluid mechanics is described

  19. Noncommutative Blackwell-Ross martingale inequality

    Science.gov (United States)

    Talebi, Ali; Moslehian, Mohammad Sal; Sadeghi, Ghadir

    We establish a noncommutative Blackwell-Ross inequality for supermartingales under a suitable condition which generalizes Khan’s work to the noncommutative setting. We then employ it to deduce an Azuma-type inequality.

  20. Noncommutative QED and anomalous dipole moments

    International Nuclear Information System (INIS)

    Riad, I.F.; Sheikh-Jabbari, M.M.

    2000-09-01

    We study QED on noncommutative spaces, NCQED. In particular we present the detailed calculation for the noncommutative electron-photon vertex and show that the Ward identity is satisfied. We discuss that in the noncommutative case moving electron will show electric dipole effects. In addition, we work out the electric and magnetic dipole moments up to one loop level. For the magnetic moment we show that noncommutative electron has an intrinsic (spin independent) magnetic moment. (author)

  1. Causal hierarchy within the thalamo-cortical network in spike and wave discharges.

    Directory of Open Access Journals (Sweden)

    Anna E Vaudano

    2009-08-01

    Full Text Available Generalised spike wave (GSW discharges are the electroencephalographic (EEG hallmark of absence seizures, clinically characterised by a transitory interruption of ongoing activities and impaired consciousness, occurring during states of reduced awareness. Several theories have been proposed to explain the pathophysiology of GSW discharges and the role of thalamus and cortex as generators. In this work we extend the existing theories by hypothesizing a role for the precuneus, a brain region neglected in previous works on GSW generation but already known to be linked to consciousness and awareness. We analysed fMRI data using dynamic causal modelling (DCM to investigate the effective connectivity between precuneus, thalamus and prefrontal cortex in patients with GSW discharges.We analysed fMRI data from seven patients affected by Idiopathic Generalized Epilepsy (IGE with frequent GSW discharges and significant GSW-correlated haemodynamic signal changes in the thalamus, the prefrontal cortex and the precuneus. Using DCM we assessed their effective connectivity, i.e. which region drives another region. Three dynamic causal models were constructed: GSW was modelled as autonomous input to the thalamus (model A, ventromedial prefrontal cortex (model B, and precuneus (model C. Bayesian model comparison revealed Model C (GSW as autonomous input to precuneus, to be the best in 5 patients while model A prevailed in two cases. At the group level model C dominated and at the population-level the p value of model C was approximately 1.Our results provide strong evidence that activity in the precuneus gates GSW discharges in the thalamo-(fronto cortical network. This study is the first demonstration of a causal link between haemodynamic changes in the precuneus -- an index of awareness -- and the occurrence of pathological discharges in epilepsy.

  2. Noncommutative products of Euclidean spaces

    Science.gov (United States)

    Dubois-Violette, Michel; Landi, Giovanni

    2018-05-01

    We present natural families of coordinate algebras on noncommutative products of Euclidean spaces R^{N_1} × _R R^{N_2} . These coordinate algebras are quadratic ones associated with an R -matrix which is involutive and satisfies the Yang-Baxter equations. As a consequence, they enjoy a list of nice properties, being regular of finite global dimension. Notably, we have eight-dimensional noncommutative euclidean spaces R4 × _R R4 . Among these, particularly well behaved ones have deformation parameter u \\in S^2 . Quotients include seven spheres S7_u as well as noncommutative quaternionic tori TH_u = S^3 × _u S^3 . There is invariance for an action of {{SU}}(2) × {{SU}}(2) on the torus TH_u in parallel with the action of U(1) × U(1) on a `complex' noncommutative torus T^2_θ which allows one to construct quaternionic toric noncommutative manifolds. Additional classes of solutions are disjoint from the classical case.

  3. Synergy and redundancy in the Granger causal analysis of dynamical networks

    International Nuclear Information System (INIS)

    Stramaglia, Sebastiano; M Cortes, Jesus; Marinazzo, Daniele

    2014-01-01

    We analyze, by means of Granger causality (GC), the effect of synergy and redundancy in the inference (from time series data) of the information flow between subsystems of a complex network. While we show that fully conditioned GC (CGC) is not affected by synergy, the pairwise analysis fails to prove synergetic effects. In cases when the number of samples is low, thus making the fully conditioned approach unfeasible, we show that partially conditioned GC (PCGC) is an effective approach if the set of conditioning variables is properly chosen. Here we consider two different strategies (based either on informational content for the candidate driver or on selecting the variables with highest pairwise influences) for PCGC and show that, depending on the data structure, either one or the other might be equally valid. On the other hand, we observe that fully conditioned approaches do not work well in the presence of redundancy, thus suggesting the strategy of separating the pairwise links in two subsets: those corresponding to indirect connections of the CGC (which should thus be excluded) and links that can be ascribed to redundancy effects and, together with the results from the fully connected approach, provide a better description of the causality pattern in the presence of redundancy. Finally we apply these methods to two different real datasets. First, analyzing electrophysiological data from an epileptic brain, we show that synergetic effects are dominant just before seizure occurrences. Second, our analysis applied to gene expression time series from HeLa culture shows that the underlying regulatory networks are characterized by both redundancy and synergy. (paper)

  4. PREFACE: Conceptual and Technical Challenges for Quantum Gravity 2014 - Parallel session: Noncommutative Geometry and Quantum Gravity

    Science.gov (United States)

    Martinetti, P.; Wallet, J.-C.; Amelino-Camelia, G.

    2015-08-01

    The conference Conceptual and Technical Challenges for Quantum Gravity at Sapienza University of Rome, from 8 to 12 September 2014, has provided a beautiful opportunity for an encounter between different approaches and different perspectives on the quantum-gravity problem. It contributed to a higher level of shared knowledge among the quantum-gravity communities pursuing each specific research program. There were plenary talks on many different approaches, including in particular string theory, loop quantum gravity, spacetime noncommutativity, causal dynamical triangulations, asymptotic safety and causal sets. Contributions from the perspective of philosophy of science were also welcomed. In addition several parallel sessions were organized. The present volume collects contributions from the Noncommutative Geometry and Quantum Gravity parallel session4, with additional invited contributions from specialists in the field. Noncommutative geometry in its many incarnations appears at the crossroad of many researches in theoretical and mathematical physics: • from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and string theory, • from early considerations on UV-divergencies in quantum field theory to recent models of gauge theories on noncommutative spacetime, • from Connes description of the standard model of elementary particles to recent Pati-Salam like extensions. This volume provides an overview of these various topics, interesting for the specialist as well as accessible to the newcomer. 4partially funded by CNRS PEPS /PTI ''Metric aspect of noncommutative geometry: from Monge to Higgs''

  5. Noncommutative QFT and renormalization

    International Nuclear Information System (INIS)

    Grosse, H.; Wulkenhaar, R.

    2006-01-01

    It was a great pleasure for me (Harald Grosse) to be invited to talk at the meeting celebrating the 70th birthday of Prof. Julius Wess. I remember various interactions with Julius during the last years: At the time of my studies at Vienna with Walter Thirring, Julius left already Vienna, I learned from his work on effective chiral Lagrangians. Next we met at various conferences and places like CERN (were I worked with Andre Martin, an old friend of Julius), and we all learned from Julius' and Bruno's creation of supersymmetry, next we realized our common interests in noncommutative quantum field theory and did have an intensive exchange. Julius influenced our perturbative approach to gauge field theories were we used the Seiberg-Witten map after his advice. And finally I lively remember the sad days when during my invitation to Vienna Julius did have the serious heart attack. So we are very happy, that you recovered so well, and we wish you all the best for the forthcoming years. Many happy recurrences. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

  6. Noncommutative CPN and CHN and their physics

    International Nuclear Information System (INIS)

    Sako, Akifumi; Suzuki, Toshiya; Umetsu, Hiroshi

    2013-01-01

    We study noncommutative deformation of manifolds by constructing star products. We start from a noncommutative R d and discuss more genaral noncommutative manifolds. In general, star products can not be described in concrete expressions without some exceptions. In this article we introduce new examples of noncommutative manifolds with explicit star products. Karabegov's deformation quantization of CP N and CH N with separation of variables gives explicit calulable star products represented by gamma functions. Using the results of star products between inhomogeneous coordinates, we find creation and anihilation operators and obtain the Fock representation of the noncommutative CP N and CH N .

  7. Noncommutative mathematics for quantum systems

    CERN Document Server

    Franz, Uwe

    2016-01-01

    Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of 'making theory noncommutative' has been extended to many areas of pure and applied mathematics. This book is divided into two parts. The first part provides an introduction to quantum probability, focusing on the notion of independence in quantum probability and on the theory of quantum stochastic processes with independent and stationary increments. The second part provides an introduction to quantum dynamical systems, discussing analogies with fundamental problems studied in classical dynamics. The desire to build an extension of the classical theory provides new, original ways to understand well-known 'commutative' results. On the other hand the richness of the quantum mathematical world presents completely novel phenomena, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probability, mathematical physi...

  8. On noncommutative open string theories

    International Nuclear Information System (INIS)

    Russo, J.G.; Sheikh-Jabbari, M.M.

    2000-08-01

    We investigate new compactifications of OM theory giving rise to a 3+1 dimensional open string theory with noncommutative x 0 -x 1 and x 2 -x 3 coordinates. The theory can be directly obtained by starting with a D3 brane with parallel (near critical) electric and magnetic field components, in the presence of a RR scalar field. The magnetic parameter permits to interpolate continuously between the x 0 -x 1 noncommutative open string theory and the x 2 -x 3 spatial noncommutative U(N) super Yang-Mills theory. We discuss SL(2, Z) transformations of this theory. Using the supergravity description of the large N limit, we also compute corrections to the quark-antiquark Coulomb potential arising in the NCOS theory. (author)

  9. Perceived causal relations between anxiety, posttraumatic stress and depression : extension to moderation, mediation, and network analysis

    NARCIS (Netherlands)

    Frewen, Paul A.; Schmittmann, Verena D.; Bringmann, Laura F.; Borsboom, Denny

    2013-01-01

    Background: Previous research demonstrates that posttraumatic memory reexperiencing, depression, anxiety, and guilt-shame are frequently co-occurring problems that may be causally related. Objectives: The present study utilized Perceived Causal Relations (PCR) scaling in order to assess

  10. Perceived causal relations between anxiety, posttraumatic stress and depression : Extension to moderation, mediation, and network analysis

    NARCIS (Netherlands)

    Frewen, P.A.; Schmittmann, V.D.; Bringmann, L.F.; Borsboom, D.

    2013-01-01

    Background Previous research demonstrates that posttraumatic memory reexperiencing, depression, anxiety, and guilt-shame are frequently co-occurring problems that may be causally related. Objectives The present study utilized Perceived Causal Relations (PCR) scaling in order to assess participants’

  11. Perceived causal relations between anxiety, posttraumatic stress and depression : Extension to moderation, mediation, and network analysis

    NARCIS (Netherlands)

    Frewen, P.A.; Schmittmann, V.D.; Bringmann, L.F.; Borsboom, D.

    2013-01-01

    Background: Previous research demonstrates that posttraumatic memory reexperiencing, depression, anxiety, and guilt-shame are frequently co-occurring problems that may be causally related. Objectives: The present study utilized Perceived Causal Relations (PCR) scaling in order to assess

  12. Assessment of network perturbation amplitudes by applying high-throughput data to causal biological networks

    Directory of Open Access Journals (Sweden)

    Martin Florian

    2012-05-01

    Full Text Available Abstract Background High-throughput measurement technologies produce data sets that have the potential to elucidate the biological impact of disease, drug treatment, and environmental agents on humans. The scientific community faces an ongoing challenge in the analysis of these rich data sources to more accurately characterize biological processes that have been perturbed at the mechanistic level. Here, a new approach is built on previous methodologies in which high-throughput data was interpreted using prior biological knowledge of cause and effect relationships. These relationships are structured into network models that describe specific biological processes, such as inflammatory signaling or cell cycle progression. This enables quantitative assessment of network perturbation in response to a given stimulus. Results Four complementary methods were devised to quantify treatment-induced activity changes in processes described by network models. In addition, companion statistics were developed to qualify significance and specificity of the results. This approach is called Network Perturbation Amplitude (NPA scoring because the amplitudes of treatment-induced perturbations are computed for biological network models. The NPA methods were tested on two transcriptomic data sets: normal human bronchial epithelial (NHBE cells treated with the pro-inflammatory signaling mediator TNFα, and HCT116 colon cancer cells treated with the CDK cell cycle inhibitor R547. Each data set was scored against network models representing different aspects of inflammatory signaling and cell cycle progression, and these scores were compared with independent measures of pathway activity in NHBE cells to verify the approach. The NPA scoring method successfully quantified the amplitude of TNFα-induced perturbation for each network model when compared against NF-κB nuclear localization and cell number. In addition, the degree and specificity to which CDK

  13. On noncommutativity with bifermionic parameter

    International Nuclear Information System (INIS)

    Acatrinei, Ciprian Sorin

    2008-01-01

    Recently Gitman and Vassilevich proposed an interesting model of noncommutative (NC) scalar field theory, with a noncommutativity parameter assumed to be the product of two Grassmann variables. They showed in particular that the model possesses a local energy-momentum tensor. Since such a property is quite unusual for a NC model, we provide here an alternative picture, based on an operatorial formulation of NC field theory. It leads to complete locality of the degrees of freedom of the theory, a property in agreement with the termination of the star-product at the second term in its series. (author)

  14. Network interactions underlying mirror feedback in stroke: A dynamic causal modeling study

    Directory of Open Access Journals (Sweden)

    Soha Saleh

    2017-01-01

    Full Text Available Mirror visual feedback (MVF is potentially a powerful tool to facilitate recovery of disordered movement and stimulate activation of under-active brain areas due to stroke. The neural mechanisms underlying MVF have therefore been a focus of recent inquiry. Although it is known that sensorimotor areas can be activated via mirror feedback, the network interactions driving this effect remain unknown. The aim of the current study was to fill this gap by using dynamic causal modeling to test the interactions between regions in the frontal and parietal lobes that may be important for modulating the activation of the ipsilesional motor cortex during mirror visual feedback of unaffected hand movement in stroke patients. Our intent was to distinguish between two theoretical neural mechanisms that might mediate ipsilateral activation in response to mirror-feedback: transfer of information between bilateral motor cortices versus recruitment of regions comprising an action observation network which in turn modulate the motor cortex. In an event-related fMRI design, fourteen chronic stroke subjects performed goal-directed finger flexion movements with their unaffected hand while observing real-time visual feedback of the corresponding (veridical or opposite (mirror hand in virtual reality. Among 30 plausible network models that were tested, the winning model revealed significant mirror feedback-based modulation of the ipsilesional motor cortex arising from the contralesional parietal cortex, in a region along the rostral extent of the intraparietal sulcus. No winning model was identified for the veridical feedback condition. We discuss our findings in the context of supporting the latter hypothesis, that mirror feedback-based activation of motor cortex may be attributed to engagement of a contralateral (contralesional action observation network. These findings may have important implications for identifying putative cortical areas, which may be targeted with

  15. Modeling the Effect of Religion on Human Empathy Based on an Adaptive Temporal-Causal Network Model

    NARCIS (Netherlands)

    van Ments, L.I.; Roelofsma, P.H.M.P.; Treur, J.

    2018-01-01

    Religion is a central aspect of many individuals’ lives around the world, and its influence on human behaviour has been extensively studied from many different perspectives. The current study integrates a number of these perspectives into one adaptive temporal-causal network model describing the

  16. Modeling the Effect of Religion on Human Empathy Based on an Adaptive Temporal-Causal Network Model

    OpenAIRE

    van Ments, L.I.; Roelofsma, P.H.M.P.; Treur, J.

    2018-01-01

    Religion is a central aspect of many individuals’ lives around the world, and its influence on human behaviour has been extensively studied from many different perspectives. The current study integrates a number of these perspectives into one adaptive temporal-causal network model describing the mental states involved, their mutual relations, and the adaptation of some of these relations over time due to learning. By first developing a conceptual representation of a network model based on lit...

  17. Time and frequency structure of causal correlation networks in the China bond market

    Science.gov (United States)

    Wang, Zhongxing; Yan, Yan; Chen, Xiaosong

    2017-07-01

    There are more than eight hundred interest rates published in the China bond market every day. Identifying the benchmark interest rates that have broad influences on most other interest rates is a major concern for economists. In this paper, a multi-variable Granger causality test is developed and applied to construct a directed network of interest rates, whose important nodes, regarded as key interest rates, are evaluated with CheiRank scores. The results indicate that repo rates are the benchmark of short-term rates, the central bank bill rates are in the core position of mid-term interest rates network, and treasury bond rates lead the long-term bond rates. The evolution of benchmark interest rates from 2008 to 2014 is also studied, and it is found that SHIBOR has generally become the benchmark interest rate in China. In the frequency domain we identify the properties of information flows between interest rates, and the result confirms the existence of market segmentation in the China bond market.

  18. Stringy Fuzziness as the Custodial of Time-Space Noncommutativity

    CERN Document Server

    Barbón, José L F

    2000-01-01

    We study aspects of obtaining field theories with noncommuting time-space coordinates as limits of open-string theories in constant electric-field backgrounds. We find that, within the standard closed-string backgrounds, there is an obstruction to decoupling the time-space noncommutativity scale from that of the string fuzziness scale. We speculate that this censorship may be string-theory's way of protecting the causality and unitarity structure. We study the moduli space of the obstruction in terms of the open- and closed-string backgrounds. Cases of both zero and infinite brane tensions as well as zero string couplings are obtained. A decoupling can be achieved formally by considering complex values of the dilaton and inverting the role of space and time of the light cone. This is reminiscent of a black-hole horizon. We study the corresponding supergravity solution in the large-N limit and find that the geometry has a naked singularity at the physical scale of noncommutativity.

  19. Stringy fuzziness as the custodian of time-space noncommutativity

    CERN Document Server

    Barbón, José L F

    2000-01-01

    We study aspects of obtaining field theories with noncommuting time- space coordinates as limits of open-string theories in constant electric-field backgrounds. We find that, within the standard closed- string backgrounds, there is an obstruction to decoupling the time- space noncommutativity scale from that of the string fuzziness scale. We speculate that this censorship may be string-theory's way of protecting the causality and unitarity structure. We study the moduli space of the obstruction in terms of the open- and closed-string backgrounds. Cases of both zero and infinite brane tensions as well as zero string couplings are obtained. A decoupling can be achieved formally by considering complex values of the dilaton and inverting the role of space and time in the light cone. This is reminiscent of a black-hole horizon. We study the corresponding supergravity solution in the large-N limit and find that the geometry has a naked singularity at the physical scale of noncommutativity. (23 refs).

  20. Causal relationship between the global foreign exchange market based on complex networks and entropy theory

    International Nuclear Information System (INIS)

    Cao, Guangxi; Zhang, Qi; Li, Qingchen

    2017-01-01

    Highlights: • Mutual information is used as the edge weights of nodes instead of PCC, which overcomes the shortcomings of linear correlation functions. • SGD turns into a new cluster center and gradually becomes a point connecting the Asian and European clusters during and after the US sub-prime crisis. • Liang's entropy theory, which has not been adopted before in the global foreign exchange market, is considered. - Abstract: The foreign exchange (FX) market is a typical complex dynamic system under the background of exchange rate marketization reform and is an important part of the financial market. This study aims to generate an international FX network based on complex network theory. This study employs the mutual information method to judge the nonlinear characteristics of 54 major currencies in international FX markets. Through this method, we find that the FX network possesses a small average path length and a large clustering coefficient under different thresholds and that it exhibits small-world characteristics as a whole. Results show that the relationship between FX rates is close. Volatility can quickly transfer in the whole market, and the FX volatility of influential individual states transfers at a fast pace and a large scale. The period from July 21, 2005 to March 31, 2015 is subdivided into three sub-periods (i.e., before, during, and after the US sub-prime crisis) to analyze the topology evolution of FX markets using the maximum spanning tree approach. Results show that the USD gradually lost its core position, EUR remained a stable center, and the center of the Asian cluster became unstable. Liang's entropy theory is used to analyze the causal relationship between the four large clusters of the world.

  1. Fermions in noncommutative emergent gravity

    International Nuclear Information System (INIS)

    Klammer, D.

    2010-01-01

    Noncommutative emergent gravity is a novel framework disclosing how gravity is contained naturally in noncommutative gauge theory formulated as a matrix model. It describes a dynamical space-time which itself is a four-dimensional brane embedded in a higher-dimensional space. In noncommutative emergent gravity, the metric is not a fundamental object of the model; rather it is determined by the Poisson structure and by the induced metric of the embedding. In this work the coupling of fermions to these matrix models is studied from the point of view of noncommutative emergent gravity. The matrix Dirac operator as given by the IKKT matrix model defines an appropriate coupling for fermions to an effective gravitational metric of noncommutative four-dimensional spaces that are embedded into a ten-dimensional ambient space. As it turns out this coupling is non-standard due to a spin connection that vanishes in the preferred but unobservable coordinates defined by the model. The purpose of this work is to study the one-loop effective action of this approach. Standard results of the literature cannot be applied due to this special coupling of the fermions. However, integrating out these fields in a nontrivial geometrical background induces indeed the Einstein-Hilbert action of the effective metric, as well as additional terms which couple the noncommutative structure to the Riemann tensor, and a dilaton-like term. It remains to be understood what the effects of these terms are and whether they can be avoided. In a second step, the existence of a duality between noncommutative gauge theory and gravity which explains the phenomenon of UV/IR mixing as a gravitational effect is discussed. We show how the gravitational coupling of fermions can be interpreted as a coupling of fermions to gauge fields, which suffers then from UV/IR mixing. This explanation does not render the model finite but it reveals why some UV/IR mixing remains even in supersymmetric models, except in the N

  2. Hip fracture in the elderly: a re-analysis of the EPIDOS study with causal Bayesian networks.

    Science.gov (United States)

    Caillet, Pascal; Klemm, Sarah; Ducher, Michel; Aussem, Alexandre; Schott, Anne-Marie

    2015-01-01

    Hip fractures commonly result in permanent disability, institutionalization or death in elderly. Existing hip-fracture predicting tools are underused in clinical practice, partly due to their lack of intuitive interpretation. By use of a graphical layer, Bayesian network models could increase the attractiveness of fracture prediction tools. Our aim was to study the potential contribution of a causal Bayesian network in this clinical setting. A logistic regression was performed as a standard control approach to check the robustness of the causal Bayesian network approach. EPIDOS is a multicenter study, conducted in an ambulatory care setting in five French cities between 1992 and 1996 and updated in 2010. The study included 7598 women aged 75 years or older, in which fractures were assessed quarterly during 4 years. A causal Bayesian network and a logistic regression were performed on EPIDOS data to describe major variables involved in hip fractures occurrences. Both models had similar association estimations and predictive performances. They detected gait speed and mineral bone density as variables the most involved in the fracture process. The causal Bayesian network showed that gait speed and bone mineral density were directly connected to fracture and seem to mediate the influence of all the other variables included in our model. The logistic regression approach detected multiple interactions involving psychotropic drug use, age and bone mineral density. Both approaches retrieved similar variables as predictors of hip fractures. However, Bayesian network highlighted the whole web of relation between the variables involved in the analysis, suggesting a possible mechanism leading to hip fracture. According to the latter results, intervention focusing concomitantly on gait speed and bone mineral density may be necessary for an optimal prevention of hip fracture occurrence in elderly people.

  3. Causality within the Epileptic Network: An EEG-fMRI Study Validated by Intracranial EEG.

    Science.gov (United States)

    Vaudano, Anna Elisabetta; Avanzini, Pietro; Tassi, Laura; Ruggieri, Andrea; Cantalupo, Gaetano; Benuzzi, Francesca; Nichelli, Paolo; Lemieux, Louis; Meletti, Stefano

    2013-01-01

    Accurate localization of the Seizure Onset Zone (SOZ) is crucial in patients with drug-resistance focal epilepsy. EEG with fMRI recording (EEG-fMRI) has been proposed as a complementary non-invasive tool, which can give useful additional information in the pre-surgical work-up. However, fMRI maps related to interictal epileptiform activities (IED) often show multiple regions of signal change, or "networks," rather than highly focal ones. Effective connectivity approaches like Dynamic Causal Modeling (DCM) applied to fMRI data potentially offers a framework to address which brain regions drives the generation of seizures and IED within an epileptic network. Here, we present a first attempt to validate DCM on EEG-fMRI data in one patient affected by frontal lobe epilepsy. Pre-surgical EEG-fMRI demonstrated two distinct clusters of blood oxygenation level dependent (BOLD) signal increases linked to IED, one located in the left frontal pole and the other in the ipsilateral dorso-lateral frontal cortex. DCM of the IED-related BOLD signal favored a model corresponding to the left dorso-lateral frontal cortex as driver of changes in the fronto-polar region. The validity of DCM was supported by: (a) the results of two different non-invasive analysis obtained on the same dataset: EEG source imaging (ESI), and "psycho-physiological interaction" analysis; (b) the failure of a first surgical intervention limited to the fronto-polar region; (c) the results of the intracranial EEG monitoring performed after the first surgical intervention confirming a SOZ located over the dorso-lateral frontal cortex. These results add evidence that EEG-fMRI together with advanced methods of BOLD signal analysis is a promising tool that can give relevant information within the epilepsy surgery diagnostic work-up.

  4. Causality within the epileptic network: an EEG-fMRI study validated by intracranial EEG.

    Directory of Open Access Journals (Sweden)

    Anna Elisabetta eVaudano

    2013-11-01

    Full Text Available Accurate localization of the Seizure Onset Zone (SOZ is crucial in patients with drug-resistance focal epilepsy. EEG with fMRI recording (EEG-fMRI has been proposed as a complementary non-invasive tool, which can give useful additional information in the pre-surgical workup. However, fMRI maps related to interictal epileptiform activities (IED often show multiple regions of signal change, or networks, rather than highly focal ones. Effective connectivity approaches like Dynamic Causal Modelling (DCM applied to fMRI data potentially offers a framework to address which brain regions drives the generation of seizures and IED within an epileptic network. Here we present a first attempt to validate DCM on EEG-fMRI data in one patient affected by frontal lobe epilepsy. Pre-surgical EEG-fMRI demonstrated two distinct clusters of BOLD signal increases linked to IED, one located in the left frontal pole and the other in the ipsilateral dorso-lateral frontal cortex. DCM of the IED-related BOLD signal favoured a model corresponding to the left dorsolateral frontal cortex as driver of changes in the fronto-polar region. The validity of DCM was supported by: (a the results of two different non-invasive analysis obtained on the same dataset: EEG source imaging (ESI, and psychophysiological interaction analysis (PPI; (b the failure of a first surgical intervention limited to the fronto-polar region; (c the results of the intracranial EEG monitoring performed after the first surgical intervention confirming a SOZ located over the dorso-lateral frontal cortex. These results add evidence that EEG-fMRI together with advanced methods of BOLD signal analysis is a promising tool that can give relevant information within the epilepsy surgery diagnostic work-up.

  5. Twisted covariant noncommutative self-dual gravity

    International Nuclear Information System (INIS)

    Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.

    2008-01-01

    A twisted covariant formulation of noncommutative self-dual gravity is presented. The formulation for constructing twisted noncommutative Yang-Mills theories is used. It is shown that the noncommutative torsion is solved at any order of the θ expansion in terms of the tetrad and some extra fields of the theory. In the process the first order expansion in θ for the Plebanski action is explicitly obtained.

  6. Causal influence in neural systems: Reconciling mechanistic-reductionist and statistical perspectives. Comment on "Foundational perspectives on causality in large-scale brain networks" by M. Mannino & S.L. Bressler

    Science.gov (United States)

    Griffiths, John D.

    2015-12-01

    The modern understanding of the brain as a large, complex network of interacting elements is a natural consequence of the Neuron Doctrine [1,2] that has been bolstered in recent years by the tools and concepts of connectomics. In this abstracted, network-centric view, the essence of neural and cognitive function derives from the flows between network elements of activity and information - or, more generally, causal influence. The appropriate characterization of causality in neural systems, therefore, is a question at the very heart of systems neuroscience.

  7. Noncommutative quantum electrodynamics in path integral framework

    Energy Technology Data Exchange (ETDEWEB)

    Bourouaine, S; Benslama, A [Departement de Physique, Faculte des Sciences, Universite Mentouri, Constantine (Algeria)

    2005-08-19

    In this paper, the dynamics of a relativistic particle of spin 1/2, interacting with an external electromagnetic field in noncommutative space, is studied in the path integral framework. By adopting the Fradkin-Gitman formulation, the exact Green's function in noncommutative space (NCGF) for the quadratic case of a constant electromagnetic field is computed, and it is shown that its form is similar to its counterpart given in commutative space. In addition, it is deduced that the effect of noncommutativity has the same effect as an additional constant field depending on a noncommutative {theta} matrix.

  8. Noncommutative quantum electrodynamics in path integral framework

    International Nuclear Information System (INIS)

    Bourouaine, S; Benslama, A

    2005-01-01

    In this paper, the dynamics of a relativistic particle of spin 1/2, interacting with an external electromagnetic field in noncommutative space, is studied in the path integral framework. By adopting the Fradkin-Gitman formulation, the exact Green's function in noncommutative space (NCGF) for the quadratic case of a constant electromagnetic field is computed, and it is shown that its form is similar to its counterpart given in commutative space. In addition, it is deduced that the effect of noncommutativity has the same effect as an additional constant field depending on a noncommutative θ matrix

  9. Canonical noncommutativity in special and general relativity

    Energy Technology Data Exchange (ETDEWEB)

    Chryssomalakos, C; Hernandez, H; Okon, E; Vazquez Montejo, P [Instituto de Ciencias Nucleares, Universidad National Autonoma de Mexico, 04510 Mexico, D.F. (Mexico)

    2007-05-15

    There are two main points that concern us in this short contribution. The first one is the conceptual distinction between a intrinsically noncommuting spacetime, i.e., one where the coordinate functions fail to commute among themselves, on the one hand, and the proposal of noncommuting position operators, on the other. The second point concerns a particular form of position operator noncommutativity, involving the spin of the particle, to which several approaches seem to converge. We also suggest an analysis of the effects of spacetime curvature on position operator noncommutativity.

  10. Noncommutative geometry and twisted conformal symmetry

    International Nuclear Information System (INIS)

    Matlock, Peter

    2005-01-01

    The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted coproduct. This allows for the definition of conformal symmetry in a noncommutative background geometry. The twisted coproduct is reviewed for the Poincare algebra and the construction is then extended to the full conformal algebra. The case of Moyal-type noncommutativity of the coordinates is considered. It is demonstrated that conformal invariance need not be viewed as incompatible with noncommutative geometry; the noncommutativity of the coordinates appears as a consequence of the twisting, as has been shown in the literature in the case of the twisted Poincare algebra

  11. Noncommutative instantons: a new approach

    International Nuclear Information System (INIS)

    Schwarz, A.

    2001-01-01

    We discuss instantons on noncommutative four-dimensional Euclidean space. In the commutative case one can consider instantons directly on Euclidean space, then we should restrict ourselves to the gauge fields that are gauge equivalent to the trivial field at infinity. However, technically it is more convenient to work on the four-dimensional sphere. We will show that the situation in the noncommutative case is quite similar. One can analyze instantons taking as a starting point the algebra of smooth functions vanishing at infinity, but it is convenient to add a unit element to this algebra (this corresponds to a transition to a sphere at the level of topology). Our approach is more rigorous than previous considerations; it seems that it is also simpler and more transparent. In particular, we obtain the ADHM equations in a very simple way. (orig.)

  12. Exploring causal networks underlying fat deposition and muscularity in pigs through the integration of phenotypic, genotypic and transcriptomic data.

    Science.gov (United States)

    Peñagaricano, Francisco; Valente, Bruno D; Steibel, Juan P; Bates, Ronald O; Ernst, Catherine W; Khatib, Hasan; Rosa, Guilherme J M

    2015-09-16

    Joint modeling and analysis of phenotypic, genotypic and transcriptomic data have the potential to uncover the genetic control of gene activity and phenotypic variation, as well as shed light on the manner and extent of connectedness among these variables. Current studies mainly report associations, i.e. undirected connections among variables without causal interpretation. Knowledge regarding causal relationships among genes and phenotypes can be used to predict the behavior of complex systems, as well as to optimize management practices and selection strategies. Here, we performed a multistep procedure for inferring causal networks underlying carcass fat deposition and muscularity in pigs using multi-omics data obtained from an F2 Duroc x Pietrain resource pig population. We initially explored marginal associations between genotypes and phenotypic and expression traits through whole-genome scans, and then, in genomic regions with multiple significant hits, we assessed gene-phenotype network reconstruction using causal structural learning algorithms. One genomic region on SSC6 showed significant associations with three relevant phenotypes, off-midline10th-rib backfat thickness, loin muscle weight, and average intramuscular fat percentage, and also with the expression of seven genes, including ZNF24, SSX2IP, and AKR7A2. The inferred network indicated that the genotype affects the three phenotypes mainly through the expression of several genes. Among the phenotypes, fat deposition traits negatively affected loin muscle weight. Our findings shed light on the antagonist relationship between carcass fat deposition and lean meat content in pigs. In addition, the procedure described in this study has the potential to unravel gene-phenotype networks underlying complex phenotypes.

  13. Modelling the effect of religion on human empathy based on an adaptive temporal–causal network model

    OpenAIRE

    van Ments, Laila; Roelofsma, Peter; Treur, Jan

    2018-01-01

    Background Religion is a central aspect of many individuals’ lives around the world, and its influence on human behaviour has been extensively studied from many different perspectives. Methods The current study integrates a number of these perspectives into one adaptive temporal–causal network model describing the mental states involved, their mutual relations, and the adaptation of some of these relations over time due to learning. Results By first developing a conceptual representation of a...

  14. Non-commutative Nash inequalities

    International Nuclear Information System (INIS)

    Kastoryano, Michael; Temme, Kristan

    2016-01-01

    A set of functional inequalities—called Nash inequalities—are introduced and analyzed in the context of quantum Markov process mixing. The basic theory of Nash inequalities is extended to the setting of non-commutative L p spaces, where their relationship to Poincaré and log-Sobolev inequalities is fleshed out. We prove Nash inequalities for a number of unital reversible semigroups

  15. Detangling complex relationships in forensic data: principles and use of causal networks and their application to clinical forensic science.

    Science.gov (United States)

    Lefèvre, Thomas; Lepresle, Aude; Chariot, Patrick

    2015-09-01

    The search for complex, nonlinear relationships and causality in data is hindered by the availability of techniques in many domains, including forensic science. Linear multivariable techniques are useful but present some shortcomings. In the past decade, Bayesian approaches have been introduced in forensic science. To date, authors have mainly focused on providing an alternative to classical techniques for quantifying effects and dealing with uncertainty. Causal networks, including Bayesian networks, can help detangle complex relationships in data. A Bayesian network estimates the joint probability distribution of data and graphically displays dependencies between variables and the circulation of information between these variables. In this study, we illustrate the interest in utilizing Bayesian networks for dealing with complex data through an application in clinical forensic science. Evaluating the functional impairment of assault survivors is a complex task for which few determinants are known. As routinely estimated in France, the duration of this impairment can be quantified by days of 'Total Incapacity to Work' ('Incapacité totale de travail,' ITT). In this study, we used a Bayesian network approach to identify the injury type, victim category and time to evaluation as the main determinants of the 'Total Incapacity to Work' (TIW). We computed the conditional probabilities associated with the TIW node and its parents. We compared this approach with a multivariable analysis, and the results of both techniques were converging. Thus, Bayesian networks should be considered a reliable means to detangle complex relationships in data.

  16. Quantum gravity from noncommutative spacetime

    International Nuclear Information System (INIS)

    Lee, Jungjai; Yang, Hyunseok

    2014-01-01

    We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative *-algebra) of quantum gravity.

  17. Quantum gravity from noncommutative spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Jungjai [Daejin University, Pocheon (Korea, Republic of); Yang, Hyunseok [Korea Institute for Advanced Study, Seoul (Korea, Republic of)

    2014-12-15

    We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative *-algebra) of quantum gravity.

  18. PPARalpha siRNA-treated expression profiles uncover the causal sufficiency network for compound-induced liver hypertrophy.

    Directory of Open Access Journals (Sweden)

    Xudong Dai

    2007-03-01

    Full Text Available Uncovering pathways underlying drug-induced toxicity is a fundamental objective in the field of toxicogenomics. Developing mechanism-based toxicity biomarkers requires the identification of such novel pathways and the order of their sufficiency in causing a phenotypic response. Genome-wide RNA interference (RNAi phenotypic screening has emerged as an effective tool in unveiling the genes essential for specific cellular functions and biological activities. However, eliciting the relative contribution of and sufficiency relationships among the genes identified remains challenging. In the rodent, the most widely used animal model in preclinical studies, it is unrealistic to exhaustively examine all potential interactions by RNAi screening. Application of existing computational approaches to infer regulatory networks with biological outcomes in the rodent is limited by the requirements for a large number of targeted permutations. Therefore, we developed a two-step relay method that requires only one targeted perturbation for genome-wide de novo pathway discovery. Using expression profiles in response to small interfering RNAs (siRNAs against the gene for peroxisome proliferator-activated receptor alpha (Ppara, our method unveiled the potential causal sufficiency order network for liver hypertrophy in the rodent. The validity of the inferred 16 causal transcripts or 15 known genes for PPARalpha-induced liver hypertrophy is supported by their ability to predict non-PPARalpha-induced liver hypertrophy with 84% sensitivity and 76% specificity. Simulation shows that the probability of achieving such predictive accuracy without the inferred causal relationship is exceedingly small (p < 0.005. Five of the most sufficient causal genes have been previously disrupted in mouse models; the resulting phenotypic changes in the liver support the inferred causal roles in liver hypertrophy. Our results demonstrate the feasibility of defining pathways mediating drug

  19. Abnormal resting state effective connectivity within the default mode network in major depressive disorder: A spectral dynamic causal modeling study.

    Science.gov (United States)

    Li, Liang; Li, Baojuan; Bai, Yuanhan; Liu, Wenlei; Wang, Huaning; Leung, Hoi-Chung; Tian, Ping; Zhang, Linchuan; Guo, Fan; Cui, Long-Biao; Yin, Hong; Lu, Hongbing; Tan, Qingrong

    2017-07-01

    Understanding the neural basis underlying major depressive disorder (MDD) is essential for the diagnosis and treatment of this mental disorder. Aberrant activation and functional connectivity of the default mode network (DMN) have been consistently found in patients with MDD. It is not known whether effective connectivity within the DMN is altered in MDD. The primary object of this study is to investigate the effective connectivity within the DMN during resting state in MDD patients before and after eight weeks of antidepressant treatment. We defined four regions of the DMN (medial frontal cortex, posterior cingulate cortex, left parietal cortex, and right parietal cortex) for each participant using a group independent component analysis. The coupling parameters reflecting the causal interactions among the DMN regions were estimated using spectral dynamic causal modeling (DCM). Twenty-seven MDD patients and 27 healthy controls were included in the statistical analysis. Our results showed declined influences from the left parietal cortex to other DMN regions in the pre-treatment patients as compared with healthy controls. After eight weeks of treatment, the influence from the right parietal cortex to the posterior cingulate cortex significantly decreased. These findings suggest that the reduced excitatory causal influence of the left parietal cortex is the key alteration of the DMN in patients with MDD, and the disrupted causal influences that parietal cortex exerts on the posterior cingulate cortex is responsive to antidepressant treatment.

  20. Identifying the default mode network structure using dynamic causal modeling on resting-state functional magnetic resonance imaging.

    Science.gov (United States)

    Di, Xin; Biswal, Bharat B

    2014-02-01

    The default mode network is part of the brain structure that shows higher neural activity and energy consumption when one is at rest. The key regions in the default mode network are highly interconnected as conveyed by both the white matter fiber tracing and the synchrony of resting-state functional magnetic resonance imaging signals. However, the causal information flow within the default mode network is still poorly understood. The current study used the dynamic causal modeling on a resting-state fMRI data set to identify the network structure underlying the default mode network. The endogenous brain fluctuations were explicitly modeled by Fourier series at the low frequency band of 0.01-0.08Hz, and those Fourier series were set as driving inputs of the DCM models. Model comparison procedures favored a model wherein the MPFC sends information to the PCC and the bilateral inferior parietal lobule sends information to both the PCC and MPFC. Further analyses provide evidence that the endogenous connectivity might be higher in the right hemisphere than in the left hemisphere. These data provided insight into the functions of each node in the DMN, and also validate the usage of DCM on resting-state fMRI data. © 2013.

  1. Black Hole Complementary Principle and Noncommutative Membrane

    International Nuclear Information System (INIS)

    Wei Ren

    2006-01-01

    In the spirit of black hole complementary principle, we have found the noncommutative membrane of Scharzchild black holes. In this paper we extend our results to Kerr black hole and see the same story. Also we make a conjecture that spacetimes are noncommutative on the stretched membrane of the more general Kerr-Newman black hole.

  2. Vector fields and differential operators: noncommutative case

    International Nuclear Information System (INIS)

    Borowiec, A.

    1997-01-01

    A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed previously. In this paper an outline is given of the construction of a noncommutative analogy of the algebra of differential operators as well as its (algebraic) Fock space realization. Co-universal vector fields and covariant derivatives will also be discussed

  3. Noncommutative de Sitter and FRW spaces

    International Nuclear Information System (INIS)

    Burić, Maja; Madore, John

    2015-01-01

    Several versions of fuzzy four-dimensional de Sitter space are constructed using the noncommutative frame formalism. Although all noncommutative spacetimes which are found have commutative de Sitter metric as a classical limit, the algebras and the differential calculi which define them have many differences, which we derive and discuss

  4. Quantum information aspects of noncommutative quantum mechanics

    Science.gov (United States)

    Bertolami, Orfeu; Bernardini, Alex E.; Leal, Pedro

    2018-01-01

    Some fundamental aspects related with the construction of Robertson-Schrödinger-like uncertainty-principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum systems in the noncommutative phase-space. Some consequences of the deformed noncommutative algebra are also considered in physical systems of interest.

  5. Noncommutative induced gauge theories on Moyal spaces

    International Nuclear Information System (INIS)

    Wallet, J-C

    2008-01-01

    Noncommutative field theories on Moyal spaces can be conveniently handled within a framework of noncommutative geometry. Several renormalisable matter field theories that are now identified are briefly reviewed. The construction of renormalisable gauge theories on these noncommutative Moyal spaces, which remains so far a challenging problem, is then closely examined. The computation in 4-D of the one-loop effective gauge theory generated from the integration over a scalar field appearing in a renormalisable theory minimally coupled to an external gauge potential is presented. The gauge invariant effective action is found to involve, beyond the expected noncommutative version of the pure Yang-Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic term, which for the noncommutative ψ 4 -theory on Moyal space ensures renormalisability. A class of possible candidates for renormalisable gauge theory actions defined on Moyal space is presented and discussed

  6. Noncommutative instantons via dressing and splitting approaches

    International Nuclear Information System (INIS)

    Horvath, Zalan; Lechtenfeld, Olaf; Wolf, Martin

    2002-01-01

    Almost all known instanton solutions in noncommutative Yang-Mills theory have been obtained in the modified ADHM scheme. In this paper we employ two alternative methods for the construction of the self-dual U(2) BPST instanton on a noncommutative euclidean four-dimensional space with self-dual noncommutativity tensor. Firstly, we use the method of dressing transformations, an iterative procedure for generating solutions from a given seed solution, and thereby generalize Belavin's and Zakharov's work to the noncommutative setup. Secondly, we relate the dressing approach with Ward's splitting method based on the twistor construction and rederive the solution in this context. It seems feasible to produce nonsingular noncommutative multi-instantons with these techniques. (author)

  7. Spin Hall effect on a noncommutative space

    International Nuclear Information System (INIS)

    Ma Kai; Dulat, Sayipjamal

    2011-01-01

    We study the spin-orbital interaction and the spin Hall effect of an electron moving on a noncommutative space under the influence of a vector potential A(vector sign). On a noncommutative space, we find that the commutator between the vector potential A(vector sign) and the electric potential V 1 (r(vector sign)) of the lattice induces a new term, which can be treated as an effective electric field, and the spin Hall conductivity obtains some correction. On a noncommutative space, the spin current and spin Hall conductivity have distinct values in different directions, and depend explicitly on the noncommutative parameter. Once this spin Hall conductivity in different directions can be measured experimentally with a high level of accuracy, the data can then be used to impose bounds on the value of the space noncommutativity parameter. We have also defined a new parameter, σ=ρθ (ρ is the electron concentration, θ is the noncommutativity parameter), which can be measured experimentally. Our approach is based on the Foldy-Wouthuysen transformation, which gives a general Hamiltonian of a nonrelativistic electron moving on a noncommutative space.

  8. Noncommutative Geometry, Quantum Fields and Motives

    CERN Document Server

    Connes, Alain

    2007-01-01

    The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book dea

  9. Noncommutative gauge theories and Kontsevich's formality theorem

    International Nuclear Information System (INIS)

    Jurco, B.; Schupp, P.; Wess, J.

    2001-01-01

    The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map.) Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; as a byproduct we obtain a 'Mini Seiberg-Witten map' that explicitly relates ordinary abelian and nonabelian gauge fields. All constructions are also valid for non-constant B-field, and even more generally for any Poisson tensor

  10. Emergent Abelian Gauge Fields from Noncommutative Gravity

    Directory of Open Access Journals (Sweden)

    Allen Stern

    2010-02-01

    Full Text Available We construct exact solutions to noncommutative gravity following the formulation of Chamseddine and show that they are in general accompanied by Abelian gauge fields which are first order in the noncommutative scale. This provides a mechanism for generating cosmological electromagnetic fields in an expanding space-time background, and also leads to multipole-like fields surrounding black holes. Exact solutions to noncommutative Einstein-Maxwell theory can give rise to first order corrections to the metric tensor, as well as to the electromagnetic fields. This leads to first order shifts in the horizons of charged black holes.

  11. Noncommutative quantum scattering in a central field

    International Nuclear Information System (INIS)

    Bellucci, Stefano; Yeranyan, Armen

    2005-01-01

    In this Letter the problem of noncommutative elastic scattering in a central field is considered. General formulas for the differential cross-section for two cases are obtained. For the case of high energy of an incident wave it is shown that the differential cross-section coincides with that on the commutative space. For the case in which noncommutativity yields only a small correction to the central potential it is shown that the noncommutativity leads to the redistribution of particles along the azimuthal angle, although the whole cross-section coincides with the commutative case

  12. Noncommutative quantum mechanics and Bohm's ontological interpretation

    International Nuclear Information System (INIS)

    Barbosa, G.D.; Pinto-Neto, N.

    2004-01-01

    We carry out an investigation into the possibility of developing a Bohmian interpretation based on the continuous motion of point particles for noncommutative quantum mechanics. The conditions for such an interpretation to be consistent are determined, and the implications of its adoption for noncommutativity are discussed. A Bohmian analysis of the noncommutative harmonic oscillator is carried out in detail. By studying the particle motion in the oscillator orbits, we show that small-scale physics can have influence at large scales, something similar to the IR-UV mixing

  13. Noncommutative geometry and fluid dynamics

    International Nuclear Information System (INIS)

    Das, Praloy; Ghosh, Subir

    2016-01-01

    In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets and the induced NC fluid bracket algebra for the Eulerian (fluid) field variables is derived. Together with a Hamiltonian this NC algebra generates the generalized fluid dynamics that satisfies exact local conservation laws for mass and energy, thereby maintaining mass and energy conservation. However, nontrivial NC correction terms appear in the charge and energy fluxes. Other non-relativistic spacetime symmetries of the NC fluid are also discussed in detail. This constitutes the study of kinematics and dynamics of NC fluid. In the second part we construct an extension of the Friedmann-Robertson-Walker (FRW) cosmological model based on the NC fluid dynamics presented here. We outline the way in which NC effects generate cosmological perturbations bringing about anisotropy and inhomogeneity in the model. We also derive a NC extended Friedmann equation. (orig.)

  14. Noncommutative geometry and fluid dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Das, Praloy; Ghosh, Subir [Indian Statistical Institute, Physics and Applied Mathematics Unit, Kolkata (India)

    2016-11-15

    In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets and the induced NC fluid bracket algebra for the Eulerian (fluid) field variables is derived. Together with a Hamiltonian this NC algebra generates the generalized fluid dynamics that satisfies exact local conservation laws for mass and energy, thereby maintaining mass and energy conservation. However, nontrivial NC correction terms appear in the charge and energy fluxes. Other non-relativistic spacetime symmetries of the NC fluid are also discussed in detail. This constitutes the study of kinematics and dynamics of NC fluid. In the second part we construct an extension of the Friedmann-Robertson-Walker (FRW) cosmological model based on the NC fluid dynamics presented here. We outline the way in which NC effects generate cosmological perturbations bringing about anisotropy and inhomogeneity in the model. We also derive a NC extended Friedmann equation. (orig.)

  15. Noncommuting observables and local realism

    International Nuclear Information System (INIS)

    Malley, James D.; Fine, Arthur

    2005-01-01

    A standard approach in the foundations of quantum mechanics studies local realism and hidden variables models exclusively in terms of violations of Bell-like inequalities. Thus quantum nonlocality is tied to the celebrated no-go theorems, and these comprise a long list that includes the Kochen-Specker and Bell theorems, as well as elegant refinements by Mermin, Peres, Hardy, GHZ, and many others. Typically entanglement or carefully prepared multipartite systems have been considered essential for violations of local realism and for understanding quantum nonlocality. Here we show, to the contrary, that sharp violations of local realism arise almost everywhere without entanglement. The pivotal fact driving these violations is just the noncommutativity of quantum observables. We demonstrate how violations of local realism occur for arbitrary noncommuting projectors, and for arbitrary quantum pure states. Finally, we point to elementary tests for local realism, using single particles and without reference to entanglement, thus avoiding experimental loopholes and efficiency issues that continue to bedevil the Bell inequality related tests

  16. Holographic entanglement in a noncommutative gauge theory

    International Nuclear Information System (INIS)

    Fischler, Willy; Kundu, Arnab; Kundu, Sandipan

    2014-01-01

    In this article we investigate aspects of entanglement entropy and mutual information in a large-N strongly coupled noncommutative gauge theory, both at zero and at finite temperature. Using the gauge-gravity duality and the Ryu-Takayanagi (RT) prescription, we adopt a scheme for defining spatial regions on such noncommutative geometries and subsequently compute the corresponding entanglement entropy. We observe that for regions which do not lie entirely in the noncommutative plane, the RT-prescription yields sensible results. In order to make sense of the divergence structure of the corresponding entanglement entropy, it is essential to introduce an additional cut-off in the theory. For regions which lie entirely in the noncommutative plane, the corresponding minimal area surfaces can only be defined at this cut-off and they have distinctly peculiar properties

  17. The local index formula in noncommutative geometry

    International Nuclear Information System (INIS)

    Higson, N.

    2003-01-01

    These notes present a partial account of the local index theorem in non-commutative geometry discovered by Alain Connes and Henri Moscovici. It includes Elliptic partial differential operators, cyclic homology theory, Chern characters, homotopy invariants and the index formulas

  18. Note on the extended noncommutativity of coordinates

    International Nuclear Information System (INIS)

    Boulahoual, Amina; Sedra, My. Brahim

    2001-04-01

    We present in this short note an idea about a possible extension of the standard noncommutative algebra to the formal differential operators framework. In this sense, we develop an analysis and derive an extended noncommutative algebra given by [x a , x b ] * =i(θ+χ) ab where θ ab , is the standard noncommutative parameter and χ ab (x)≡χ ab μ (x)δ μ =1/2(x a θ μ b -x b θ a )δ μ is an antisymmetric non-constant vector-field shown to play the role of the extended deformation parameter. This idea was motivated by the importance of noncommutative geometry framework in the current subject of D-brane and matrix theory physics. (author)

  19. Covariant non-commutative space–time

    Directory of Open Access Journals (Sweden)

    Jonathan J. Heckman

    2015-05-01

    Full Text Available We introduce a covariant non-commutative deformation of 3+1-dimensional conformal field theory. The deformation introduces a short-distance scale ℓp, and thus breaks scale invariance, but preserves all space–time isometries. The non-commutative algebra is defined on space–times with non-zero constant curvature, i.e. dS4 or AdS4. The construction makes essential use of the representation of CFT tensor operators as polynomials in an auxiliary polarization tensor. The polarization tensor takes active part in the non-commutative algebra, which for dS4 takes the form of so(5,1, while for AdS4 it assembles into so(4,2. The structure of the non-commutative correlation functions hints that the deformed theory contains gravitational interactions and a Regge-like trajectory of higher spin excitations.

  20. Foundations of free noncommutative function theory

    CERN Document Server

    Kaliuzhnyi-Verbovetskyi, Dmitry S

    2014-01-01

    In this book the authors develop a theory of free noncommutative functions, in both algebraic and analytic settings. Such functions are defined as mappings from square matrices of all sizes over a module (in particular, a vector space) to square matrices over another module, which respect the size, direct sums, and similarities of matrices. Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions. Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. An important application area is "dimensionless" matrix inequalities; these arise, e.g., in various optimization problems of system engineering. Among other related areas are those of polynomial identities in rings, formal languages and finite automata, quasideterminants, noncommutative symmetric functions, operator spaces and operator algebras, and quantum control.

  1. Entropic force, noncommutative gravity, and ungravity

    International Nuclear Information System (INIS)

    Nicolini, Piero

    2010-01-01

    After recalling the basic concepts of gravity as an emergent phenomenon, we analyze the recent derivation of Newton's law in terms of entropic force proposed by Verlinde. By reviewing some points of the procedure, we extend it to the case of a generic quantum gravity entropic correction to get compelling deviations to the Newton's law. More specifically, we study: (1) noncommutative geometry deviations and (2) ungraviton corrections. As a special result in the noncommutative case, we find that the noncommutative character of the manifold would be equivalent to the temperature of a thermodynamic system. Therefore, in analogy to the zero temperature configuration, the description of spacetime in terms of a differential manifold could be obtained only asymptotically. Finally, we extend the Verlinde's derivation to a general case, which includes all possible effects, noncommutativity, ungravity, asymptotically safe gravity, electrostatic energy, and extra dimensions, showing that the procedure is solid versus such modifications.

  2. Noncommutative gauge theory for Poisson manifolds

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, Branislav E-mail: jurco@mpim-bonn.mpg.de; Schupp, Peter E-mail: schupp@theorie.physik.uni-muenchen.de; Wess, Julius E-mail: wess@theorie.physik.uni-muenchen.de

    2000-09-25

    A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.

  3. Noncommutative gauge theory for Poisson manifolds

    International Nuclear Information System (INIS)

    Jurco, Branislav; Schupp, Peter; Wess, Julius

    2000-01-01

    A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem

  4. Noncommutative Gauge Theory with Covariant Star Product

    International Nuclear Information System (INIS)

    Zet, G.

    2010-01-01

    We present a noncommutative gauge theory with covariant star product on a space-time with torsion. In order to obtain the covariant star product one imposes some restrictions on the connection of the space-time. Then, a noncommutative gauge theory is developed applying this product to the case of differential forms. Some comments on the advantages of using a space-time with torsion to describe the gravitational field are also given.

  5. Non-commutative tomography and signal processing

    International Nuclear Information System (INIS)

    Mendes, R Vilela

    2015-01-01

    Non-commutative tomography is a technique originally developed and extensively used by Professors M A Man’ko and V I Man’ko in quantum mechanics. Because signal processing deals with operators that, in general, do not commute with time, the same technique has a natural extension to this domain. Here, a review is presented of the theory and some applications of non-commutative tomography for time series as well as some new results on signal processing on graphs. (paper)

  6. Photon defects in noncommutative standard model candidates

    International Nuclear Information System (INIS)

    Abel, S.A.; Khoze, V.V.

    2006-06-01

    Restrictions imposed by gauge invariance in noncommutative spaces together with the effects of ultraviolet/infrared mixing lead to strong constraints on possible candidates for a noncommutative extension of the Standard Model. We study a general class of noncommutative models consistent with these restrictions. Specifically we consider models based upon a gauge theory with the gauge group U(N 1 ) x U(N 2 ) x.. x U(N m ) coupled to matter fields transforming in the (anti)-fundamental, bi-fundamental and adjoint representations. We pay particular attention to overall trace-U(1) factors of the gauge group which are affected by the ultraviolet/infrared mixing. Typically, these trace-U(1) gauge fields do not decouple sufficiently fast in the infrared, and lead to sizable Lorentz symmetry violating effects in the low-energy effective theory. In a 4-dimensional theory on a continuous space-time making these effects unobservable would require making the effects of noncommutativity tiny, M NC >> M P . This severely limits the phenomenological prospects of such models. However, adding additional universal extra dimensions the trace-U(1) factors decouple with a power law and the constraint on the noncommutativity scale is weakened considerably. Finally, we briefly mention some interesting properties of the photon that could arise if the noncommutative theory is modified at a high energy scale. (Orig.)

  7. Non-commutative standard model: model building

    CERN Document Server

    Chaichian, Masud; Presnajder, P

    2003-01-01

    A non-commutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: (1) although we can have non-commutative U(n) (which we denote by U sub * (n)) gauge theory we cannot have non-commutative SU(n) and (2) the charges in non-commutative QED are quantized to just 0,+-1. We show how the latter problem with charge quantization, as well as with the gauge group, can be resolved by taking the U sub * (3) x U sub * (2) x U sub * (1) gauge group and reducing the extra U(1) factors in an appropriate way. Then we proceed with building the non-commutative version of the standard model by specifying the proper representations for the entire particle content of the theory, the gauge bosons, the fermions and Higgs. We also present the full action for the non-commutative standard model (NCSM). In addition, among several peculiar features of our model, we address the inherentCP violation and new neutrino interactions. (orig.)

  8. Extension of noncommutative soliton hierarchies

    International Nuclear Information System (INIS)

    Dimakis, Aristophanes; Mueller-Hoissen, Folkert

    2004-01-01

    A linear system, which generates a Moyal-deformed two-dimensional soliton equation as an integrability condition, can be extended to a three-dimensional linear system, treating the deformation parameter as an additional coordinate. The supplementary integrability conditions result in a first-order differential equation with respect to the deformation parameter, the flow of which commutes with the flow of the deformed soliton equation. In this way, a deformed soliton hierarchy can be extended to a bigger hierarchy by including the corresponding deformation equations. We prove the extended hierarchy properties for the deformed AKNS hierarchy, and specialize to the cases of deformed NLS, KdV and mKdV hierarchies. Corresponding results are also obtained for the deformed KP hierarchy. A deformation equation determines a kind of Seiberg-Witten map from classical solutions to solutions of the respective 'noncommutative' deformed equation

  9. Noncommutative Common Cause Principles in algebraic quantum field theory

    International Nuclear Information System (INIS)

    Hofer-Szabó, Gábor; Vecsernyés, Péter

    2013-01-01

    States in algebraic quantum field theory “typically” establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V A and V B , respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V A and V B and the set {C, C ⊥ } screens off the correlation between A and B.

  10. Causal networks clarify productivity-richness interrelations, bivariate plots do not

    Science.gov (United States)

    Grace, James B.; Adler, Peter B.; Harpole, W. Stanley; Borer, Elizabeth T.; Seabloom, Eric W.

    2014-01-01

    Perhaps no other pair of variables in ecology has generated as much discussion as species richness and ecosystem productivity, as illustrated by the reactions by Pierce (2013) and others to Adler et al.'s (2011) report that empirical patterns are weak and inconsistent. Adler et al. (2011) argued we need to move beyond a focus on simplistic bivariate relationships and test mechanistic, multivariate causal hypotheses. We feel the continuing debate over productivity–richness relationships (PRRs) provides a focused context for illustrating the fundamental difficulties of using bivariate relationships to gain scientific understanding.

  11. Effective Connectivity within the Default Mode Network: Dynamic Causal Modeling of Resting-State fMRI Data.

    Science.gov (United States)

    Sharaev, Maksim G; Zavyalova, Viktoria V; Ushakov, Vadim L; Kartashov, Sergey I; Velichkovsky, Boris M

    2016-01-01

    The Default Mode Network (DMN) is a brain system that mediates internal modes of cognitive activity, showing higher neural activation when one is at rest. Nowadays, there is a lot of interest in assessing functional interactions between its key regions, but in the majority of studies only association of Blood-oxygen-level dependent (BOLD) activation patterns is measured, so it is impossible to identify causal influences. There are some studies of causal interactions (i.e., effective connectivity), however often with inconsistent results. The aim of the current work is to find a stable pattern of connectivity between four DMN key regions: the medial prefrontal cortex (mPFC), the posterior cingulate cortex (PCC), left and right intraparietal cortex (LIPC and RIPC). For this purpose functional magnetic resonance imaging (fMRI) data from 30 healthy subjects (1000 time points from each one) was acquired and spectral dynamic causal modeling (DCM) on a resting-state fMRI data was performed. The endogenous brain fluctuations were explicitly modeled by Discrete Cosine Set at the low frequency band of 0.0078-0.1 Hz. The best model at the group level is the one where connections from both bilateral IPC to mPFC and PCC are significant and symmetrical in strength (p bidirectional, significant in the group and weaker than connections originating from bilateral IPC. In general, all connections from LIPC/RIPC to other DMN regions are much stronger. One can assume that these regions have a driving role within the DMN. Our results replicate some data from earlier works on effective connectivity within the DMN as well as provide new insights on internal DMN relationships and brain's functioning at resting state.

  12. Effective connectivity within the default mode network: dynamic causal modeling of resting-state fMRI data

    Directory of Open Access Journals (Sweden)

    Maksim eSharaev

    2016-02-01

    Full Text Available The Default Mode Network (DMN is a brain system that mediates internal modes of cognitive activity, showing higher neural activation when one is at rest. Nowadays, there is a lot of interest in assessing functional interactions between its key regions, but in the majority of studies only association of BOLD (Blood-oxygen-level dependent activation patterns is measured, so it is impossible to identify causal influences. There are some studies of causal interactions (i.e. effective connectivity, however often with inconsistent results. The aim of the current work is to find a stable pattern of connectivity between four DMN key regions: the medial prefrontal cortex mPFC, the posterior cingulate cortex PCC, left and right intraparietal cortex LIPC and RIPC. For this purpose fMRI (functional magnetic resonance imaging data from 30 healthy subjects (1000 time points from each one was acquired and spectral dynamic causal modeling (DCM on a resting-state fMRI data was performed. The endogenous brain fluctuations were explicitly modeled by Discrete Cosine Set at the low frequency band of 0.0078–0.1 Hz. The best model at the group level is the one where connections from both bilateral IPC to mPFC and PCC are significant and symmetrical in strength (p<0.05. Connections between mPFC and PCC are bidirectional, significant in the group and weaker than connections originating from bilateral IPC. In general, all connections from LIPC/RIPC to other DMN regions are much stronger. One can assume that these regions have a driving role within the DMN. Our results replicate some data from earlier works on effective connectivity within the DMN as well as provide new insights on internal DMN relationships and brain’s functioning at resting state.

  13. On the Generalized Geometry Origin of Noncommutative Gauge Theory

    CERN Document Server

    Jurco, Branislav; Vysoky, Jan

    2013-01-01

    We discuss noncommutative gauge theory from the generalized geometry point of view. We argue that the equivalence between the commutative and semiclassically noncommutative DBI actions is naturally encoded in the generalized geometry of D-branes.

  14. Noncommutative black-body radiation: Implications on cosmic microwave background

    International Nuclear Information System (INIS)

    Fatollahi, A.H.; Hajirahimi, M.

    2006-01-01

    Including loop corrections, black-body radiation in noncommutative space is anisotropic. A direct implication of possible space non-commutativity on the cosmic microwave background map is argued. (authors)

  15. Labeling Actors and Uncovering Causal Accounts of Their States in Social Networks and Social Media

    Science.gov (United States)

    Bui, Ngot P.

    2016-01-01

    The emergence of social networks and social media has resulted in exponential increase in the amount of data that link diverse types of richly structured digital objects e.g., individuals, articles, images, videos, music, etc. Such data are naturally represented as heterogeneous networks with multiple types of objects e.g., actors, video,…

  16. Causal structure of oscillations in gene regulatory networks: Boolean analysis of ordinary differential equation attractors.

    Science.gov (United States)

    Sun, Mengyang; Cheng, Xianrui; Socolar, Joshua E S

    2013-06-01

    A common approach to the modeling of gene regulatory networks is to represent activating or repressing interactions using ordinary differential equations for target gene concentrations that include Hill function dependences on regulator gene concentrations. An alternative formulation represents the same interactions using Boolean logic with time delays associated with each network link. We consider the attractors that emerge from the two types of models in the case of a simple but nontrivial network: a figure-8 network with one positive and one negative feedback loop. We show that the different modeling approaches give rise to the same qualitative set of attractors with the exception of a possible fixed point in the ordinary differential equation model in which concentrations sit at intermediate values. The properties of the attractors are most easily understood from the Boolean perspective, suggesting that time-delay Boolean modeling is a useful tool for understanding the logic of regulatory networks.

  17. Dynamic causal modeling of hippocampal links within the human default mode network: Lateralization and computational stability of effective connections

    Directory of Open Access Journals (Sweden)

    Vadim Leonidovich Ushakov

    2016-10-01

    Full Text Available The purpose of this paper was to study causal relationships between left and right hippocampal regions (LHIP and RHIP, respectively within the default mode network (DMN as represented by its key structures: the medial prefrontal cortex (MPFC, posterior cingulate cortex (PCC and the inferior parietal cortex of left (LIPC and right (RIPC hemispheres. Furthermore, we were interested in testing the stability of the connectivity patterns when adding or deleting regions of interest. The functional magnetic resonance imaging (fMRI data from a group of 30 healthy right-handed subjects in the resting state were collected and a connectivity analysis was performed. To model the effective connectivity, we used the spectral Dynamic Causal Modeling (DCM. Three DCM analyses were completed. Two of them modeled interaction between five nodes that included four DMN key structures in addition to either LHIP or RHIP. The last DCM analysis modeled interactions between four nodes whereby one of the main DMN structures, PCC, was excluded from the analysis. The results of all DCM analyses indicated a high level of stability in the computational method: those parts of the winning models that included the key DMN structures demonstrated causal relations known from recent research. However, we discovered new results as well. First of all, we found a pronounced asymmetry in LHIP and RHIP connections. LHIP demonstrated a high involvement of DMN activity with preponderant information outflow to all other DMN regions. Causal interactions of LHIP were bidirectional only in the case of LIPC. On the contrary, RHIP was primarily affected by inputs from LIPC, RIPC and LHIP without influencing these or other DMN key structures. For the first time, an inhibitory link was found from MPFC to LIPC, which may indicate the subjects’ effort to maintain a resting state. Functional connectivity data echoed these results, though they also showed links not reflected in the patterns of

  18. Continual Lie algebras and noncommutative counterparts of exactly solvable models

    Science.gov (United States)

    Zuevsky, A.

    2004-01-01

    Noncommutative counterparts of exactly solvable models are introduced on the basis of a generalization of Saveliev-Vershik continual Lie algebras. Examples of noncommutative Liouville and sin/h-Gordon equations are given. The simplest soliton solution to the noncommutative sine-Gordon equation is found.

  19. Two-dimensional black holes and non-commutative spaces

    International Nuclear Information System (INIS)

    Sadeghi, J.

    2008-01-01

    We study the effects of non-commutative spaces on two-dimensional black hole. The event horizon of two-dimensional black hole is obtained in non-commutative space up to second order of perturbative calculations. A lower limit for the non-commutativity parameter is also obtained. The observer in that limit in contrast to commutative case see two horizon

  20. Some remarks on K_0 of noncommutative tori

    OpenAIRE

    Chakraborty, Sayan

    2017-01-01

    Using Rieffel's construction of projective modules over higher dimensional noncommutative tori, we construct projective modules over some continuous field of C*-algebras whose fibers are noncommutative tori. Using a result of Echterhoff et al., our construction gives generators of K_0 of all noncommutative tori.

  1. Mapping spaces and automorphism groups of toric noncommutative spaces

    Science.gov (United States)

    Barnes, Gwendolyn E.; Schenkel, Alexander; Szabo, Richard J.

    2017-09-01

    We develop a sheaf theory approach to toric noncommutative geometry which allows us to formalize the concept of mapping spaces between two toric noncommutative spaces. As an application, we study the `internalized' automorphism group of a toric noncommutative space and show that its Lie algebra has an elementary description in terms of braided derivations.

  2. Quantum electrodynamics with arbitrary charge on a noncommutative space

    International Nuclear Information System (INIS)

    Zhou Wanping; Long Zhengwen; Cai Shaohong

    2009-01-01

    Using the Seiberg-Witten map, we obtain a quantum electrodynamics on a noncommutative space, which has arbitrary charge and keep the gauge invariance to at the leading order in theta. The one-loop divergence and Compton scattering are reinvestigated. The noncommutative effects are larger than those in ordinary noncommutative quantum electrodynamics. (authors)

  3. Noncommutativity and unitarity violation in gauge boson scattering

    International Nuclear Information System (INIS)

    Hewett, J. L.; Petriello, F. J.; Rizzo, T. G.

    2002-01-01

    We examine the unitarity properties of spontaneously broken noncommutative gauge theories. We find that the symmetry breaking mechanism in the noncommutative standard model of Chaichian et al. leads to an unavoidable violation of tree-level unitarity in gauge boson scattering at high energies. We then study a variety of simplified spontaneously broken noncommutative theories and isolate the source of this unitarity violation. Given the group theoretic restrictions endemic to noncommutative model building, we conclude that it is difficult to build a noncommutative standard model under the Weyl-Moyal approach that preserves unitarity

  4. Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole

    Directory of Open Access Journals (Sweden)

    G. Abbas

    2014-01-01

    Full Text Available Few years ago, Setare (2006 has investigated the Cardy-Verlinde formula of noncommutative black hole obtained by noncommutativity of coordinates. In this paper, we apply the same procedure to a noncommutative black hole obtained by the coordinate coherent approach. The Cardy-Verlinde formula is entropy formula of conformal field theory in an arbitrary dimension. It relates the entropy of conformal field theory to its total energy and Casimir energy. In this paper, we have calculated the total energy and Casimir energy of noncommutative Schwarzschild black hole and have shown that entropy of noncommutative Schwarzschild black hole horizon can be expressed in terms of Cardy-Verlinde formula.

  5. Discreteness of area in noncommutative space

    Energy Technology Data Exchange (ETDEWEB)

    Amelino-Camelia, Giovanni [Dipartimento di Fisica, Universita di Roma ' La Sapienza' and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma (Italy)], E-mail: amelino@roma1.infn.it; Gubitosi, Giulia; Mercati, Flavio [Dipartimento di Fisica, Universita di Roma ' La Sapienza' and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma (Italy)

    2009-06-08

    We introduce an area operator for the Moyal noncommutative plane. We find that the spectrum is discrete, but, contrary to the expectation formulated by other authors, not characterized by a 'minimum-area principle'. We show that an intuitive analysis of the uncertainty relations obtained from Moyal-plane noncommutativity is fully consistent with our results for the spectrum, and we argue that our area operator should be generalizable to several other noncommutative spaces. We also observe that the properties of distances and areas in the Moyal plane expose some weaknesses in the line of reasoning adopted in some of the heuristic analyses of the measurability of geometric spacetime observables in the quantum-gravity realm.

  6. Discreteness of area in noncommutative space

    International Nuclear Information System (INIS)

    Amelino-Camelia, Giovanni; Gubitosi, Giulia; Mercati, Flavio

    2009-01-01

    We introduce an area operator for the Moyal noncommutative plane. We find that the spectrum is discrete, but, contrary to the expectation formulated by other authors, not characterized by a 'minimum-area principle'. We show that an intuitive analysis of the uncertainty relations obtained from Moyal-plane noncommutativity is fully consistent with our results for the spectrum, and we argue that our area operator should be generalizable to several other noncommutative spaces. We also observe that the properties of distances and areas in the Moyal plane expose some weaknesses in the line of reasoning adopted in some of the heuristic analyses of the measurability of geometric spacetime observables in the quantum-gravity realm.

  7. Non-commutativity in polar coordinates

    Energy Technology Data Exchange (ETDEWEB)

    Edwards, James P. [Universidad Michoacana de San Nicolas de Hidalgo, Ciudad Universitaria, Instituto de Fisica y Matematicas, Morelia, Michoacan (Mexico)

    2017-05-15

    We reconsider the fundamental commutation relations for non-commutative R{sup 2} described in polar coordinates with non-commutativity parameter θ. Previous analysis found that the natural transition from Cartesian coordinates to the traditional polar system led to a representation of [r, φ] as an everywhere diverging series. In this article we compute the Borel resummation of this series, showing that it can subsequently be extended throughout parameter space and hence provide an interpretation of this commutator. Our analysis provides a complete solution for arbitrary r and θ that reproduces the earlier calculations at lowest order and benefits from being generally applicable to problems in a two-dimensional non-commutative space. We compare our results to previous literature in the (pseudo-)commuting limit, finding a surprising spatial dependence for the coordinate commutator when θ >> r{sup 2}. Finally, we raise some questions for future study in light of this progress. (orig.)

  8. Time-space noncommutativity: quantised evolutions

    International Nuclear Information System (INIS)

    Balachandran, Aiyalam P.; Govindarajan, Thupil R.; Teotonio-Sobrinho, Paulo; Martins, Andrey Gomes

    2004-01-01

    In previous work, we developed quantum physics on the Moyal plane with time-space noncommutativity, basing ourselves on the work of Doplicher et al. Here we extend it to certain noncommutative versions of the cylinder, R 3 and Rx S 3 . In all these models, only discrete time translations are possible, a result known before in the first two cases. One striking consequence of quantised time translations is that even though a time independent hamiltonian is an observable, in scattering processes, it is conserved only modulo 2π/θ, where θ is the noncommutative parameter. (In contrast, on a one-dimensional periodic lattice of lattice spacing a and length L = Na, only momentum mod 2π/L is observable (and can be conserved).) Suggestions for further study of this effect are made. Scattering theory is formulated and an approach to quantum field theory is outlined. (author)

  9. Index theory for locally compact noncommutative geometries

    CERN Document Server

    Carey, A L; Rennie, A; Sukochev, F A

    2014-01-01

    Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.

  10. Neural Correlates of Causal Power Judgments

    Directory of Open Access Journals (Sweden)

    Denise Dellarosa Cummins

    2014-12-01

    Full Text Available Causal inference is a fundamental component of cognition and perception. Probabilistic theories of causal judgment (most notably causal Bayes networks derive causal judgments using metrics that integrate contingency information. But human estimates typically diverge from these normative predictions. This is because human causal power judgments are typically strongly influenced by beliefs concerning underlying causal mechanisms, and because of the way knowledge is retrieved from human memory during the judgment process. Neuroimaging studies indicate that the brain distinguishes causal events from mere covariation, and between perceived and inferred causality. Areas involved in error prediction are also activated, implying automatic activation of possible exception cases during causal decision-making.

  11. Modelling the effect of religion on human empathy based on an adaptive temporal-causal network model.

    Science.gov (United States)

    van Ments, Laila; Roelofsma, Peter; Treur, Jan

    2018-01-01

    Religion is a central aspect of many individuals' lives around the world, and its influence on human behaviour has been extensively studied from many different perspectives. The current study integrates a number of these perspectives into one adaptive temporal-causal network model describing the mental states involved, their mutual relations, and the adaptation of some of these relations over time due to learning. By first developing a conceptual representation of a network model based on the literature, and then formalizing this model into a numerical representation, simulations can be done for almost any kind of religion and person, showing different behaviours for persons with different religious backgrounds and characters. The focus was mainly on the influence of religion on human empathy and dis-empathy, a topic very relevant today. The developed model could be valuable for many uses, involving support for a better understanding, and even prediction, of the behaviour of religious individuals. It is illustrated for a number of different scenarios based on different characteristics of the persons and of the religion.

  12. Exact multi-line soliton solutions of noncommutative KP equation

    International Nuclear Information System (INIS)

    Wang, Ning; Wadati, Miki

    2003-01-01

    A method of solving noncommutative linear algebraic equations plays a key role in the extension of the ∂-bar -dressing on the noncommutative space-time manifold. In this paper, a solution-generating method of noncommutative linear algebraic equations is proposed. By use of the proposed method, a class of multi-line soliton solutions of noncommutative KP (ncKP) equation is constructed explicitly. The method is expected to be of use for constructions of noncommutative soliton equations. The significance of the noncommutativity of coordinates is investigated. It is found that the noncommutativity of the space-time coordinate has a role to split the spatial waveform of the classical multi-line solitons and reform it to a new configuration. (author)

  13. Noncommutative gauge field theories: A no-go theorem

    International Nuclear Information System (INIS)

    Chaichian, M.; Tureanu, A.; Presnajder, P.; Sheikh-Jabbari, M.M.

    2001-06-01

    Studying the mathematical structure of the noncommutative groups in more detail, we prove a no-go theorem for the noncommutative gauge theories. According to this theorem, the closure condition of the gauge algebra implies that: 1) the local noncommutative u(n) algebra only admits the irreducible nxn matrix-representation. Hence the gauge fields, as elements of the algebra, are in nxn matrix form, while the matter fields can only be either in fundamental, adjoint or singlet states; 2) for any gauge group consisting of several simple group factors, the matter fields can transform nontrivially under at most two noncommutative group factors. In other words, the matter fields cannot carry more than two simple noncommutative gauge group charges. This no-go theorem imposes strong restrictions on the construction of the noncommutative version of the Standard Model and in resolving the standing problem of charge quantization in noncommutative QED. (author)

  14. How to model mutually exclusive events based on independent causal pathways in Bayesian network models

    OpenAIRE

    Fenton, N.; Neil, M.; Lagnado, D.; Marsh, W.; Yet, B.; Constantinou, A.

    2016-01-01

    We show that existing Bayesian network (BN) modelling techniques cannot capture the correct intuitive reasoning in the important case when a set of mutually exclusive events need to be modelled as separate nodes instead of states of a single node. A previously proposed ‘solution’, which introduces a simple constraint node that enforces mutual exclusivity, fails to preserve the prior probabilities of the events, while other proposed solutions involve major changes to the original model. We pro...

  15. Noncommutative Black Holes at the LHC

    Science.gov (United States)

    Villhauer, Elena Michelle

    2017-12-01

    Based on the latest public results, 13 TeV data from the Large Hadron Collider at CERN has not indicated any evidence of hitherto tested models of quantum black holes, semiclassical black holes, or string balls. Such models have predicted signatures of particles with high transverse momenta. Noncommutative black holes remain an untested model of TeV-scale gravity that offers the starkly different signature of particles with relatively low transverse momenta. Considerations for a search for charged noncommutative black holes using the ATLAS detector will be discussed.

  16. Noncommutative gauge theory without Lorentz violation

    International Nuclear Information System (INIS)

    Carlson, Carl E.; Carone, Christopher D.; Zobin, Nahum

    2002-01-01

    The most popular noncommutative field theories are characterized by a matrix parameter θ μν that violates Lorentz invariance. We consider the simplest algebra in which the θ parameter is promoted to an operator and Lorentz invariance is preserved. This algebra arises through the contraction of a larger one for which explicit representations are already known. We formulate a star product and construct the gauge-invariant Lagrangian for Lorentz-conserving noncommutative QED. Three-photon vertices are absent in the theory, while a four-photon coupling exists and leads to a distinctive phenomenology

  17. The boosts in the noncommutative special relativity

    International Nuclear Information System (INIS)

    Lagraa, M.

    2001-01-01

    From the quantum analogue of the Iwasawa decomposition of SL(2, C) group and the correspondence between quantum SL(2, C) and Lorentz groups we deduce the different properties of the Hopf algebra representing the boost of particles in noncommutative special relativity. The representation of the boost in the Hilbert space states is investigated and the addition rules of the velocities are established from the coaction. The q-deformed Clebsch-Gordon coefficients describing the transformed states of the evolution of particles in noncommutative special relativity are introduced and their explicit calculation are given. (author)

  18. SCENERY: a web application for (causal) network reconstruction from cytometry data

    KAUST Repository

    Papoutsoglou, Georgios

    2017-05-08

    Flow and mass cytometry technologies can probe proteins as biological markers in thousands of individual cells simultaneously, providing unprecedented opportunities for reconstructing networks of protein interactions through machine learning algorithms. The network reconstruction (NR) problem has been well-studied by the machine learning community. However, the potentials of available methods remain largely unknown to the cytometry community, mainly due to their intrinsic complexity and the lack of comprehensive, powerful and easy-to-use NR software implementations specific for cytometry data. To bridge this gap, we present Single CEll NEtwork Reconstruction sYstem (SCENERY), a web server featuring several standard and advanced cytometry data analysis methods coupled with NR algorithms in a user-friendly, on-line environment. In SCENERY, users may upload their data and set their own study design. The server offers several data analysis options categorized into three classes of methods: data (pre)processing, statistical analysis and NR. The server also provides interactive visualization and download of results as ready-to-publish images or multimedia reports. Its core is modular and based on the widely-used and robust R platform allowing power users to extend its functionalities by submitting their own NR methods. SCENERY is available at scenery.csd.uoc.gr or http://mensxmachina.org/en/software/.

  19. Synaptic plasticity, memory and the hippocampus: a neural network approach to causality.

    Science.gov (United States)

    Neves, Guilherme; Cooke, Sam F; Bliss, Tim V P

    2008-01-01

    Two facts about the hippocampus have been common currency among neuroscientists for several decades. First, lesions of the hippocampus in humans prevent the acquisition of new episodic memories; second, activity-dependent synaptic plasticity is a prominent feature of hippocampal synapses. Given this background, the hypothesis that hippocampus-dependent memory is mediated, at least in part, by hippocampal synaptic plasticity has seemed as cogent in theory as it has been difficult to prove in practice. Here we argue that the recent development of transgenic molecular devices will encourage a shift from mechanistic investigations of synaptic plasticity in single neurons towards an analysis of how networks of neurons encode and represent memory, and we suggest ways in which this might be achieved. In the process, the hypothesis that synaptic plasticity is necessary and sufficient for information storage in the brain may finally be validated.

  20. Drug-Induced Liver Injury Network Causality Assessment: Criteria and Experience in the United States

    Directory of Open Access Journals (Sweden)

    Paul H. Hayashi

    2016-02-01

    Full Text Available Hepatotoxicity due to drugs, herbal or dietary supplements remains largely a clinical diagnosis based on meticulous history taking and exclusion of other causes of liver injury. In 2004, the U.S. Drug-Induced Liver Injury Network (DILIN was created under the auspices of the U.S. National Institute of Diabetes and Digestive and Kidney Diseases with the aims of establishing a large registry of cases for clinical, epidemiological and mechanistic study. From inception, the DILIN has used an expert opinion process that incorporates consensus amongst three different DILIN hepatologists assigned to each case. It is the most well-established, well-described and vigorous expert opinion process for DILI to date, and yet it is an imperfect standard. This review will discuss the DILIN expert opinion process, its strengths and weaknesses, psychometric performance and future.

  1. Causal functional contributions and interactions in the attention network of the brain: an objective multi-perturbation analysis.

    Science.gov (United States)

    Zavaglia, Melissa; Hilgetag, Claus C

    2016-06-01

    prediction of unknown performances. The results suggest that the MSA approach is sensitive to categorical, but insensitive to gradual changes in the input data. Finally, we created a basic network model that was based on the known anatomical interactions among cortical-tectal regions and reproduced the experimentally observed behavior in visual orienting. We discuss the structural organization of the network model relative to the causal modulations identified by MSA, to aid a mechanistic understanding of the attention network of the brain.

  2. Moving vortices in noncommutative gauge theory

    International Nuclear Information System (INIS)

    Horvathy, P.A.; Stichel, P.C.

    2004-01-01

    Exact time-dependent solutions of nonrelativistic noncommutative Chern-Simons gauge theory are presented in closed analytic form. They are different from (indeed orthogonal to) those discussed recently by Hadasz, Lindstroem, Rocek and von Unge. Unlike theirs, our solutions can move with an arbitrary constant velocity, and can be obtained from the previously known static solutions by the recently found 'exotic' boost symmetry

  3. Holographic complexity and noncommutative gauge theory

    Science.gov (United States)

    Couch, Josiah; Eccles, Stefan; Fischler, Willy; Xiao, Ming-Lei

    2018-03-01

    We study the holographic complexity of noncommutative field theories. The four-dimensional N=4 noncommutative super Yang-Mills theory with Moyal algebra along two of the spatial directions has a well known holographic dual as a type IIB supergravity theory with a stack of D3 branes and non-trivial NS-NS B fields. We start from this example and find that the late time holographic complexity growth rate, based on the "complexity equals action" conjecture, experiences an enhancement when the non-commutativity is turned on. This enhancement saturates a new limit which is exactly 1/4 larger than the commutative value. We then attempt to give a quantum mechanics explanation of the enhancement. Finite time behavior of the complexity growth rate is also studied. Inspired by the non-trivial result, we move on to more general setup in string theory where we have a stack of D p branes and also turn on the B field. Multiple noncommutative directions are considered in higher p cases.

  4. Noncommutative phase spaces on Aristotle group

    Directory of Open Access Journals (Sweden)

    Ancille Ngendakumana

    2012-03-01

    Full Text Available We realize noncommutative phase spaces as coadjoint orbits of extensions of the Aristotle group in a two dimensional space. Through these constructions the momenta of the phase spaces do not commute due to the presence of a naturally introduced magnetic eld. These cases correspond to the minimal coupling of the momentum with a magnetic potential.

  5. Group field theory with noncommutative metric variables.

    Science.gov (United States)

    Baratin, Aristide; Oriti, Daniele

    2010-11-26

    We introduce a dual formulation of group field theories as a type of noncommutative field theories, making their simplicial geometry manifest. For Ooguri-type models, the Feynman amplitudes are simplicial path integrals for BF theories. We give a new definition of the Barrett-Crane model for gravity by imposing the simplicity constraints directly at the level of the group field theory action.

  6. On total noncommutativity in quantum mechanics

    Science.gov (United States)

    Lahti, Pekka J.; Ylinen, Kari

    1987-11-01

    It is shown within the Hilbert space formulation of quantum mechanics that the total noncommutativity of any two physical quantities is necessary for their satisfying the uncertainty relation or for their being complementary. The importance of these results is illustrated with the canonically conjugate position and momentum of a free particle and of a particle closed in a box.

  7. Finite quantum physics and noncommutative geometry

    International Nuclear Information System (INIS)

    Balachandran, A.P.; Ercolessi, E.; Landi, G.; Teotonio-Sobrinho, P.; Lizzi, F.; Sparano, G.

    1994-04-01

    Conventional discrete approximations of a manifold do not preserve its nontrivial topological features. In this article we describe an approximation scheme due to Sorkin which reproduces physically important aspects of manifold topology with striking fidelity. The approximating topological spaces in this scheme are partially ordered sets (posets). Now, in ordinary quantum physics on a manifold M, continuous probability densities generate the commutative C * -algebra C(M) of continuous functions on M. It has a fundamental physical significance, containing the information to reconstruct the topology of M, and serving to specify the domains of observables like the Hamiltonian. For a poset, the role of this algebra is assumed by a noncommutative C * -algebra A. As noncommutative geometries are based on noncommutative C * -algebra, we therefore have a remarkable connection between finite approximations to quantum physics and noncommutative geometries. Varies methods for doing quantum physics using A are explored. Particular attention is paid to developing numerically viable approximation schemes which at the same time preserve important topological features of continuum physics. (author). 21 refs, 13 figs

  8. Non-commutative arithmetic circuits with division

    Czech Academy of Sciences Publication Activity Database

    Hrubeš, Pavel; Wigderson, A.

    2015-01-01

    Roč. 11, Article 14 (2015), s. 357-393 ISSN 1557-2862 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : arithmetic circuits * non-commutative rational function * skew field Subject RIV: BA - General Mathematics http://theoryofcomputing.org/articles/v011a014/

  9. Non-commutative geometry and supersymmetry 2

    International Nuclear Information System (INIS)

    Hussain, F.; Thompson, G.

    1991-05-01

    Following the general construction of supersymmetric models, the model based on the idea of non-commutative geometry is formulated as a Yang-Mills theory of the graded Lie algebra U(2/1) over a graded space-time manifold. 4 refs

  10. Geometry of time-spaces non-commutative algebraic geometry, applied to quantum theory

    CERN Document Server

    Landau, Olav Arnfinn

    2011-01-01

    This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory o

  11. Causal universe

    CERN Document Server

    Ellis, George FR; Pabjan, Tadeusz

    2013-01-01

    Written by philosophers, cosmologists, and physicists, this collection of essays deals with causality, which is a core issue for both science and philosophy. Readers will learn about different types of causality in complex systems and about new perspectives on this issue based on physical and cosmological considerations. In addition, the book includes essays pertaining to the problem of causality in ancient Greek philosophy, and to the problem of God's relation to the causal structures of nature viewed in the light of contemporary physics and cosmology.

  12. Causal and causally separable processes

    Science.gov (United States)

    Oreshkov, Ognyan; Giarmatzi, Christina

    2016-09-01

    The idea that events are equipped with a partial causal order is central to our understanding of physics in the tested regimes: given two pointlike events A and B, either A is in the causal past of B, B is in the causal past of A, or A and B are space-like separated. Operationally, the meaning of these order relations corresponds to constraints on the possible correlations between experiments performed in the vicinities of the respective events: if A is in the causal past of B, an experimenter at A could signal to an experimenter at B but not the other way around, while if A and B are space-like separated, no signaling is possible in either direction. In the context of a concrete physical theory, the correlations compatible with a given causal configuration may obey further constraints. For instance, space-like correlations in quantum mechanics arise from local measurements on joint quantum states, while time-like correlations are established via quantum channels. Similarly to other variables, however, the causal order of a set of events could be random, and little is understood about the constraints that causality implies in this case. A main difficulty concerns the fact that the order of events can now generally depend on the operations performed at the locations of these events, since, for instance, an operation at A could influence the order in which B and C occur in A’s future. So far, no formal theory of causality compatible with such dynamical causal order has been developed. Apart from being of fundamental interest in the context of inferring causal relations, such a theory is imperative for understanding recent suggestions that the causal order of events in quantum mechanics can be indefinite. Here, we develop such a theory in the general multipartite case. Starting from a background-independent definition of causality, we derive an iteratively formulated canonical decomposition of multipartite causal correlations. For a fixed number of settings and

  13. Causal and causally separable processes

    International Nuclear Information System (INIS)

    Oreshkov, Ognyan; Giarmatzi, Christina

    2016-01-01

    The idea that events are equipped with a partial causal order is central to our understanding of physics in the tested regimes: given two pointlike events A and B , either A is in the causal past of B , B is in the causal past of A , or A and B are space-like separated. Operationally, the meaning of these order relations corresponds to constraints on the possible correlations between experiments performed in the vicinities of the respective events: if A is in the causal past of B , an experimenter at A could signal to an experimenter at B but not the other way around, while if A and B are space-like separated, no signaling is possible in either direction. In the context of a concrete physical theory, the correlations compatible with a given causal configuration may obey further constraints. For instance, space-like correlations in quantum mechanics arise from local measurements on joint quantum states, while time-like correlations are established via quantum channels. Similarly to other variables, however, the causal order of a set of events could be random, and little is understood about the constraints that causality implies in this case. A main difficulty concerns the fact that the order of events can now generally depend on the operations performed at the locations of these events, since, for instance, an operation at A could influence the order in which B and C occur in A ’s future. So far, no formal theory of causality compatible with such dynamical causal order has been developed. Apart from being of fundamental interest in the context of inferring causal relations, such a theory is imperative for understanding recent suggestions that the causal order of events in quantum mechanics can be indefinite. Here, we develop such a theory in the general multipartite case. Starting from a background-independent definition of causality, we derive an iteratively formulated canonical decomposition of multipartite causal correlations. For a fixed number of settings and

  14. Construction of non-Abelian gauge theories on noncommutative spaces

    International Nuclear Information System (INIS)

    Jurco, B.; Schupp, P.; Moeller, L.; Wess, J.; Max-Planck-Inst. fuer Physik, Muenchen; Humboldt-Univ., Berlin; Schraml, S.; Humboldt-Univ., Berlin

    2001-01-01

    We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. (orig.)

  15. Construction of non-Abelian gauge theories on noncommutative spaces

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, B.; Schupp, P. [Sektion Physik, Muenchen Univ. (Germany); Moeller, L.; Wess, J. [Sektion Physik, Muenchen Univ. (Germany); Max-Planck-Inst. fuer Physik, Muenchen (Germany); Humboldt-Univ., Berlin (Germany). Inst. fuer Physik; Schraml, S. [Sektion Physik, Muenchen Univ. (Germany)

    2001-06-01

    We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. (orig.)

  16. Recursive relations for processes with n photons of noncommutative QED

    International Nuclear Information System (INIS)

    Jafari, Abolfazl

    2007-01-01

    Recursion relations are derived in the sense of Berends-Giele for the multi-photon processes of noncommutative QED. The relations concern purely photonic processes as well as the processes with two fermions involved, both for arbitrary number of photons at tree level. It is shown that despite of the dependence of noncommutative vertices on momentum, in contrast to momentum-independent color factors of QCD, the recursion relation method can be employed for multi-photon processes of noncommutative QED

  17. Noncommutative gravity and quantum field theory on noncummutative curved spacetimes

    Energy Technology Data Exchange (ETDEWEB)

    Schenkel, Alexander

    2011-10-24

    The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the

  18. Deformation quantization of noncommutative quantum mechanics and dissipation

    Energy Technology Data Exchange (ETDEWEB)

    Bastos, C [Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisbon (Portugal); Bertolami, O [Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisbon (Portugal); Dias, N C [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Avenida Campo Grande 376, 1749-024 Lisbon (Portugal); Prata, J N [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Avenida Campo Grande 376, 1749-024 Lisbon (Portugal)

    2007-05-15

    We review the main features of the Weyl-Wigner formulation of noncommutative quantum mechanics. In particular, we present a *-product and a Moyal bracket suitable for this theory as well as the concept of noncommutative Wigner function. The properties of these quasi-distributions are discussed as well as their relation to the sets of ordinary Wigner functions and positive Liouville probability densities. Based on these notions we propose criteria for assessing whether a commutative regime has emerged in the realm of noncommutative quantum mechanics. To induce this noncommutative-commutative transition, we couple a particle to an external bath of oscillators. The master equation for the Brownian particle is deduced.

  19. Classical mechanics in non-commutative phase space

    International Nuclear Information System (INIS)

    Wei Gaofeng; Long Chaoyun; Long Zhengwen; Qin Shuijie

    2008-01-01

    In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space. The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity. First, new Poisson brackets have been defined in non-commutative phase space. They contain corrections due to the non-commutativity of coordinates and momenta. On the basis of this new Poisson brackets, a new modified second law of Newton has been obtained. For two cases, the free particle and the harmonic oscillator, the equations of motion are derived on basis of the modified second law of Newton and the linear transformation (Phys. Rev. D, 2005, 72: 025010). The consistency between both methods is demonstrated. It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space, but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative. (authors)

  20. Cancellation of soft and collinear divergences in noncommutative QED

    International Nuclear Information System (INIS)

    Mirza, B.; Zarei, M.

    2006-01-01

    In this paper, we investigate the behavior of noncommutative IR divergences and will also discuss their cancellation in the physical cross sections. The commutative IR (soft) divergences existing in the nonplanar diagrams will be examined in order to prove an all-order cancellation of these divergences using the Weinberg's method. In noncommutative QED, collinear divergences due to triple photon splitting vertex, were encountered, which are shown to be canceled out by the noncommutative version of KLN theorem. This guarantees that there is no mixing between the Collinear, soft divergences and noncommutative IR divergences

  1. Noncommutative gravity and quantum field theory on noncummutative curved spacetimes

    International Nuclear Information System (INIS)

    Schenkel, Alexander

    2011-01-01

    The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the noncommutative

  2. Discrete symmetries (C,P,T) in noncommutative field theories

    International Nuclear Information System (INIS)

    Sheikh-Jabbari, M.M.

    2000-01-01

    In this paper we study the invariance of the noncommutative gauge theories tinder C, P and T transformations. For the noncommutative space (when only the spatial part of θ is non-zero) we show that NCQED is Parity invariant. In addition, we show that under charge conjugation the theory on noncommutative R θ 4 is transformed to the theory on R -θ 4 , so NCQED is a CP violating theory. The theory remains invariant under time reversal if, together with proper changes in fields, we also change θ by -θ. Hence altogether NCQED is CPT invariant. Moreover we show that the CPT invariance holds for general noncommutative space-time. (author)

  3. Non-invasive clinical parameters for the prediction of urodynamic bladder outlet obstruction: analysis using causal Bayesian networks.

    Directory of Open Access Journals (Sweden)

    Myong Kim

    Full Text Available To identify non-invasive clinical parameters to predict urodynamic bladder outlet obstruction (BOO in patients with benign prostatic hyperplasia (BPH using causal Bayesian networks (CBN.From October 2004 to August 2013, 1,381 eligible BPH patients with complete data were selected for analysis. The following clinical variables were considered: age, total prostate volume (TPV, transition zone volume (TZV, prostate specific antigen (PSA, maximum flow rate (Qmax, and post-void residual volume (PVR on uroflowmetry, and International Prostate Symptom Score (IPSS. Among these variables, the independent predictors of BOO were selected using the CBN model. The predictive performance of the CBN model using the selected variables was verified through a logistic regression (LR model with the same dataset.Mean age, TPV, and IPSS were 6.2 (±7.3, SD years, 48.5 (±25.9 ml, and 17.9 (±7.9, respectively. The mean BOO index was 35.1 (±25.2 and 477 patients (34.5% had urodynamic BOO (BOO index ≥40. By using the CBN model, we identified TPV, Qmax, and PVR as independent predictors of BOO. With these three variables, the BOO prediction accuracy was 73.5%. The LR model showed a similar accuracy (77.0%. However, the area under the receiver operating characteristic curve of the CBN model was statistically smaller than that of the LR model (0.772 vs. 0.798, p = 0.020.Our study demonstrated that TPV, Qmax, and PVR are independent predictors of urodynamic BOO.

  4. Prime divisors and noncommutative valuation theory

    CERN Document Server

    Marubayashi, Hidetoshi

    2012-01-01

    Classical valuation theory has applications in number theory and class field theory as well as in algebraic geometry, e.g. in a divisor theory for curves.  But the noncommutative equivalent is mainly applied to finite dimensional skewfields.  Recently however, new types of algebras have become popular in modern algebra; Weyl algebras, deformed and quantized algebras, quantum groups and Hopf algebras, etc. The advantage of valuation theory in the commutative case is that it allows effective calculations, bringing the arithmetical properties of the ground field into the picture.  This arithmetical nature is also present in the theory of maximal orders in central simple algebras.  Firstly, we aim at uniting maximal orders, valuation rings, Dubrovin valuations, etc. in a common theory, the theory of primes of algebras.  Secondly, we establish possible applications of the noncommutative arithmetics to interesting classes of algebras, including the extension of central valuations to nice classes of quantized a...

  5. Worldline approach to noncommutative field theory

    International Nuclear Information System (INIS)

    Bonezzi, R; Corradini, O; Viñas, S A Franchino; Pisani, P A G

    2012-01-01

    The study of the heat-trace expansion in non-commutative field theory has shown the existence of Moyal non-local Seeley–DeWitt coefficients which are related to the UV/IR mixing and manifest, in some cases, the non-renormalizability of the theory. We show that these models can be studied in a worldline approach implemented in phase space and arrive at a master formula for the n-point contribution to the heat-trace expansion. This formulation could be useful in understanding some open problems in this area, as the heat-trace expansion for the non-commutative torus or the introduction of renormalizing terms in the action, as well as for generalizations to other non-local operators. (paper)

  6. Strings from position-dependent noncommutativity

    International Nuclear Information System (INIS)

    Fring, Andreas; Gouba, Laure; Scholtz, Frederik G

    2010-01-01

    We introduce a new set of noncommutative spacetime commutation relations in two space dimensions. The space-space commutation relations are deformations of the standard flat noncommutative spacetime relations taken here to have position-dependent structure constants. Some of the new variables are non-Hermitian in the most natural choice. We construct their Hermitian counterparts by means of a Dyson map, which also serves to introduce a new metric operator. We propose PT-like symmetries, i.e. antilinear involutory maps, respected by these deformations. We compute minimal lengths and momenta arising in this space from generalized versions of Heisenberg's uncertainty relations and find that any object in this two-dimensional space is string like, i.e. having a fundamental length in one direction beyond which a resolution is impossible. Subsequently, we formulate and partly solve some simple models in these new variables, the free particle, its PT-symmetric deformations and the harmonic oscillator.

  7. Exact BPS bound for noncommutative baby Skyrmions

    International Nuclear Information System (INIS)

    Domrin, Andrei; Lechtenfeld, Olaf; Linares, Román; Maceda, Marco

    2013-01-01

    The noncommutative baby Skyrme model is a Moyal deformation of the two-dimensional sigma model plus a Skyrme term, with a group-valued or Grassmannian target. Exact abelian solitonic solutions have been identified analytically in this model, with a singular commutative limit. Inside any given Grassmannian, we establish a BPS bound for the energy functional, which is saturated by these baby Skyrmions. This asserts their stability for unit charge, as we also test in second-order perturbation theory

  8. Noncommutative Phase Spaces by Coadjoint Orbits Method

    Directory of Open Access Journals (Sweden)

    Ancille Ngendakumana

    2011-12-01

    Full Text Available We introduce noncommutative phase spaces by minimal couplings (usual one, dual one and their mixing. We then realize some of them as coadjoint orbits of the anisotropic Newton-Hooke groups in two- and three-dimensional spaces. Through these constructions the positions and the momenta of the phase spaces do not commute due to the presence of a magnetic field and a dual magnetic field.

  9. Gravity and the structure of noncommutative algebras

    International Nuclear Information System (INIS)

    Buric, Maja; Madore, John; Grammatikopoulos, Theodoros; Zoupanos, George

    2006-01-01

    A gravitational field can be defined in terms of a moving frame, which when made noncommutative yields a preferred basis for a differential calculus. It is conjectured that to a linear perturbation of the commutation relations which define the algebra there corresponds a linear perturbation of the gravitational field. This is shown to be true in the case of a perturbation of Minkowski space-time

  10. Cosmological production of noncommutative black holes

    International Nuclear Information System (INIS)

    Mann, Robert B.; Nicolini, Piero

    2011-01-01

    We investigate the pair creation of noncommutative black holes in a background with a positive cosmological constant. As a first step we derive the noncommutative geometry inspired Schwarzschild-de Sitter solution. By varying the mass and the cosmological constant parameters, we find several spacetimes compatible with the new solution: positive-mass spacetimes admit one cosmological horizon and two, one, or no black hole horizons, while negative-mass spacetimes have just a cosmological horizon. These new black holes share the properties of the corresponding asymptotically flat solutions, including the nonsingular core and thermodynamic stability in the final phase of the evaporation. As a second step we determine the action which generates the matter sector of gravitational field equations and we construct instantons describing the pair production of black holes and the other admissible topologies. As a result we find that for current values of the cosmological constant the de Sitter background is quantum mechanically stable according to experience. However, positive-mass noncommutative black holes and solitons would have plentifully been produced during inflationary times for Planckian values of the cosmological constant. As a special result we find that, in these early epochs of the Universe, Planck size black holes production would have been largely disfavored. We also find a potential instability for production of negative-mass solitons.

  11. Dynamics of Strings in Noncommutative Gauge Theory

    International Nuclear Information System (INIS)

    Gross, David J.; Nekrasov, Nikia A.

    2000-01-01

    We continue our study of solitons in noncommutative gauge theories and present an extremely simple BPS solution of N=4 U(1) noncommutative gauge theory in 4 dimensions, which describes N infinite D1 strings that pierce a D3 brane at various points, in the presence of a background B-field in the Seiberg-Witten limit. We call this solution the N-fluxon. For N=1 we calculate the complete spectrum of small fluctuations about the fluxon and find three kinds of modes: the fluctuations of the superstring in 10 dimensions arising from fundamental strings attached to the D1 strings, the ordinary particles of the gauge theory in 4 dimensions and a set of states with discrete spectrum, localized at the intersection point - corresponding to fundamental strings stretched between the D1 string and the D3 brane. We discuss the fluctuations about the N-fluxon as well and derive explicit expressions for the amplitudes of interactions between these various modes. We show that translations in noncommutative gauge theories are equivalent to gauge transformations (plus a constant shift of the gauge field) and discuss the implications for the translational zeromodes of our solitons. We also find the dyonic versions of N-fluxon, as well as of our previous string-monopole solution. (author)

  12. Probing noncommutative theories with quantum optical experiments

    Directory of Open Access Journals (Sweden)

    Sanjib Dey

    2017-11-01

    Full Text Available One of the major difficulties of modern science underlies at the unification of general relativity and quantum mechanics. Different approaches towards such theory have been proposed. Noncommutative theories serve as the root of almost all such approaches. However, the identification of the appropriate passage to quantum gravity is suffering from the inadequacy of experimental techniques. It is beyond our ability to test the effects of quantum gravity thorough the available scattering experiments, as it is unattainable to probe such high energy scale at which the effects of quantum gravity appear. Here we propose an elegant alternative scheme to test such theories by detecting the deformations emerging from the noncommutative structures. Our protocol relies on the novelty of an opto-mechanical experimental setup where the information of the noncommutative oscillator is exchanged via the interaction with an optical pulse inside an optical cavity. We also demonstrate that our proposal is within the reach of current technology and, thus, it could uncover a feasible route towards the realization of quantum gravitational phenomena thorough a simple table-top experiment.

  13. Noncommutative quantum field theory: attempts on renormalization

    International Nuclear Information System (INIS)

    Popp, L.

    2002-05-01

    Quantum field theory is the art of dealing with problems at small distances or, equivalently, large momenta. Although there are different approaches (string theory, for example), it is generally accepted that these principles cannot be extrapolated to arbitrarily small distances as can be shown by applying simple, heuristic arguments. Therefore, the concept of space-time as a differential manifold has to be replaced by something else at such scales, the road we have chosen to follow is noncommutative geometry. We start from the basic relation [ x μ , x ν ] = i θ { μν}, where θ is a (usually) constant, antisymmetric matrix. This relation amounts to a noncommutativity of position measurements, or, put differently, the points are somehow 'smeared' out, which should have a positive effect on field theory since infinities arise from point-like interactions. However, it was shown that the effects of the commutation relation (leading to the so-called Moyal product) do not necessarily cure the divergences but introduce a new kind of problem: whereas UV-divergent integrals are rendered finite by phase factors (that arise as a consequence of the Moyal product), this same kind of 'regularization' introduces IR-divergences which led to the name 'UV/IR-mixing' for this problem. In order to overcome this peculiarity, one expands the action in θ which is immediate for the phase factors but requires the so-called Seiberg-Witten map for the fields. In this thesis, we emphasize the derivation of the Seiberg-Witten map by using noncommutative Lorentz symmetries, which is more general than the original derivation. After that, we concentrate on a treatment of θ-expanded theories and their renormalization, where it can be shown that the photon self-energy of noncommutative Maxwell theory can be renormalized to all orders in hbar and θ when the freedom in the Seiberg-Witten map (there are ambiguities in the map) is exploited. Although this is very promising, it cannot be

  14. On tea, donuts and non-commutative geometry

    Directory of Open Access Journals (Sweden)

    Igor V. Nikolaev

    2018-03-01

    Full Text Available As many will agree, it feels good to complement a cup of tea by a donut or two. This sweet relationship is also a guiding principle of non-commutative geometry known as Serre Theorem. We explain the algebra behind this theorem and prove that elliptic curves are complementary to the so-called non-commutative tori.

  15. Black-body radiation of noncommutative gauge fields

    International Nuclear Information System (INIS)

    Fatollahi, Amir H.; Hajirahimi, Maryam

    2006-01-01

    The black-body radiation is considered in a theory with noncommutative electRomegnetic fields; that is noncommutativity is introduced in field space, rather than in real space. A direct implication of the result on cosmic microwave background map is argued

  16. Hydrogen atom spectrum and the Lamb shift in noncommutative QED

    International Nuclear Information System (INIS)

    Chaichian, M. . Helsinki Institute of Physics, Helsinki; Tureanu, A. . Helsinki Institute of Physics, Helsinki; FI)

    2000-10-01

    We have calculated the energy levels of the hydrogen atom and as well the Lamb shift within the noncommutative quantum electrodynamics theory. The results show deviations from the usual QED both on the classical and on the quantum levels. On both levels, the deviations depend on the parameter of space/space noncommutativity. (author)

  17. Linearization of non-commuting operators in the partition function

    International Nuclear Information System (INIS)

    Ahmed, M.

    1983-06-01

    A generalization of the Stratonovich-Hubbard scheme for evaluating the grand canonical partition function is given. The scheme involves linearization of products of non-commuting operators using the functional integral method. The non-commutivity of the operators leads to an additional term which can be absorbed in the single-particle Hamiltonian. (author)

  18. Noncommutative conformally coupled scalar field cosmology and its commutative counterpart

    International Nuclear Information System (INIS)

    Barbosa, G.D.

    2005-01-01

    We study the implications of a noncommutative geometry of the minisuperspace variables for the Friedmann-Robertson-Walker universe with a conformally coupled scalar field. The investigation is carried out by means of a comparative study of the universe evolution in four different scenarios: classical commutative, classical noncommutative, quantum commutative, and quantum noncommutative, the last two employing the Bohmian formalism of quantum trajectories. The role of noncommutativity is discussed by drawing a parallel between its realizations in two possible frameworks for physical interpretation: the NC frame, where it is manifest in the universe degrees of freedom, and in the C frame, where it is manifest through θ-dependent terms in the Hamiltonian. As a result of our comparative analysis, we find that noncommutative geometry can remove singularities in the classical context for sufficiently large values of θ. Moreover, under special conditions, the classical noncommutative model can admit bouncing solutions characteristic of the commutative quantum Friedmann-Robertson-Walker universe. In the quantum context, we find nonsingular universe solutions containing bounces or being periodic in the quantum commutative model. When noncommutativity effects are turned on in the quantum scenario, they can introduce significant modifications that change the singular behavior of the universe solutions or that render them dynamical whenever they are static in the commutative case. The effects of noncommutativity are completely specified only when one of the frames for its realization is adopted as the physical one. Nonsingular solutions in the NC frame can be mapped into singular ones in the C frame

  19. Epidemiological causality.

    Science.gov (United States)

    Morabia, Alfredo

    2005-01-01

    Epidemiological methods, which combine population thinking and group comparisons, can primarily identify causes of disease in populations. There is therefore a tension between our intuitive notion of a cause, which we want to be deterministic and invariant at the individual level, and the epidemiological notion of causes, which are invariant only at the population level. Epidemiologists have given heretofore a pragmatic solution to this tension. Causal inference in epidemiology consists in checking the logical coherence of a causality statement and determining whether what has been found grossly contradicts what we think we already know: how strong is the association? Is there a dose-response relationship? Does the cause precede the effect? Is the effect biologically plausible? Etc. This approach to causal inference can be traced back to the English philosophers David Hume and John Stuart Mill. On the other hand, the mode of establishing causality, devised by Jakob Henle and Robert Koch, which has been fruitful in bacteriology, requires that in every instance the effect invariably follows the cause (e.g., inoculation of Koch bacillus and tuberculosis). This is incompatible with epidemiological causality which has to deal with probabilistic effects (e.g., smoking and lung cancer), and is therefore invariant only for the population.

  20. Causal inference in econometrics

    CERN Document Server

    Kreinovich, Vladik; Sriboonchitta, Songsak

    2016-01-01

    This book is devoted to the analysis of causal inference which is one of the most difficult tasks in data analysis: when two phenomena are observed to be related, it is often difficult to decide whether one of them causally influences the other one, or whether these two phenomena have a common cause. This analysis is the main focus of this volume. To get a good understanding of the causal inference, it is important to have models of economic phenomena which are as accurate as possible. Because of this need, this volume also contains papers that use non-traditional economic models, such as fuzzy models and models obtained by using neural networks and data mining techniques. It also contains papers that apply different econometric models to analyze real-life economic dependencies.

  1. A noncommutative convexity in C*-bimodules

    Directory of Open Access Journals (Sweden)

    Mohsen Kian

    2017-02-01

    Full Text Available Let A and B be C*-algebras. We consider a noncommutative convexity in Hilbert A-B-bimodules, called A-B-convexity, as a generalization of C*-convexity in C*-algebras. We show that if X is a Hilbert A-B-bimodule, then Mn(X is a Hilbert Mn(A-Mn(B-bimodule and apply it to show that the closed unit ball of every Hilbert A-B-bimodule is A-B-convex. Some properties of this kind of convexity and various examples have been given.

  2. Remarks on twisted noncommutative quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

    Zahn, J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2006-04-15

    We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation relations in this setting and show that the twisted structure is so rigid that it is hard to derive any predictions, unless one gives up general principles of quantum theory. It is also shown that the twisted structure is not responsible for the presence or absence of UV/IR-mixing, as claimed in the literature. (Orig.)

  3. S-duality and noncommutative gauge theory

    International Nuclear Information System (INIS)

    Gopakumar, R.; Maldacena, J.; Minwalla, S.; Strominger, A.

    2000-01-01

    It is conjectured that strongly coupled, spatially noncommutative CN=4 Yang-Mills theory has a dual description as a weakly coupled open string theory in a near critical electric field, and that this dual theory is fully decoupled from closed strings. Evidence for this conjecture is given by the absence of physical closed string poles in the non-planar one-loop open string diagram. The open string theory can be viewed as living in a geometry in which space and time coordinates do not commute. (author)

  4. Non-commutative tools for topological insulators

    International Nuclear Information System (INIS)

    Prodan, Emil

    2010-01-01

    This paper reviews several analytic tools for the field of topological insulators, developed with the aid of non-commutative calculus and geometry. The set of tools includes bulk topological invariants defined directly in the thermodynamic limit and in the presence of disorder, whose robustness is shown to have nontrivial physical consequences for the bulk states. The set of tools also includes a general relation between the current of an observable and its edge index, a relation that can be used to investigate the robustness of the edge states against disorder. The paper focuses on the motivations behind creating such tools and on how to use them.

  5. Introduction to Dubois-Violette's non-commutative differential geometry

    International Nuclear Information System (INIS)

    Djemai, A.E.F.

    1994-07-01

    In this work, one presents a detailed review of Dubois-Violette et al. approach to non-commutative differential calculus. The non-commutative differential geometry of matrix algebras and the non-commutative Poisson structures are treated in some details. We also present the analog of the Maxwell's theory and the new models of Yang-Mills-Higgs theories that can be constructed in this framework. In particular, some simple models are compared with the standard model. Finally, we discuss some perspectives and open questions. (author). 32 refs

  6. Non-Commutative Mechanics in Mathematical & in Condensed Matter Physics

    Directory of Open Access Journals (Sweden)

    Peter A. Horváthy

    2006-12-01

    Full Text Available Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table 1. Souriau's construction applied to the two-parameter central extension of the planar Galilei group leads to the ''exotic'' particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical model that has been used to explain the anomalous/spin/optical Hall effects. The non-commutative parameter is momentum-dependent in this case, and can take the form of a monopole in momentum space.

  7. Computational commutative and non-commutative algebraic geometry

    CERN Document Server

    Cojocaru, S; Ufnarovski, V

    2005-01-01

    This publication gives a good insight in the interplay between commutative and non-commutative algebraic geometry. The theoretical and computational aspects are the central theme in this study. The topic is looked at from different perspectives in over 20 lecture reports. It emphasizes the current trends in commutative and non-commutative algebraic geometry and algebra. The contributors to this publication present the most recent and state-of-the-art progresses which reflect the topic discussed in this publication. Both researchers and graduate students will find this book a good source of information on commutative and non-commutative algebraic geometry.

  8. The application of *-products to noncommutative geometry and gauge theory

    International Nuclear Information System (INIS)

    Sykora, A.

    2004-06-01

    Due to the singularities arising in quantum field theory and the difficulties in quantizing gravity it is often believed that the description of spacetime by a smooth manifold should be given up at small length scales or high energies. In this work we will replace spacetime by noncommutative structures arising within the framework of deformation quantization. The ordinary product between functions will be replaced by a *-product, an associative product for the space of functions on a manifold. We develop a formalism to realize algebras defined by relations on function spaces. For this purpose we construct the Weyl-ordered *-product and present a method how to calculate *-products with the help of commuting vector fields. Concepts developed in noncommutative differential geometry will be applied to this type of algebras and we construct actions for noncommutative field theories. In the classical limit these noncommutative theories become field theories on manifolds with nonvanishing curvature. It becomes clear that the application of *-products is very fruitful to the solution of noncommutative problems. In the semiclassical limit every *-product is related to a Poisson structure, every derivation of the algebra to a vector field on the manifold. Since in this limit many problems are reduced to a couple of differential equations the *-product representation makes it possible to construct noncommutative spaces corresponding to interesting Riemannian manifolds. Derivations of *-products makes it further possible to extend noncommutative gauge theory in the Seiberg-Witten formalism with covariant derivatives. The resulting noncommutative gauge fields may be interpreted as one forms of a generalization of the exterior algebra of a manifold. For the Formality *-product we prove the existence of the abelian Seiberg-Witten map for derivations of these *-products. We calculate the enveloping algebra valued non abelian Seiberg-Witten map pertubatively up to second order for

  9. What is the nature of causality in the brain? - Inherently probabilistic. Comment on "Foundational perspectives on causality in large-scale brain networks" by M. Mannino and S.L. Bressler

    Science.gov (United States)

    Dhamala, Mukesh

    2015-12-01

    Understanding cause-and-effect (causal) relations from observations concerns all sciences including neuroscience. Appropriately defining causality and its nature, though, has been a topic of active discussion for philosophers and scientists for centuries. Although brain research, particularly functional neuroimaging research, is now moving rapidly beyond identification of brain regional activations towards uncovering causal relations between regions, the nature of causality has not be been thoroughly described and resolved. In the current review article [1], Mannino and Bressler take us on a beautiful journey into the history of the work on causality and make a well-reasoned argument that the causality in the brain is inherently probabilistic. This notion is consistent with brain anatomy and functions, and is also inclusive of deterministic cases of inputs leading to outputs in the brain.

  10. Using large-scale Granger causality to study changes in brain network properties in the Clinically Isolated Syndrome (CIS) stage of multiple sclerosis

    Science.gov (United States)

    Abidin, Anas Z.; Chockanathan, Udaysankar; DSouza, Adora M.; Inglese, Matilde; Wismüller, Axel

    2017-03-01

    Clinically Isolated Syndrome (CIS) is often considered to be the first neurological episode associated with Multiple sclerosis (MS). At an early stage the inflammatory demyelination occurring in the CNS can manifest as a change in neuronal metabolism, with multiple asymptomatic white matter lesions detected in clinical MRI. Such damage may induce topological changes of brain networks, which can be captured by advanced functional MRI (fMRI) analysis techniques. We test this hypothesis by capturing the effective relationships of 90 brain regions, defined in the Automated Anatomic Labeling (AAL) atlas, using a large-scale Granger Causality (lsGC) framework. The resulting networks are then characterized using graph-theoretic measures that quantify various network topology properties at a global as well as at a local level. We study for differences in these properties in network graphs obtained for 18 subjects (10 male and 8 female, 9 with CIS and 9 healthy controls). Global network properties captured trending differences with modularity and clustering coefficient (pdifferences in some regions of the inferior frontal and parietal lobe. We conclude that multivariate analysis of fMRI time-series can reveal interesting information about changes occurring in the brain in early stages of MS.

  11. Wigner Functions for the Bateman System on Noncommutative Phase Space

    Science.gov (United States)

    Heng, Tai-Hua; Lin, Bing-Sheng; Jing, Si-Cong

    2010-09-01

    We study an important dissipation system, i.e. the Bateman model on noncommutative phase space. Using the method of deformation quantization, we calculate the Exp functions, and then derive the Wigner functions and the corresponding energy spectra.

  12. Wigner Functions for the Bateman System on Noncommutative Phase Space

    International Nuclear Information System (INIS)

    Tai-Hua, Heng; Bing-Sheng, Lin; Si-Cong, Jing

    2010-01-01

    We study an important dissipation system, i.e. the Bateman model on noncommutative phase space. Using the method of deformation quantization, we calculate the Exp functions, and then derive the Wigner functions and the corresponding energy spectra

  13. Noncommutative GUTs, Standard Model and C,P,T

    International Nuclear Information System (INIS)

    Aschieri, P.; Jurco, B.; Schupp, P.; Wess, J.

    2003-01-01

    Noncommutative Yang-Mills theories are sensitive to the choice of the representation that enters in the gauge kinetic term. We constrain this ambiguity by considering grand unified theories. We find that at first order in the noncommutativity parameter θ, SU(5) is not truly a unified theory, while SO(10) has a unique noncommutative generalization. In view of these results we discuss the noncommutative SM theory that is compatible with SO(10) GUT and find that there are no modifications to the SM gauge kinetic term at lowest order in θ. We study in detail the reality, Hermiticity and C,P,T properties of the Seiberg-Witten map and of the resulting effective actions expanded in ordinary fields. We find that in models of GUTs (or compatible with GUTs) right-handed fermions and left-handed ones appear with opposite Seiberg-Witten map

  14. Noncommutative Yang-Mills from equivalence of star products

    International Nuclear Information System (INIS)

    Jurco, B.; Schupp, P.

    2000-01-01

    It is shown that the transformation between ordinary and noncommutative Yang-Mills theory as formulated by Seiberg and Witten is due to the equivalence of certain star products on the D-brane world-volume. (orig.)

  15. Noncommutative Yang-Mills from equivalence of star products

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, B. [Max-Planck-Institut fuer Mathematik, Bonn (Germany); Schupp, P. [Sektion Physik, Universitaet Muenchen, Theresienstrasse 37, 80333 Muenchen (Germany)

    2000-05-01

    It is shown that the transformation between ordinary and noncommutative Yang-Mills theory as formulated by Seiberg and Witten is due to the equivalence of certain star products on the D-brane world-volume. (orig.)

  16. Noncommutative GUTs, Standard Model and C,P,T

    Energy Technology Data Exchange (ETDEWEB)

    Aschieri, P. E-mail: aschieri@theorie.physik.uni-muenchen.de; Jurco, B. E-mail: jurco@theorie.physik.uni-muenchen.de; Schupp, P. E-mail: p.schupp@iu-bremen.de; Wess, J. E-mail: wess@theorie.physik.uni-muenchen.de

    2003-02-17

    Noncommutative Yang-Mills theories are sensitive to the choice of the representation that enters in the gauge kinetic term. We constrain this ambiguity by considering grand unified theories. We find that at first order in the noncommutativity parameter {theta}, SU(5) is not truly a unified theory, while SO(10) has a unique noncommutative generalization. In view of these results we discuss the noncommutative SM theory that is compatible with SO(10) GUT and find that there are no modifications to the SM gauge kinetic term at lowest order in {theta}. We study in detail the reality, Hermiticity and C,P,T properties of the Seiberg-Witten map and of the resulting effective actions expanded in ordinary fields. We find that in models of GUTs (or compatible with GUTs) right-handed fermions and left-handed ones appear with opposite Seiberg-Witten map.

  17. Noncommutative SO(n) and Sp(n) gauge theories

    International Nuclear Information System (INIS)

    Bonora, L.; INFN, Sezione di Trieste, Trieste; Schnabl, M.; INFN, Sezione di Trieste, Trieste; Sheikh-Jabbari, M.M.; Tomasiello, A.

    2000-08-01

    We study the generalization of noncommutative gauge theories to the case of orthogonal and symplectic groups. We find out that this is possible, since we are allowed to define orthogonal and symplectic subgroups of noncommutative unitary gauge transformations even though the gauge potentials and gauge transformations are not valued in the orthogonal and symplectic subalgebras of the Lie algebra of antihermitean matrices. Our construction relies on an antiautomorphism of the basic noncommutative algebra of functions which generalizes the charge conjugation operator of ordinary field theory. We show that the corresponding noncommutative picture from low energy string theory is obtained via orientifold projection in the presence of a non-trivial NSNS B-field. (author)

  18. Deformed two-photon squeezed states in noncommutative space

    International Nuclear Information System (INIS)

    Zhang Jianzu

    2004-01-01

    Recent studies on nonperturbation aspects of noncommutative quantum mechanics explored a new type of boson commutation relations at the deformed level, described by deformed annihilation-creation operators in noncommutative space. This correlated boson commutator correlates different degrees of freedom, and shows an essential influence on dynamics. This Letter devotes to the development of formalism of deformed two-photon squeezed states in noncommutative space. General representations of deformed annihilation-creation operators and the consistency condition for the electromagnetic wave with a single mode of frequency in noncommunicative space are obtained. Two-photon squeezed states are studied. One finds that variances of the dimensionless Hermitian quadratures of the annihilation operator in one degree of freedom include variances in the other degree of freedom. Such correlations show the new feature of spatial noncommutativity and allow a deeper understanding of the correlated boson commutator

  19. Exact master equation for a noncommutative Brownian particle

    International Nuclear Information System (INIS)

    Costa Dias, Nuno; Nuno Prata, Joao

    2009-01-01

    We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale

  20. Minimal length uncertainty and generalized non-commutative geometry

    International Nuclear Information System (INIS)

    Farmany, A.; Abbasi, S.; Darvishi, M.T.; Khani, F.; Naghipour, A.

    2009-01-01

    A generalized formulation of non-commutative geometry for the Bargmann-Fock space of quantum field theory is presented. The analysis is related to the symmetry of the simplistic space and a minimal length uncertainty.

  1. Quantum group of isometries in classical and noncommutative geometry

    International Nuclear Information System (INIS)

    Goswami, D.

    2007-04-01

    We formulate a quantum generalization of the notion of the group of Riemannian isometries for a compact Riemannian manifold, by introducing a natural notion of smooth and isometric action by a compact quantum group on a classical or noncommutative manifold described by spectral triples, and then proving the existence of a universal object (called the quantum isometry group) in the category of compact quantum groups acting smoothly and isometrically on a given (possibly noncommutative) manifold. Our formulation accommodates spectral triples which are not of type II. We give an explicit description of quantum isometry groups of commutative and noncommutative tori, and in this context, obtain the quantum double torus defined in [7] as the universal quantum group of holomorphic isometries of the noncommutative torus. (author)

  2. Accretion onto a noncommutative-inspired Schwarzschild black hole

    Science.gov (United States)

    Gangopadhyay, Sunandan; Paik, Biplab; Mandal, Rituparna

    2018-05-01

    In this paper, we investigate the problem of ordinary baryonic matter accretion onto the noncommutative (NC) geometry-inspired Schwarzschild black hole. The fundamental equations governing the spherically symmetric steady state matter accretion are deduced. These equations are seen to be modified due to the presence of noncommutativity. The matter accretion rate is computed and is found to increase rapidly with the increase in strength of the NC parameter. The sonic radius reduces while the sound speed at the sonic point increases with the increase in the strength of noncommutativity. The profile of the thermal environment is finally investigated below the sonic radius and at the event horizon and is found to be affected by noncommutativity.

  3. Vectors and covectors in non-commutative setting

    OpenAIRE

    Parfionov, G. N.; Romashev, Yu. A.; Zapatrine, R. R.

    1995-01-01

    Following the guidelines of classical differential geometry the `building material' for the tensor calculus in non-commutative geometry is suggested. The algebraic account of moduli of vectors and covectors is carried out.

  4. Some aspects of noncommutative integrable systems a la Moyal

    International Nuclear Information System (INIS)

    Dafounansou, O.; El Boukili, A.; Sedra, M.B.

    2005-12-01

    Besides its various applications in string and D-brane physics, the non commutativity of space (-time) coordinates, based on the *-product, behaves as a more general framework providing more mathematical and physical information about the associated system. Similar to the Gelfand-Dickey framework of pseudo differential operators, the non commutativity a la Moyal applied to physical problems makes the study more systematic. Using these facts, as well as the backgrounds of Moyal momentum algebra introduced in previous works, we look for the important task of studying integrability in the noncommutativity framework. The main focus is on the noncommutative version of the Lax representation of two principal examples: the noncommutative sl 2 KdV equation and the noncommutative version of Burgers systems. Important properties are presented. (author)

  5. Non-commutative geometry on quantum phase-space

    International Nuclear Information System (INIS)

    Reuter, M.

    1995-06-01

    A non-commutative analogue of the classical differential forms is constructed on the phase-space of an arbitrary quantum system. The non-commutative forms are universal and are related to the quantum mechanical dynamics in the same way as the classical forms are related to classical dynamics. They are constructed by applying the Weyl-Wigner symbol map to the differential envelope of the linear operators on the quantum mechanical Hilbert space. This leads to a representation of the non-commutative forms considered by A. Connes in terms of multiscalar functions on the classical phase-space. In an appropriate coincidence limit they define a quantum deformation of the classical tensor fields and both commutative and non-commutative forms can be studied in a unified framework. We interprete the quantum differential forms in physical terms and comment on possible applications. (orig.)

  6. Scalar-graviton interaction in the noncommutative space

    International Nuclear Information System (INIS)

    Brandt, F. T.; Elias-Filho, M. R.

    2006-01-01

    We obtain the leading order interaction between the graviton and the neutral scalar boson in the context of noncommutative field theory. Our approach makes use of the Ward identity associated with the invariance under a subgroup of symplectic diffeomorphisms

  7. Paradoxical Behavior of Granger Causality

    Science.gov (United States)

    Witt, Annette; Battaglia, Demian; Gail, Alexander

    2013-03-01

    Granger causality is a standard tool for the description of directed interaction of network components and is popular in many scientific fields including econometrics, neuroscience and climate science. For time series that can be modeled as bivariate auto-regressive processes we analytically derive an expression for spectrally decomposed Granger Causality (SDGC) and show that this quantity depends only on two out of four groups of model parameters. Then we present examples of such processes whose SDGC expose paradoxical behavior in the sense that causality is high for frequency ranges with low spectral power. For avoiding misinterpretations of Granger causality analysis we propose to complement it by partial spectral analysis. Our findings are illustrated by an example from brain electrophysiology. Finally, we draw implications for the conventional definition of Granger causality. Bernstein Center for Computational Neuroscience Goettingen

  8. Dirac equation in noncommutative space for hydrogen atom

    Energy Technology Data Exchange (ETDEWEB)

    Adorno, T.C., E-mail: tadorno@nonada.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05508-090 Sao Paulo, SP (Brazil); Baldiotti, M.C., E-mail: baldiott@fma.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05508-090 Sao Paulo, SP (Brazil); Chaichian, M., E-mail: Masud.Chaichian@helsinki.f [Department of Physics, University of Helsinki and Helsinki Institute of Physics, PO Box 64, FIN-00014 Helsinki (Finland); Gitman, D.M., E-mail: gitman@dfn.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05508-090 Sao Paulo, SP (Brazil); Tureanu, A., E-mail: Anca.Tureanu@helsinki.f [Department of Physics, University of Helsinki and Helsinki Institute of Physics, PO Box 64, FIN-00014 Helsinki (Finland)

    2009-11-30

    We consider the energy levels of a hydrogen-like atom in the framework of theta-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S{sub 1/2}, 2P{sub 1/2} and 2P{sub 3/2} is lifted completely, such that new transition channels are allowed.

  9. Dirac equation in noncommutative space for hydrogen atom

    International Nuclear Information System (INIS)

    Adorno, T.C.; Baldiotti, M.C.; Chaichian, M.; Gitman, D.M.; Tureanu, A.

    2009-01-01

    We consider the energy levels of a hydrogen-like atom in the framework of θ-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S 1/2 , 2P 1/2 and 2P 3/2 is lifted completely, such that new transition channels are allowed.

  10. Baecklund transformation of the noncommutative Gelfand-Dickey hierarchy

    International Nuclear Information System (INIS)

    Zheng Zhong; He Jingsong; Cheng Yi

    2004-01-01

    We study the Baecklund transformation of the noncommutative Gelfand-Dickey(ncGD) hierarchy. By factorizing its Lax operator into the multiplication form of first order differential operator, the noncommutative modified KdV(ncMKdV) hierarchy and the Miura transformations are defined. Our results show that the ncMKdV equations are invariant under the cyclic permutation, and hence induces the Baecklund transformation of the ncGD hierarchy. (author)

  11. Differential Galois obstructions for non-commutative integrability

    Energy Technology Data Exchange (ETDEWEB)

    Maciejewski, Andrzej J. [Institute of Astronomy, University of Zielona Gora, Podgorna 50, PL-65-246 Zielona Gora (Poland)], E-mail: maciejka@astro.ia.uz.zgora.pl; Przybylska, Maria [Torun Centre for Astronomy, N. Copernicus University, Gagarina 11, PL-87-100 Torun (Poland)], E-mail: mprzyb@astri.uni.torun.pl

    2008-08-11

    We show that if a holomorphic Hamiltonian system is holomorphically integrable in the non-commutative sense in a neighbourhood of a non-equilibrium phase curve which is located at a regular level of the first integrals, then the identity component of the differential Galois group of the variational equations along the phase curve is Abelian. Thus necessary conditions for the commutative and non-commutative integrability given by the differential Galois approach are the same.

  12. Extensin network formation in Vitis vinifera callus cells is an essential and causal event in rapid and H2O2-induced reduction in primary cell wall hydration

    Science.gov (United States)

    2011-01-01

    Background Extensin deposition is considered important for the correct assembly and biophysical properties of primary cell walls, with consequences to plant resistance to pathogens, tissue morphology, cell adhesion and extension growth. However, evidence for a direct and causal role for the extensin network formation in changes to cell wall properties has been lacking. Results Hydrogen peroxide treatment of grapevine (Vitis vinifera cv. Touriga) callus cell walls was seen to induce a marked reduction in their hydration and thickness. An analysis of matrix proteins demonstrated this occurs with the insolubilisation of an abundant protein, GvP1, which displays a primary structure and post-translational modifications typical of dicotyledon extensins. The hydration of callus cell walls free from saline-soluble proteins did not change in response to H2O2, but fully regained this capacity after addition of extensin-rich saline extracts. To assay the specific contribution of GvP1 cross-linking and other wall matrix proteins to the reduction in hydration, GvP1 levels in cell walls were manipulated in vitro by binding selected fractions of extracellular proteins and their effect on wall hydration during H2O2 incubation assayed. Conclusions This approach allowed us to conclude that a peroxidase-mediated formation of a covalently linked network of GvP1 is essential and causal in the reduction of grapevine callus wall hydration in response to H2O2. Importantly, this approach also indicated that extensin network effects on hydration was only partially irreversible and remained sensitive to changes in matrix charge. We discuss this mechanism and the importance of these changes to primary wall properties in the light of extensin distribution in dicotyledons. PMID:21672244

  13. Towards Noncommutative Linking Numbers via the Seiberg-Witten Map

    Directory of Open Access Journals (Sweden)

    H. García-Compeán

    2015-01-01

    Full Text Available Some geometric and topological implications of noncommutative Wilson loops are explored via the Seiberg-Witten map. In the abelian Chern-Simons theory on a three-dimensional manifold, it is shown that the effect of noncommutativity is the appearance of 6n new knots at the nth order of the Seiberg-Witten expansion. These knots are trivial homology cycles which are Poincaré dual to the higher-order Seiberg-Witten potentials. Moreover the linking number of a standard 1-cycle with the Poincaré dual of the gauge field is shown to be written as an expansion of the linking number of this 1-cycle with the Poincaré dual of the Seiberg-Witten gauge fields. In the process we explicitly compute the noncommutative “Jones-Witten” invariants up to first order in the noncommutative parameter. Finally in order to exhibit a physical example, we apply these ideas explicitly to the Aharonov-Bohm effect. It is explicitly displayed at first order in the noncommutative parameter; we also show the relation to the noncommutative Landau levels.

  14. Trace Dynamics and a non-commutative special relativity

    International Nuclear Information System (INIS)

    Lochan, Kinjalk; Singh, T.P.

    2011-01-01

    Trace Dynamics is a classical dynamical theory of non-commuting matrices in which cyclic permutation inside a trace is used to define the derivative with respect to an operator. We use the methods of Trace Dynamics to construct a non-commutative special relativity. We define a line-element using the Trace over space-time coordinates which are assumed to be operators. The line-element is shown to be invariant under standard Lorentz transformations, and is used to construct a non-commutative relativistic dynamics. The eventual motivation for constructing such a non-commutative relativity is to relate the statistical thermodynamics of this classical theory to quantum mechanics. -- Highlights: → Classical time is external to quantum mechanics. → This implies need for a formulation of quantum theory without classical time. → A starting point could be a non-commutative special relativity. → Such a relativity is developed here using the theory of Trace Dynamics. → A line-element is defined using the Trace over non-commuting space-time operators.

  15. Abelian Toda field theories on the noncommutative plane

    Science.gov (United States)

    Cabrera-Carnero, Iraida

    2005-10-01

    Generalizations of GL(n) abelian Toda and GL with tilde above(n) abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by algebra-valued gauge potentials dependent on the fields. This condition can be expressed as noncommutative Leznov-Saveliev equations which make possible to define the noncommutative generalizations as systems of second order differential equations, with an infinite chain of conserved currents. The actions corresponding to these field theories are also provided. The special cases of GL(2) Liouville and GL with tilde above(2) sinh/sine-Gordon are explicitly studied. It is also shown that from the noncommutative (anti-)self-dual Yang-Mills equations in four dimensions it is possible to obtain by dimensional reduction the equations of motion of the two-dimensional models constructed. This fact supports the validity of the noncommutative version of the Ward conjecture. The relation of our proposal to previous versions of some specific Toda field theories reported in the literature is presented as well.

  16. Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space

    Energy Technology Data Exchange (ETDEWEB)

    Zahn, J.W.

    2006-12-15

    We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation function of the field strength in noncommutative quantum electrodynamics to second order. At this, we take into account the covariant coordinates that allow the construction of local gauge invariant quantities (observables). It turns out that this does not remove the well-known severe infrared problem, as one might have hoped. Instead, things become worse, since nonlocal divergences appear. We also show that these cancel in a supersymmetric version of the theory if the covariant coordinates are adjusted accordingly. Furthermore, we study the {phi}{sup 3} and the Wess-Zumino model and show that the distortion of the dispersion relations is moderate for parameters typical for the Higgs field. We also discuss the formulation of gauge theories on noncommutative spaces and study classical electrodynamics on the noncommutative Minkowski space using covariant coordinates. In particular, we compute the change of the speed of light due to nonlinear effects in the presence of a background field. Finally, we examine the so-called twist approach to quantum field theory on the noncommutative Minkowski space and point out some conceptual problems of this approach. (orig.)

  17. Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space

    International Nuclear Information System (INIS)

    Zahn, J.W.

    2006-12-01

    We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation function of the field strength in noncommutative quantum electrodynamics to second order. At this, we take into account the covariant coordinates that allow the construction of local gauge invariant quantities (observables). It turns out that this does not remove the well-known severe infrared problem, as one might have hoped. Instead, things become worse, since nonlocal divergences appear. We also show that these cancel in a supersymmetric version of the theory if the covariant coordinates are adjusted accordingly. Furthermore, we study the Φ 3 and the Wess-Zumino model and show that the distortion of the dispersion relations is moderate for parameters typical for the Higgs field. We also discuss the formulation of gauge theories on noncommutative spaces and study classical electrodynamics on the noncommutative Minkowski space using covariant coordinates. In particular, we compute the change of the speed of light due to nonlinear effects in the presence of a background field. Finally, we examine the so-called twist approach to quantum field theory on the noncommutative Minkowski space and point out some conceptual problems of this approach. (orig.)

  18. Noncommuting limits of oscillator wave functions

    International Nuclear Information System (INIS)

    Daboul, J.; Pogosyan, G. S.; Wolf, K. B.

    2007-01-01

    Quantum harmonic oscillators with spring constants k > 0 plus constant forces f exhibit rescaled and displaced Hermite-Gaussian wave functions, and discrete, lower bound spectra. We examine their limits when (k, f) → (0, 0) along two different paths. When f → 0 and then k → 0, the contraction is standard: the system becomes free with a double continuous, positive spectrum, and the wave functions limit to plane waves of definite parity. On the other hand, when k → 0 first, the contraction path passes through the free-fall system, with a continuous, nondegenerate, unbounded spectrum and displaced Airy wave functions, while parity is lost. The subsequent f → 0 limit of the nonstandard path shows the dc hysteresis phenomenon of noncommuting contractions: the lost parity reappears as an infinitely oscillating superposition of the two limiting solutions that are related by the symmetry

  19. Noncommutative spaces and Poincaré symmetry

    Energy Technology Data Exchange (ETDEWEB)

    Meljanac, Stjepan, E-mail: meljanac@irb.hr [Division of Theoretical Physics, Rudjer Bošković Institute, Bijenička c. 54, HR-10002 Zagreb (Croatia); Meljanac, Daniel [Division of Theoretical Physics, Rudjer Bošković Institute, Bijenička c. 54, HR-10002 Zagreb (Croatia); Mercati, Flavio [Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5 (Canada); Pikutić, Danijel [Division of Theoretical Physics, Rudjer Bošković Institute, Bijenička c. 54, HR-10002 Zagreb (Croatia)

    2017-03-10

    We present a framework which unifies a large class of noncommutative spacetimes that can be described in terms of a deformed Heisenberg algebra. The commutation relations between spacetime coordinates are up to linear order in the coordinates, with structure constants depending on the momenta plus terms depending only on the momenta. The possible implementations of the action of Lorentz transformations on these deformed phase spaces are considered, together with the consistency requirements they introduce. It is found that Lorentz transformations in general act nontrivially on tensor products of momenta. In particular the Lorentz group element which acts on the left and on the right of a composition of two momenta is different, and depends on the momenta involved in the process. We conclude with two representative examples, which illustrate the mentioned effect.

  20. Noncommutative analysis, operator theory and applications

    CERN Document Server

    Cipriani, Fabio; Colombo, Fabrizio; Guido, Daniele; Sabadini, Irene; Sauvageot, Jean-Luc

    2016-01-01

    This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics. It is addressed to specialists but also to graduate students in several fields including global analysis, Schur analysis, complex analysis, C*-algebras, noncommutative geometry, operator algebras, operator theory and their applications. Contributors: F. Arici, S. Bernstein, V. Bolotnikov, J. Bourgain, P. Cerejeiras, F. Cipriani, F. Colombo, F. D'Andrea, G. Dell'Antonio, M. Elin, U. Franz, D. Guido, T. Isola, A. Kula, L.E. Labuschagne, G. Landi, W.A. Majewski, I. Sabadini, J.-L. Sauvageot, D. Shoikhet, A. Skalski, H. de Snoo, D. C. Struppa, N. Vieira, D.V. Voiculescu, and H. Woracek.

  1. A first course in noncommutative rings

    CERN Document Server

    Lam, T Y

    2001-01-01

    A First Course in Noncommutative Rings, an outgrowth of the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-semester course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semisimple rings, Jacobson's theory of the radical, representation theory of groups and algebras, prime and semiprime rings, local and semilocal rings, perfect and semiperfect rings, etc. By aiming the level of writing at the novice rather than the connoisseur and by stressing th the role of examples and motivation, the author has produced a text that is suitable not only for use in a graduate course, but also for self- study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition.

  2. Non-commutative representation for quantum systems on Lie groups

    Energy Technology Data Exchange (ETDEWEB)

    Raasakka, Matti Tapio

    2014-01-27

    The topic of this thesis is a new representation for quantum systems on weakly exponential Lie groups in terms of a non-commutative algebra of functions, the associated non-commutative harmonic analysis, and some of its applications to specific physical systems. In the first part of the thesis, after a review of the necessary mathematical background, we introduce a {sup *}-algebra that is interpreted as the quantization of the canonical Poisson structure of the cotangent bundle over a Lie group. From the physics point of view, this represents the algebra of quantum observables of a physical system, whose configuration space is a Lie group. We then show that this quantum algebra can be represented either as operators acting on functions on the group, the usual group representation, or (under suitable conditions) as elements of a completion of the universal enveloping algebra of the Lie group, the algebra representation. We further apply the methods of deformation quantization to obtain a representation of the same algebra in terms of a non-commutative algebra of functions on a Euclidean space, which we call the non-commutative representation of the original quantum algebra. The non-commutative space that arises from the construction may be interpreted as the quantum momentum space of the physical system. We derive the transform between the group representation and the non-commutative representation that generalizes in a natural way the usual Fourier transform, and discuss key properties of this new non-commutative harmonic analysis. Finally, we exhibit the explicit forms of the non-commutative Fourier transform for three elementary Lie groups: R{sup d}, U(1) and SU(2). In the second part of the thesis, we consider application of the non-commutative representation and harmonic analysis to physics. First, we apply the formalism to quantum mechanics of a point particle on a Lie group. We define the dual non-commutative momentum representation, and derive the phase

  3. Non-commutative representation for quantum systems on Lie groups

    International Nuclear Information System (INIS)

    Raasakka, Matti Tapio

    2014-01-01

    The topic of this thesis is a new representation for quantum systems on weakly exponential Lie groups in terms of a non-commutative algebra of functions, the associated non-commutative harmonic analysis, and some of its applications to specific physical systems. In the first part of the thesis, after a review of the necessary mathematical background, we introduce a * -algebra that is interpreted as the quantization of the canonical Poisson structure of the cotangent bundle over a Lie group. From the physics point of view, this represents the algebra of quantum observables of a physical system, whose configuration space is a Lie group. We then show that this quantum algebra can be represented either as operators acting on functions on the group, the usual group representation, or (under suitable conditions) as elements of a completion of the universal enveloping algebra of the Lie group, the algebra representation. We further apply the methods of deformation quantization to obtain a representation of the same algebra in terms of a non-commutative algebra of functions on a Euclidean space, which we call the non-commutative representation of the original quantum algebra. The non-commutative space that arises from the construction may be interpreted as the quantum momentum space of the physical system. We derive the transform between the group representation and the non-commutative representation that generalizes in a natural way the usual Fourier transform, and discuss key properties of this new non-commutative harmonic analysis. Finally, we exhibit the explicit forms of the non-commutative Fourier transform for three elementary Lie groups: R d , U(1) and SU(2). In the second part of the thesis, we consider application of the non-commutative representation and harmonic analysis to physics. First, we apply the formalism to quantum mechanics of a point particle on a Lie group. We define the dual non-commutative momentum representation, and derive the phase space path

  4. Dynamic causal modeling revealed dysfunctional effective connectivity in both, the cortico-basal-ganglia and the cerebello-cortical motor network in writers' cramp

    Directory of Open Access Journals (Sweden)

    Inken Rothkirch

    Full Text Available Writer's cramp (WC is a focal task-specific dystonia characterized by sustained or intermittent muscle contractions while writing, particularly with the dominant hand. Since structural lesions rarely cause WC, it has been assumed that the disease might be caused by a functional maladaptation within the sensory-motor system. Therefore, our objective was to examine the differences between patients suffering from WC and a healthy control (HC group with regard to the effective connectivity that describes causal influences one brain region exerts over another within the motor network. The effective connectivity within a network including contralateral motor cortex (M1, supplementary motor area (SMA, globus pallidus (GP, putamen (PU and ipsilateral cerebellum (CB was investigated using dynamic causal modeling (DCM for fMRI. Eight connectivity models of functional motor systems were compared. Fifteen WC patients and 18 age-matched HC performed a sequential, five-element finger-tapping task with the non-dominant and non-affected left hand within a 3 T MRI-scanner as quickly and accurately as possible. The task was conducted in a fixed block design repeated 15 times and included 30 s of tapping followed by 30 s of rest. DCM identified the same model in WC and HC as superior for reflecting basal ganglia and cerebellar motor circuits of healthy subjects. The M1-PU, as well as M1-CB connectivity, was more strongly influenced by tapping in WC, but the intracortical M1-SMA connection was more facilitating in controls. Inhibiting influences originating from GP to M1 were stronger in controls compared to WC patients whereby facilitating influences the PU exerts over CB and CB exerts over M1 were not as strong. Although the same model structure explains the given data best, DCM confirms previous research demonstrating a malfunction in effective connectivity intracortically (M1-SMA and in the cortico-basal ganglia circuitry in WC. In addition, DCM analysis

  5. BioCreative V track 4: a shared task for the extraction of causal network information using the Biological Expression Language.

    Science.gov (United States)

    Rinaldi, Fabio; Ellendorff, Tilia Renate; Madan, Sumit; Clematide, Simon; van der Lek, Adrian; Mevissen, Theo; Fluck, Juliane

    2016-01-01

    Automatic extraction of biological network information is one of the most desired and most complex tasks in biological and medical text mining. Track 4 at BioCreative V attempts to approach this complexity using fragments of large-scale manually curated biological networks, represented in Biological Expression Language (BEL), as training and test data. BEL is an advanced knowledge representation format which has been designed to be both human readable and machine processable. The specific goal of track 4 was to evaluate text mining systems capable of automatically constructing BEL statements from given evidence text, and of retrieving evidence text for given BEL statements. Given the complexity of the task, we designed an evaluation methodology which gives credit to partially correct statements. We identified various levels of information expressed by BEL statements, such as entities, functions, relations, and introduced an evaluation framework which rewards systems capable of delivering useful BEL fragments at each of these levels. The aim of this evaluation method is to help identify the characteristics of the systems which, if combined, would be most useful for achieving the overall goal of automatically constructing causal biological networks from text. © The Author(s) 2016. Published by Oxford University Press.

  6. The Event Horizon of The Schwarzschild Black Hole in Noncommutative Spaces

    OpenAIRE

    Nasseri, Forough

    2005-01-01

    The event horizon of Schwarzschild black hole is obtained in noncommutative spaces up to the second order of perturbative calculations. Because this type of black hole is non-rotating, to the first order there is no any effect on the event horizon due to the noncommutativity of space. A lower limit for the noncommutativity parameter is also obtained. As a result, the event horizon in noncommutative spaces is less than the event horizon in commutative spaces.

  7. Nonperturbative studies of quantum field theories on noncommutative spaces

    Energy Technology Data Exchange (ETDEWEB)

    Volkholz, J.

    2007-11-16

    This work deals with three quantum field theories on spaces with noncommuting position operators. Noncommutative models occur in the study of string theories and quantum gravity. They usually elude treatment beyond the perturbative level. Due to the technique of dimensional reduction, however, we are able to investigate these theories nonperturbatively. This entails translating the action functionals into a matrix language, which is suitable for numerical simulations. First we explore the {lambda}{phi}{sup 4} model on a noncommutative plane. We investigate the continuum limit at fixed noncommutativity, which is known as the double scaling limit. Here we focus especially on the fate of the striped phase, a phase peculiar to the noncommutative version of the regularized {lambda}{phi}{sup 4} model. We find no evidence for its existence in the double scaling limit. Next we examine the U(1) gauge theory on a four-dimensional spacetime, where two spatial directions are noncommutative. We examine the phase structure and find a new phase with a spontaneously broken translation symmetry. In addition we demonstrate the existence of a finite double scaling limit which confirms the renormalizability of the theory. Furthermore we investigate the dispersion relation of the photon. In the weak coupling phase our results are consistent with an infrared instability predicted by perturbation theory. If the translational symmetry is broken, however, we find a dispersion relation corresponding to a massless particle. Finally, we investigate a supersymmetric theory on the fuzzy sphere, which features scalar neutral bosons and Majorana fermions. The supersymmetry is exact in the limit of infinitely large matrices. We investigate the phase structure of the model and find three distinct phases. Summarizing, we study noncommutative field theories beyond perturbation theory. Moreover, we simulate a supersymmetric theory on the fuzzy sphere, which might provide an alternative to attempted

  8. Nonperturbative studies of quantum field theories on noncommutative spaces

    International Nuclear Information System (INIS)

    Volkholz, J.

    2007-01-01

    This work deals with three quantum field theories on spaces with noncommuting position operators. Noncommutative models occur in the study of string theories and quantum gravity. They usually elude treatment beyond the perturbative level. Due to the technique of dimensional reduction, however, we are able to investigate these theories nonperturbatively. This entails translating the action functionals into a matrix language, which is suitable for numerical simulations. First we explore the λφ 4 model on a noncommutative plane. We investigate the continuum limit at fixed noncommutativity, which is known as the double scaling limit. Here we focus especially on the fate of the striped phase, a phase peculiar to the noncommutative version of the regularized λφ 4 model. We find no evidence for its existence in the double scaling limit. Next we examine the U(1) gauge theory on a four-dimensional spacetime, where two spatial directions are noncommutative. We examine the phase structure and find a new phase with a spontaneously broken translation symmetry. In addition we demonstrate the existence of a finite double scaling limit which confirms the renormalizability of the theory. Furthermore we investigate the dispersion relation of the photon. In the weak coupling phase our results are consistent with an infrared instability predicted by perturbation theory. If the translational symmetry is broken, however, we find a dispersion relation corresponding to a massless particle. Finally, we investigate a supersymmetric theory on the fuzzy sphere, which features scalar neutral bosons and Majorana fermions. The supersymmetry is exact in the limit of infinitely large matrices. We investigate the phase structure of the model and find three distinct phases. Summarizing, we study noncommutative field theories beyond perturbation theory. Moreover, we simulate a supersymmetric theory on the fuzzy sphere, which might provide an alternative to attempted lattice formulations. (orig.)

  9. On a direct approach to quasideterminant solutions of a noncommutative modified KP equation

    International Nuclear Information System (INIS)

    Gilson, C R; Nimmo, J J C; Sooman, C M

    2008-01-01

    A noncommutative version of the modified KP equation and a family of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux transformations and the solutions are verified directly. We also verify directly an explicit connection between quasideterminant solutions of the noncommutative mKP equation and the noncommutative KP equation arising from the Miura transformation

  10. Moving mirrors and black hole evaporation in noncommutative space-times

    International Nuclear Information System (INIS)

    Casadio, R.; Cox, P.H.; Harms, B.; Micu, O.

    2006-01-01

    We study the evaporation of black holes in noncommutative space-times. We do this by calculating the correction to the detector's response function for a moving mirror in terms of the noncommutativity parameter Θ and then extracting the number density as modified by this parameter. We find that allowing space and time to be noncommutative increases the decay rate of a black hole

  11. Consequences of media and Internet use for offline and online network capital and well-being. A causal model approach

    NARCIS (Netherlands)

    Vergeer, M.R.M.; Pelzer, B.J.

    2009-01-01

    This study sets out to identify relations between people's media use, network capital as a resource, and loneliness. Unlike many studies on this topic, this study aimed to test hypotheses on a national sample, and used insights from empirical research and theoretical notions from different research

  12. CMB statistical anisotropy from noncommutative gravitational waves

    Energy Technology Data Exchange (ETDEWEB)

    Shiraishi, Maresuke; Ricciardone, Angelo [Dipartimento di Fisica e Astronomia ' ' G. Galilei' ' , Università degli Studi di Padova, via Marzolo 8, I-35131, Padova (Italy); Mota, David F. [Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, N-0315 Oslo (Norway); Arroja, Frederico, E-mail: maresuke.shiraishi@pd.infn.it, E-mail: d.f.mota@astro.uio.no, E-mail: angelo.ricciardone@pd.infn.it, E-mail: arroja@pd.infn.it [INFN, Sezione di Padova, via Marzolo 8, I-35131, Padova (Italy)

    2014-07-01

    Primordial statistical anisotropy is a key indicator to investigate early Universe models and has been probed by the cosmic microwave background (CMB) anisotropies. In this paper, we examine tensor-mode CMB fluctuations generated from anisotropic gravitational waves, parametrised by P{sub h}(k) = P{sub h}{sup (0)}(k) [ 1 + ∑{sub LM} f{sub L}(k) g{sub LM} Y{sub LM} ( k-circumflex )], where P{sub h}{sup (0)}(k) is the usual scale-invariant power spectrum. Such anisotropic tensor fluctuations may arise from an inflationary model with noncommutativity of fields. It is verified that in this model, an isotropic component and a quadrupole asymmetry with f{sub 0}(k) = f{sub 2}(k) ∝ k{sup -2} are created and hence highly red-tilted off-diagonal components arise in the CMB power spectra, namely ℓ{sub 2} = ℓ{sub 1} ± 2 in TT, TE, EE and BB, and ℓ{sub 2} = ℓ{sub 1} ± 1 in TB and EB. We find that B-mode polarisation is more sensitive to such signals than temperature and E-mode polarisation due to the smallness of large-scale cosmic variance and we can potentially measure g{sub 00} = 30 and g{sub 2M} = 58 at 68% CL in a cosmic-variance-limited experiment. Such a level of signal may be measured in a PRISM like experiment, while the instrumental noise contaminates it in the Planck experiment. These results imply that it is impossible to measure the noncommutative parameter if it is small enough for the perturbative treatment to be valid. Our formalism and methodology for dealing with the CMB tensor statistical anisotropy are general and straightforwardly applicable to other early Universe models.

  13. Instantons, quivers and noncommutative Donaldson-Thomas theory

    Science.gov (United States)

    Cirafici, Michele; Sinkovics, Annamaria; Szabo, Richard J.

    2011-12-01

    We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.

  14. Soldering formalism in noncommutative field theory: a brief note

    International Nuclear Information System (INIS)

    Ghosh, Subir

    2004-01-01

    In this Letter, I develop the soldering formalism in a new domain--the noncommutative planar field theories. The soldering mechanism fuses two distinct theories showing opposite or complimentary properties of some symmetry, taking into account the interference effects. The above mentioned symmetry is hidden in the composite (or soldered) theory. In the present work it is shown that a pair of noncommutative Maxwell-Chern-Simons theories, having opposite signs in their respective topological terms, can be consistently soldered to yield the Proca model (Maxwell theory with a mass term) with corrections that are at least quadratic in the noncommutativity parameter. We further argue that this model can be thought of as the noncommutative generalization of the Proca theory of ordinary spacetime. It is well known that abelian noncommutative gauge theory bears a close structural similarity with non-abelian gauge theory. This fact is manifested in a non-trivial way if the present Letter is compared with existing literature, where soldering of non-abelian models are discussed. Thus the present work further establishes the robustness of the soldering programme. The subtle role played by gauge invariance (or the lack of it), in the above soldering process, is revealed in an interesting way

  15. Instantons, quivers and noncommutative Donaldson-Thomas theory

    Energy Technology Data Exchange (ETDEWEB)

    Cirafici, Michele, E-mail: cirafici@math.ist.utl.pt [Centro de Analise Matematica, Geometria e Sistemas Dinamicos, Departamento de Matematica, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Sinkovics, Annamaria, E-mail: A.Sinkovics@damtp.cam.ac.uk [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Szabo, Richard J., E-mail: R.J.Szabo@ma.hw.ac.uk [Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS (United Kingdom); Maxwell Institute for Mathematical Sciences, Edinburgh (United Kingdom)

    2011-12-11

    We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.

  16. Conformal quantum mechanics and holography in noncommutative space-time

    Science.gov (United States)

    Gupta, Kumar S.; Harikumar, E.; Zuhair, N. S.

    2017-09-01

    We analyze the effects of noncommutativity in conformal quantum mechanics (CQM) using the κ-deformed space-time as a prototype. Up to the first order in the deformation parameter, the symmetry structure of the CQM algebra is preserved but the coupling in a canonical model of the CQM gets deformed. We show that the boundary conditions that ensure a unitary time evolution in the noncommutative CQM can break the scale invariance, leading to a quantum mechanical scaling anomaly. We calculate the scaling dimensions of the two and three point functions in the noncommutative CQM which are shown to be deformed. The AdS2 / CFT1 duality for the CQM suggests that the corresponding correlation functions in the holographic duals are modified. In addition, the Breitenlohner-Freedman bound also picks up a noncommutative correction. The strongly attractive regime of a canonical model of the CQM exhibit quantum instability. We show that the noncommutativity softens this singular behaviour and its implications for the corresponding holographic duals are discussed.

  17. Paired quantum Hall states on noncommutative two-tori

    Energy Technology Data Exchange (ETDEWEB)

    Marotta, Vincenzo [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' and INFN, Sezione di Napoli, Compl. universitario M. Sant' Angelo, Via Cinthia, 80126 Napoli (Italy); Naddeo, Adele, E-mail: naddeo@sa.infn.i [CNISM, Unita di Ricerca di Salerno and Dipartimento di Fisica ' E. R. Caianiello' , Universita degli Studi di Salerno, Via Salvador Allende, 84081 Baronissi (Italy)

    2010-08-01

    By exploiting the notion of Morita equivalence for field theories on noncommutative tori and choosing rational values of the noncommutativity parameter theta (in appropriate units), a one-to-one correspondence between an Abelian noncommutative field theory (NCFT) and a non-Abelian theory of twisted fields on ordinary space can be established. Starting from this general result, we focus on the conformal field theory (CFT) describing a quantum Hall fluid (QHF) at paired states fillings nu=m/(pm+2) Cristofano et al. (2000) , recently obtained by means of m-reduction procedure, and show that it is the Morita equivalent of a NCFT. In this way we extend the construction proposed in Marotta and Naddeo (2008) for the Jain series nu=m/(2pm+1) . The case m=2 is explicitly discussed and the role of noncommutativity in the physics of quantum Hall bilayers is emphasized. Our results represent a step forward the construction of a new effective low energy description of certain condensed matter phenomena and help to clarify the relationship between noncommutativity and quantum Hall fluids.

  18. An integrable noncommutative version of the sine-Gordon system

    International Nuclear Information System (INIS)

    Grisaru, Marcus T.; Penati, Silvia

    2003-01-01

    Using the bicomplex approach we discuss an integrable noncommutative system in two-dimensional Euclidean space. It is described by an equation of motion which reduces to the ordinary sine-Gordon equation when the noncommutation parameter is removed, plus a constraint equation which is nontrivial only in the noncommutative case. The implications of this constraint, which is required by integrability but seems to reduce the space of classical solutions, remain to be understood. We show that the system has an infinite number of conserved currents and we give the general recursive relation for constructing them. For the particular cases of lower spin nontrivial currents we work out the explicit expressions and perform a direct check of their conservation. These currents reduce to the usual sine-Gordon currents in the commutative limit. We find classical 'localized' solutions to first order in the noncommutativity parameter and describe the Backlund transformations for our system. Finally, we comment on the relation of our noncommutative system to the commutative sine-Gordon system

  19. The network of causal interactions for beta oscillations in the pedunculopontine nucleus, primary motor cortex, and subthalamic nucleus of walking parkinsonian rats.

    Science.gov (United States)

    Li, Min; Zhou, Ming; Wen, Peng; Wang, Qiang; Yang, Yong; Xiao, Hu; Xie, Zhengyuan; Li, Xing; Wang, Ning; Wang, Jinyan; Luo, Fei; Chang, Jingyu; Zhang, Wangming

    2016-08-01

    Oscillatory activity has been well-studied in many structures within cortico-basal ganglia circuits, but it is not well understood within the pedunculopontine nucleus (PPN), which was recently introduced as a potential target for the treatment of gait and postural impairments in advanced stages of Parkinson's disease (PD). To investigate oscillatory activity in the PPN and its relationship with oscillatory activity in cortico-basal ganglia circuits, we simultaneously recorded local field potentials in the PPN, primary motor cortex (M1), and subthalamic nucleus (STN) of 6-hydroxydopamine (6-OHDA)-induced hemiparkinsonian rats during resting and walking. After analysis of power spectral density, coherence, and partial Granger causality, three major findings emerged: 1) after 6-OHDA lesions, beta band oscillations were enhanced in all three regions during walking; 2) the direction of information flow for beta oscillations among the three structures was STN→M1, STN→PPN, and PPN→M1; 3) after the treatment of levodopa, beta activity in the three regions was reduced significantly and the flow of beta band was also abrogated. Our results suggest that beta activity in the PPN is transmitted from the basal ganglia and probably comes from the STN, and the STN plays a dominant role in the network of causal interactions for beta activity. Thus, the STN may be a potential source of aberrant beta band oscillations in PD. Levodopa can inhibit beta activity in the PPN of parkinsonian rats but cannot relieve parkinsonian patients' axial symptoms clinically. Therefore, beta oscillations may not be the major cause of axial symptoms. Copyright © 2016 Elsevier Inc. All rights reserved.

  20. Non-commutative and commutative vacua effects in a scalar torsion scenario

    Energy Technology Data Exchange (ETDEWEB)

    Sheikhahmadi, Haidar, E-mail: h.sh.ahmadi@gmail.com [Department of Physics, Faculty of Science, University of Kurdistan, Sanandaj (Iran, Islamic Republic of); Aghamohammadi, Ali, E-mail: a.aghamohamadi@iausdj.ac.ir [Sanandaj Branch, Islamic Azad University, Sanandaj (Iran, Islamic Republic of); Saaidi, Khaled, E-mail: ksaaidi@uok.ac.ir [Department of Physics, Faculty of Science, University of Kurdistan, Sanandaj (Iran, Islamic Republic of)

    2015-10-07

    In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.

  1. Non-commutative and commutative vacua effects in a scalar torsion scenario

    International Nuclear Information System (INIS)

    Sheikhahmadi, Haidar; Aghamohammadi, Ali; Saaidi, Khaled

    2015-01-01

    In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.

  2. Non-commutative and commutative vacua effects in a scalar torsion scenario

    Directory of Open Access Journals (Sweden)

    Haidar Sheikhahmadi

    2015-10-01

    Full Text Available In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.

  3. The standard model on non-commutative space-time

    International Nuclear Information System (INIS)

    Calmet, X.; Jurco, B.; Schupp, P.; Wohlgenannt, M.; Wess, J.

    2002-01-01

    We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter θ μν . No new particles are introduced; the structure group is SU(3) x SU(2) x U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in θ μν we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered. (orig.)

  4. The standard model on non-commutative space-time

    Energy Technology Data Exchange (ETDEWEB)

    Calmet, X.; Jurco, B.; Schupp, P.; Wohlgenannt, M. [Sektion Physik, Universitaet Muenchen (Germany); Wess, J. [Sektion Physik, Universitaet Muenchen (Germany); Max-Planck-Institut fuer Physik, Muenchen (Germany)

    2002-03-01

    We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter {theta}{sup {mu}}{sup {nu}}. No new particles are introduced; the structure group is SU(3) x SU(2) x U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in {theta}{sup {mu}}{sup {nu}} we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered. (orig.)

  5. Interacting open Wilson lines from noncommutative field theories

    International Nuclear Information System (INIS)

    Kiem, Youngjai; Lee, Sangmin; Rey, Soo-Jong; Sato, Haru-Tada

    2002-01-01

    In noncommutative field theories, it is known that the one-loop effective action describes the propagation of noninteracting open Wilson lines, obeying the flying dipole's relation. We show that the two-loop effective action describes the cubic interaction among 'closed string' states created by open Wilson line operators. Taking d-dimensional λ[Φ 3 ] * theory as the simplest setup, we compute the nonplanar contribution at a low-energy and large noncommutativity limit. We find that the contribution is expressible in a remarkably simple cubic interaction involving scalar open Wilson lines only and nothing else. We show that the interaction is purely geometrical and noncommutative in nature, depending only on the size of each open Wilson line

  6. On the energy crisis in noncommutative CP(1) model

    International Nuclear Information System (INIS)

    Sourrouille, Lucas

    2010-01-01

    We study the CP(1) system in (2+1)-dimensional noncommutative space with and without Chern-Simons term. Using the Seiberg-Witten map we convert the noncommutative CP(1) system to an action written in terms of the commutative fields. We find that this system presents the same infinite size instanton solution as the commutative Chern-Simons-CP(1) model without a potential term. Based on this result we argue that the BPS equations are compatible with the full variational equations of motion, rejecting the hypothesis of an 'energy crisis'. In addition we examine the noncommutative CP(1) system with a Chern-Simons interaction. In this case we find that when the theory is transformed by the Seiberg-Witten map it also presents the same instanton solution as the commutative Chern-Simons-CP(1) model.

  7. A deformation quantization theory for noncommutative quantum mechanics

    International Nuclear Information System (INIS)

    Costa Dias, Nuno; Prata, Joao Nuno; Gosson, Maurice de; Luef, Franz

    2010-01-01

    We show that the deformation quantization of noncommutative quantum mechanics previously considered by Dias and Prata ['Weyl-Wigner formulation of noncommutative quantum mechanics', J. Math. Phys. 49, 072101 (2008)] and Bastos, Dias, and Prata ['Wigner measures in non-commutative quantum mechanics', e-print arXiv:math-ph/0907.4438v1; Commun. Math. Phys. (to appear)] can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef ['A new approach to the *-genvalue equation', Lett. Math. Phys. 85, 173-183 (2008)].

  8. Optimization of polynomials in non-commuting variables

    CERN Document Server

    Burgdorf, Sabine; Povh, Janez

    2016-01-01

    This book presents recent results on positivity and optimization of polynomials in non-commuting variables. Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. Theoretical results are matched with algorithmic considerations; several examples and information on how to use NCSOStools open source package to obtain the results provided. Results are presented on detecting the eigenvalue and trace positivity of polynomials in non-commuting variables using Newton chip method and Newton cyclic chip method, relaxations for constrained and unconstrained optimization problems, semidefinite programming formulations of the relaxations and finite convergence of the hierarchies of these relaxations, and the practical efficiency of algorithms.

  9. Spectral theorem in noncommutative field theories: Jacobi dynamics

    International Nuclear Information System (INIS)

    Géré, Antoine; Wallet, Jean-Christophe

    2015-01-01

    Jacobi operators appear as kinetic operators of several classes of noncommutative field theories (NCFT) considered recently. This paper deals with the case of bounded Jacobi operators. A set of tools mainly issued from operator and spectral theory is given in a way applicable to the study of NCFT. As an illustration, this is applied to a gauge-fixed version of the induced gauge theory on the Moyal plane expanded around a symmetric vacuum. The characterization of the spectrum of the kinetic operator is given, showing a behavior somewhat similar to a massless theory. An attempt to characterize the noncommutative geometry related to the gauge fixed action is presented. Using a Dirac operator obtained from the kinetic operator, it is shown that one can construct an even, regular, weakly real spectral triple. This spectral triple does not define a noncommutative metric space for the Connes spectral distance. (paper)

  10. Einstein-Podolski-Rosen experiment from noncommutative quantum gravity

    International Nuclear Information System (INIS)

    Heller, Michael; Sasin, Wieslaw

    1998-01-01

    It is shown that the Einstein-Podolski-Rosen type experiments are the natural consequence of the groupoid approach to noncommutative unification of general relativity and quantum mechanics. The geometry of this model is determined by the noncommutative algebra A=C c ∞ (G,C) of complex valued, compactly supported, functions (with convolution as multiplication) on the groupoid G=ExΓ. In the model considered in the present paper E is the total space of the frame bundle over space-time and Γ is the Lorentz group. The correlations of the EPR type should be regarded as remnants of the totally non-local physics below the Planck threshold which is modelled by a noncommutative geometry

  11. Quantization, geometry and noncommutative structures in mathematics and physics

    CERN Document Server

    Morales, Pedro; Ocampo, Hernán; Paycha, Sylvie; Lega, Andrés

    2017-01-01

    This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics. The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics. A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt. The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf a...

  12. Non-commutative flux representation for loop quantum gravity

    Science.gov (United States)

    Baratin, A.; Dittrich, B.; Oriti, D.; Tambornino, J.

    2011-09-01

    The Hilbert space of loop quantum gravity is usually described in terms of cylindrical functionals of the gauge connection, the electric fluxes acting as non-commuting derivation operators. It has long been believed that this non-commutativity prevents a dual flux (or triad) representation of loop quantum gravity to exist. We show here, instead, that such a representation can be explicitly defined, by means of a non-commutative Fourier transform defined on the loop gravity state space. In this dual representation, flux operators act by sstarf-multiplication and holonomy operators act by translation. We describe the gauge invariant dual states and discuss their geometrical meaning. Finally, we apply the construction to the simpler case of a U(1) gauge group and compare the resulting flux representation with the triad representation used in loop quantum cosmology.

  13. Altered effective connectivity network of the basal ganglia in low-grade hepatic encephalopathy: a resting-state fMRI study with Granger causality analysis.

    Directory of Open Access Journals (Sweden)

    Rongfeng Qi

    Full Text Available BACKGROUND: The basal ganglia often show abnormal metabolism and intracranial hemodynamics in cirrhotic patients with hepatic encephalopathy (HE. Little is known about how the basal ganglia affect other brain system and is affected by other brain regions in HE. The purpose of this study was to investigate whether the effective connectivity network associated with the basal ganglia is disturbed in HE patients by using resting-state functional magnetic resonance imaging (rs-fMRI. METHODOLOGY/PRINCIPAL FINDINGS: Thirty five low-grade HE patients and thirty five age- and gender- matched healthy controls participated in the rs-fMRI scans. The effective connectivity networks associated with the globus pallidus, the primarily affected region within basal ganglia in HE, were characterized by using the Granger causality analysis and compared between HE patients and healthy controls. Pearson correlation analysis was performed between the abnormal effective connectivity and venous blood ammonia levels and neuropsychological performances of all HE patients. Compared with the healthy controls, patients with low-grade HE demonstrated mutually decreased influence between the globus pallidus and the anterior cingulate cortex (ACC, cuneus, bi-directionally increased influence between the globus pallidus and the precuneus, and either decreased or increased influence from and to the globus pallidus in many other frontal, temporal, parietal gyri, and cerebellum. Pearson correlation analyses revealed that the blood ammonia levels in HE patients negatively correlated with effective connectivity from the globus pallidus to ACC, and positively correlated with that from the globus pallidus to precuneus; and the number connectivity test scores in patients negatively correlated with the effective connectivity from the globus pallidus to ACC, and from superior frontal gyrus to globus pallidus. CONCLUSIONS/SIGNIFICANCE: Low-grade HE patients had disrupted effective

  14. Phase transition and entropy inequality of noncommutative black holes in a new extended phase space

    Energy Technology Data Exchange (ETDEWEB)

    Miao, Yan-Gang; Xu, Zhen-Ming, E-mail: miaoyg@nankai.edu.cn, E-mail: xuzhenm@mail.nankai.edu.cn [School of Physics, Nankai University, Tianjin 300071 (China)

    2017-03-01

    We analyze the thermodynamics of the noncommutative high-dimensional Schwarzschild-Tangherlini AdS black hole with the non-Gaussian smeared matter distribution by regarding a noncommutative parameter as an independent thermodynamic variable named as the noncommutative pressure . In the new extended phase space that includes this noncommutative pressure and its conjugate variable, we reveal that the noncommutative pressure and the original thermodynamic pressure related to the negative cosmological constant make the opposite effects in the phase transition of the noncommutative black hole, i.e. the former dominates the UV regime while the latter does the IR regime, respectively. In addition, by means of the reverse isoperimetric inequality, we indicate that only the black hole with the Gaussian smeared matter distribution holds the maximum entropy for a given thermodynamic volume among the noncommutative black holes with various matter distributions.

  15. Modular Theory, Non-Commutative Geometry and Quantum Gravity

    Directory of Open Access Journals (Sweden)

    Wicharn Lewkeeratiyutkul

    2010-08-01

    Full Text Available This paper contains the first written exposition of some ideas (announced in a previous survey on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spectral geometries from an operational formalism of states and categories of observables in a covariant theory. Care has been taken to provide a coverage of the relevant background on modular theory, its applications in non-commutative geometry and physics and to the detailed discussion of the main foundational issues raised by the proposal.

  16. Intersecting Quantum Gravity with Noncommutative Geometry - a Review

    Directory of Open Access Journals (Sweden)

    Johannes Aastrup

    2012-03-01

    Full Text Available We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present the construction of a spectral triple over an algebra of holonomy loops. The spectral triple, which encodes the kinematics of quantum gravity, gives rise to a natural class of semiclassical states which entail emerging fermionic degrees of freedom. In the particular semiclassical approximation where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges. We end the paper with an extended outlook section.

  17. Non-commutative covering spaces and their symmetries

    DEFF Research Database (Denmark)

    Canlubo, Clarisson

    dened and its corresponding Galois theory. Using this and basic concepts from algebraic geometryand spectral theory, we will give a full description of the general structure of non-centralcoverings. Examples of coverings of the rational and irrational non-commutative tori will alsobe studied. Using...... will explain this and relate it to bi-Galois theory.Using the OZ-transform, we will show that non-commutative covering spaces come in pairs.Several categories of covering spaces will be dened and studied. Appealing to Tannaka duality,we will explain how this lead to a notion of an etale fundamental group...

  18. Infinite volume of noncommutative black hole wrapped by finite surface

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Baocheng, E-mail: zhangbc.zhang@yahoo.com [School of Mathematics and Physics, China University of Geosciences, Wuhan 430074 (China); You, Li, E-mail: lyou@mail.tsinghua.edu.cn [State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084 (China)

    2017-02-10

    The volume of a black hole under noncommutative spacetime background is found to be infinite, in contradiction with the surface area of a black hole, or its Bekenstein–Hawking (BH) entropy, which is well-known to be finite. Our result rules out the possibility of interpreting the entropy of a black hole by counting the number of modes wrapped inside its surface if the final evaporation stage can be properly treated. It implies the statistical interpretation for the BH entropy can be independent of the volume, provided spacetime is noncommutative. The effect of radiation back reaction is found to be small and doesn't influence the above conclusion.

  19. Relativistic Hydrogen-Like Atom on a Noncommutative Phase Space

    Science.gov (United States)

    Masum, Huseyin; Dulat, Sayipjamal; Tohti, Mutallip

    2017-09-01

    The energy levels of hydrogen-like atom on a noncommutative phase space were studied in the framework of relativistic quantum mechanics. The leading order corrections to energy levels 2 S 1/2, 2 P 1/2 and 2 P 3/2 were obtained by using the 𝜃 and the \\bar θ modified Dirac Hamiltonian of hydrogen-like atom on a noncommutative phase space. The degeneracy of the energy levels 2 P 1/2 and 2 P 3/2 were removed completely by 𝜃-correction. And the \\bar θ -correction shifts these energy levels.

  20. Charged thin-shell gravastars in noncommutative geometry

    Energy Technology Data Exchange (ETDEWEB)

    Oevguen, Ali [Pontificia Universidad Catolica de Valparaiso, Instituto de Fisica, Valparaiso (Chile); Eastern Mediterranean University, Physics Department, Famagusta, Northern Cyprus (Turkey); Banerjee, Ayan [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Jusufi, Kimet [State University of Tetovo, Physics Department, Tetovo (Macedonia, The Former Yugoslav Republic of); Institute of Physics, Ss. Cyril and Methodius University, Faculty of Natural Sciences and Mathematics, Skopje (Macedonia, The Former Yugoslav Republic of)

    2017-08-15

    In this paper we construct a charged thin-shell gravastar model within the context of noncommutative geometry. To do so, we choose the interior of the nonsingular de Sitter spacetime with an exterior charged noncommutative solution by cut-and-paste technique and apply the generalized junction conditions. We then investigate the stability of a charged thin-shell gravastar under linear perturbations around the static equilibrium solutions as well as the thermodynamical stability of the charged gravastar. We find the stability regions, by choosing appropriate parameter values, located sufficiently close to the event horizon. (orig.)

  1. Klein-Gordon oscillators in noncommutative phase space

    International Nuclear Information System (INIS)

    Wang Jianhua

    2008-01-01

    We study the Klein-Gordon oscillators in non-commutative (NC) phase space. We find that the Klein-Gordon oscillators in NC space and NC phase-space have a similar behaviour to the dynamics of a particle in commutative space moving in a uniform magnetic field. By solving the Klein-Gordon equation in NC phase space, we obtain the energy levels of the Klein-Gordon oscillators, where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly. (authors)

  2. Noncommutative vector bundles over fuzzy CPN and their covariant derivatives

    International Nuclear Information System (INIS)

    Dolan, Brian P.; Huet, Idrish; Murray, Sean; O'Connor, Denjoe

    2007-01-01

    We generalise the construction of fuzzy CP N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S 2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space

  3. Can noncommutativity resolve the Big-Bang singularity?

    CERN Document Server

    Maceda, M; Manousselis, P; Zoupanos, George

    2004-01-01

    A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has noncommutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a noncommutative version of the Kasner metric is constructed which is nonsingular at all scales and becomes commutative at large length scales.

  4. Causally nonseparable processes admitting a causal model

    International Nuclear Information System (INIS)

    Feix, Adrien; Araújo, Mateus; Brukner, Caslav

    2016-01-01

    A recent framework of quantum theory with no global causal order predicts the existence of ‘causally nonseparable’ processes. Some of these processes produce correlations incompatible with any causal order (they violate so-called ‘causal inequalities’ analogous to Bell inequalities ) while others do not (they admit a ‘causal model’ analogous to a local model ). Here we show for the first time that bipartite causally nonseparable processes with a causal model exist, and give evidence that they have no clear physical interpretation. We also provide an algorithm to generate processes of this kind and show that they have nonzero measure in the set of all processes. We demonstrate the existence of processes which stop violating causal inequalities but are still causally nonseparable when mixed with a certain amount of ‘white noise’. This is reminiscent of the behavior of Werner states in the context of entanglement and nonlocality. Finally, we provide numerical evidence for the existence of causally nonseparable processes which have a causal model even when extended with an entangled state shared among the parties. (paper)

  5. Classification of digital affine noncommutative geometries

    Science.gov (United States)

    Majid, Shahn; Pachoł, Anna

    2018-03-01

    It is known that connected translation invariant n-dimensional noncommutative differentials dxi on the algebra k[x1, …, xn] of polynomials in n-variables over a field k are classified by commutative algebras V on the vector space spanned by the coordinates. These data also apply to construct differentials on the Heisenberg algebra "spacetime" with relations [xμ, xν] = λΘμν, where Θ is an antisymmetric matrix, as well as to Lie algebras with pre-Lie algebra structures. We specialise the general theory to the field k =F2 of two elements, in which case translation invariant metrics (i.e., with constant coefficients) are equivalent to making V a Frobenius algebra. We classify all of these and their quantum Levi-Civita bimodule connections for n = 2, 3, with partial results for n = 4. For n = 2, we find 3 inequivalent differential structures admitting 1, 2, and 3 invariant metrics, respectively. For n = 3, we find 6 differential structures admitting 0, 1, 2, 3, 4, 7 invariant metrics, respectively. We give some examples for n = 4 and general n. Surprisingly, not all our geometries for n ≥ 2 have zero quantum Riemann curvature. Quantum gravity is normally seen as a weighted "sum" over all possible metrics but our results are a step towards a deeper approach in which we must also "sum" over differential structures. Over F2 we construct some of our algebras and associated structures by digital gates, opening up the possibility of "digital geometry."

  6. Connecting dissipation and noncommutativity: A Bateman system case study

    Science.gov (United States)

    Pal, Sayan Kumar; Nandi, Partha; Chakraborty, Biswajit

    2018-06-01

    We present an approach to the problem of quantization of the damped harmonic oscillator. To start with, we adopt the standard method of doubling the degrees of freedom of the system (Bateman form) and then, by introducing some new parameters, we get a generalized coupled set of equations from the Bateman form. Using the corresponding time-independent Lagrangian, quantum effects on a pair of Bateman oscillators embedded in an ambient noncommutative space (Moyal plane) are analyzed by using both path integral and canonical quantization schemes within the framework of the Hilbert-Schmidt operator formulation. Our method is distinct from those existing in the literature and where the ambient space was taken to be commutative. Our quantization shows that we end up again with a Bateman system except that the damping factor undergoes renormalization. Strikingly, the corresponding expression shows that the renormalized damping factor can be nonzero even if "bare" one is zero to begin with. In other words, noncommutativity can act as a source of dissipation. Conversely, the noncommutative parameter θ , taken to be a free one now, can be fine tuned to get a vanishing renormalized damping factor. This indicates in some sense a "duality" between dissipation and noncommutativity. Our results match the existing results in the commutative limit.

  7. Metric interpretation of gauge fields in noncommutative geometry

    International Nuclear Information System (INIS)

    Martinetti, P.

    2007-01-01

    We shall give an overview of the metric interpretation of gauge fields in noncommutative geometry, via Connes distance formula. Especially we shall focus on the Higgs fields in the standard model, and gauge fields in various models of fiber bundle. (author)

  8. Two lectures on D-geometry and noncommutative geometry

    International Nuclear Information System (INIS)

    Douglas, M.R.

    1999-01-01

    This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)

  9. 3D quantum gravity and effective noncommutative quantum field theory.

    Science.gov (United States)

    Freidel, Laurent; Livine, Etera R

    2006-06-09

    We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.

  10. The M5-brane and non-commutative open strings

    NARCIS (Netherlands)

    Bergshoeff, E.; Berman, D.S.; Schaar, J.P. van der; Sundell, P.

    2001-01-01

    The M-theory origin of non-commutative open-string theory is examined by investigating the M-theory 5-brane at near critical field strength. In particular, it is argued that the open-membrane metric provides the appropriate moduli when calculating the duality relations between M and II

  11. General classical solutions in the noncommutative CPN-1 model

    International Nuclear Information System (INIS)

    Foda, O.; Jack, I.; Jones, D.R.T.

    2002-01-01

    We give an explicit construction of general classical solutions for the noncommutative CP N-1 model in two dimensions, showing that they correspond to integer values for the action and topological charge. We also give explicit solutions for the Dirac equation in the background of these general solutions and show that the index theorem is satisfied

  12. Nucleon structure functions in noncommutative space-time

    Energy Technology Data Exchange (ETDEWEB)

    Rafiei, A.; Rezaei, Z.; Mirjalili, A. [Yazd University, Physics Department, Yazd (Iran, Islamic Republic of)

    2017-05-15

    In the context of noncommutative space-time we investigate the nucleon structure functions which play an important role in identifying the internal structure of nucleons. We use the corrected vertices and employ new vertices that appear in two approaches of noncommutativity and calculate the proton structure functions in terms of the noncommutative tensor θ{sub μν}. To check our results we plot the nucleon structure function (NSF), F{sub 2}(x), and compare it with experimental data and the results from the GRV, GJR and CT10 parametrization models. We show that with the new vertex that arises the noncommutativity correction will lead to a better consistency between theoretical results and experimental data for the NSF. This consistency will be better for small values of the Bjorken variable x. To indicate and confirm the validity of our calculations we also act conversely. We obtain a lower bound for the numerical values of Λ{sub NC} scale which correspond to recent reports. (orig.)

  13. Notes on algebraic invariants for non-commutative dynamical systems

    Energy Technology Data Exchange (ETDEWEB)

    Longo, R [Rome Univ. (Italy). Istituto di Matematica

    1979-11-01

    We consider an algebraic invariant for non-commutative dynamical systems naturally arising as the spectrum of the modular operator associated to an invariant state, provided certain conditions of mixing type are present. This invariant turns out to be exactly the annihilator of the invariant T of Connes. Further comments are included, in particular on the type of certain algebras of local observables

  14. Newton's second law in a non-commutative space

    International Nuclear Information System (INIS)

    Romero, Juan M.; Santiago, J.A.; Vergara, J. David

    2003-01-01

    In this Letter we show that corrections to Newton's second law appear if we assume a symplectic structure consistent with the commutation rules of the non-commutative quantum mechanics. For central field we find that the correction term breaks the rotational symmetry. For the Kepler problem, this term is similar to a Coriolis force

  15. Quadratic algebras in the noncommutative integration method of wave equation

    International Nuclear Information System (INIS)

    Varaksin, O.L.

    1995-01-01

    The paper deals with the investigation of applications of the method of noncommutative integration of linear differential equations by partial derivatives. Nontrivial example was taken for integration of three-dimensions wave equation with the use of non-Abelian quadratic algebras

  16. Noncommutative geometry-inspired rotating black hole in three ...

    Indian Academy of Sciences (India)

    We find a new rotating black hole in three-dimensional anti-de Sitter space using an anisotropic perfect fluid inspired by the noncommutative black hole. We deduce the thermodynamical quantities of this black hole and compare them with those of a rotating BTZ solution and give corrections to the area law to get the exact ...

  17. quasi hyperrigidity and weak peak points for non-commutative ...

    Indian Academy of Sciences (India)

    7

    Abstract. In this article, we introduce the notions of weak boundary repre- sentation, quasi hyperrigidity and weak peak points in the non-commutative setting for operator systems in C∗-algebras. An analogue of Saskin's theorem relating quasi hyperrigidity and weak Choquet boundary for particular classes of C∗-algebras is ...

  18. Noncommutativity into Dirac Equation with mass dependent on the position

    International Nuclear Information System (INIS)

    Bastos, Samuel Batista; Almeida, Carlos Alberto Santos; Nunes, Luciana Angelica da Silva

    2013-01-01

    Full text: In recent years, there is growing interest in the study of theories in non-commutative spaces. Non-commutative fields theories are related with compactifications of M theory, string theory and the quantum Hall effect. Moreover, the role of the non-commutativity of theories of a particle finds large applications when analyzed in scenarios of quantum mechanics and relativistic quantum mechanics. In these contexts investigations on the Schrodinger and Dirac equations with mass depending on the position (MDP) has attracted much attention in the literature. Systems endowed with MDP models are useful for the study of many physical problems. In particular, they are used to study the energy density in problems of many bodies, determining the electronic properties of semiconductor heterostructures and also to describe the properties of heterojunctions and quantum dots. In particular, the investigation of relativistic effects it is important for systems containing heavy atoms or doping by heavy ions. For these types of materials, the study of the properties of the Dirac equation, in the case where the mass becomes variable is of great interest. In this paper, we seek for the non-relativistic limit of the Dirac Hamiltonian in the context of a theory of effective mass, through a Foldy-Wouthuysen transformation. We analyse the Dirac equation with mass dependent on the position, in a smooth step shape mass distribution, in non-commutative space (NC). This potential type kink was recently discussed by several authors in the commutative context and now we present our results in the non-commutative context. (author)

  19. Space and time in perceptual causality

    Directory of Open Access Journals (Sweden)

    Benjamin Straube

    2010-04-01

    Full Text Available Inferring causality is a fundamental feature of human cognition that allows us to theorize about and predict future states of the world. Michotte suggested that humans automatically perceive causality based on certain perceptual features of events. However, individual differences in judgments of perceptual causality cast doubt on Michotte’s view. To gain insights in the neural basis of individual difference in the perception of causality, our participants judged causal relationships in animations of a blue ball colliding with a red ball (a launching event while fMRI-data were acquired. Spatial continuity and temporal contiguity were varied parametrically in these stimuli. We did not find consistent brain activation differences between trials judged as caused and those judged as non-caused, making it unlikely that humans have universal instantiation of perceptual causality in the brain. However, participants were slower to respond to and showed greater neural activity for violations of causality, suggesting that humans are biased to expect causal relationships when moving objects appear to interact. Our participants demonstrated considerable individual differences in their sensitivity to spatial and temporal characteristics in perceiving causality. These qualitative differences in sensitivity to time or space in perceiving causality were instantiated in individual differences in activation of the left basal ganglia or right parietal lobe, respectively. Thus, the perception that the movement of one object causes the movement of another is triggered by elemental spatial and temporal sensitivities, which themselves are instantiated in specific distinct neural networks.

  20. Causal reasoning in physics

    CERN Document Server

    Frisch, Mathias

    2014-01-01

    Much has been written on the role of causal notions and causal reasoning in the so-called 'special sciences' and in common sense. But does causal reasoning also play a role in physics? Mathias Frisch argues that, contrary to what influential philosophical arguments purport to show, the answer is yes. Time-asymmetric causal structures are as integral a part of the representational toolkit of physics as a theory's dynamical equations. Frisch develops his argument partly through a critique of anti-causal arguments and partly through a detailed examination of actual examples of causal notions in physics, including causal principles invoked in linear response theory and in representations of radiation phenomena. Offering a new perspective on the nature of scientific theories and causal reasoning, this book will be of interest to professional philosophers, graduate students, and anyone interested in the role of causal thinking in science.

  1. Theories of Causality

    Science.gov (United States)

    Jones, Robert

    2010-03-01

    There are a wide range of views on causality. To some (e.g. Karl Popper) causality is superfluous. Bertrand Russell said ``In advanced science the word cause never occurs. Causality is a relic of a bygone age.'' At the other extreme Rafael Sorkin and L. Bombelli suggest that space and time do not exist but are only an approximation to a reality that is simply a discrete ordered set, a ``causal set.'' For them causality IS reality. Others, like Judea Pearl and Nancy Cartwright are seaking to build a complex fundamental theory of causality (Causality, Cambridge Univ. Press, 2000) Or perhaps a theory of causality is simply the theory of functions. This is more or less my take on causality.

  2. Causality and matter propagation in 3D spin foam quantum gravity

    International Nuclear Information System (INIS)

    Oriti, Daniele; Tlas, Tamer

    2006-01-01

    In this paper we tackle the issue of causality in quantum gravity, in the context of 3d spin foam models. We identify the correct procedure for implementing the causality/orientation dependence restriction that reduces the path integral for BF theory to that of quantum gravity in first order form. We construct explicitly the resulting causal spin foam model. We then add matter degrees of freedom to it and construct a causal spin foam model for 3d quantum gravity coupled to matter fields. Finally, we show that the corresponding spin foam amplitudes admit a natural approximation as the Feynman amplitudes of a noncommutative quantum field theory, with the appropriate Feynman propagators weighting the lines of propagation, and that this effective field theory reduces to the usual quantum field theory in flat space in the no-gravity limit

  3. Causality in Science

    Directory of Open Access Journals (Sweden)

    Cristina Puente Águeda

    2011-10-01

    Full Text Available Causality is a fundamental notion in every field of science. Since the times of Aristotle, causal relationships have been a matter of study as a way to generate knowledge and provide for explanations. In this paper I review the notion of causality through different scientific areas such as physics, biology, engineering, etc. In the scientific area, causality is usually seen as a precise relation: the same cause provokes always the same effect. But in the everyday world, the links between cause and effect are frequently imprecise or imperfect in nature. Fuzzy logic offers an adequate framework for dealing with imperfect causality, so a few notions of fuzzy causality are introduced.

  4. One-loop beta functions for the orientable non-commutative Gross Neveu model TH1"-->

    Science.gov (United States)

    Lakhoua, A.; Vignes-Tourneret, F.; Wallet, J.-C.

    2007-11-01

    We compute at the one-loop order the β-functions for a renormalisable non-commutative analog of the Gross Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this non-commutative field theory exhibits asymptotic freedom for any number of colors. The β-function for the non-commutative counterpart of the Thirring model is found to be non vanishing.

  5. PURE STATE ENTANGLEMENT ENTROPY IN NONCOMMUTATIVE 2D DE SITTER SPACE TIME

    Directory of Open Access Journals (Sweden)

    M.F Ghiti

    2014-12-01

    Full Text Available Using the general modified field equation, a general noncommutative Klein-Gordon equation up to the second order of the noncommutativity parameter is derived in the context of noncommutative 2D De Sitter space-time. Using Bogoliubov coefficients and a special technics called conformal time; the boson-antiboson pair creation density is determined. The Von Neumann boson-antiboson pair creation quantum entanglement entropy is presented to compute the entanglement between the modes created presented.

  6. Dispersion relations for the self-energy in noncommutative field theories

    International Nuclear Information System (INIS)

    Brandt, F.T.; Das, Ashok; Frenkel, J.

    2002-01-01

    We study the IR-UV connection in noncommutative φ 3 theory as well as in noncommutative QED from the point of view of the dispersion relation for self-energy. We show that, although the imaginary part of the self-energy is well behaved as the parameter of noncommutativity vanishes, the real part becomes divergent as a consequence of the high energy behavior of the dispersion integral. Some other interesting features that arise from this analysis are also briefly discussed

  7. Open membranes in a constant C-field background and noncommutative boundary strings

    International Nuclear Information System (INIS)

    Kawamoto, Shoichi; Sasakura, Naoki

    2000-01-01

    We investigate the dynamics of open membrane boundaries in a constant C-field background. We follow the analysis for open strings in a B-field background, and take some approximations. We find that open membrane boundaries do show noncommutativity in this case by explicit calculations. Membrane boundaries are one dimensional strings, so we face a new type of noncommutativity, that is, noncommutative strings. (author)

  8. Pair production of Dirac particles in a d + 1-dimensional noncommutative space-time

    Energy Technology Data Exchange (ETDEWEB)

    Ousmane Samary, Dine [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin); N' Dolo, Emanonfi Elias; Hounkonnou, Mahouton Norbert [University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin)

    2014-11-15

    This work addresses the computation of the probability of fermionic particle pair production in d + 1-dimensional noncommutative Moyal space. Using Seiberg-Witten maps, which establish relations between noncommutative and commutative field variables, up to the first order in the noncommutative parameter θ, we derive the probability density of vacuum-vacuum pair production of Dirac particles. The cases of constant electromagnetic, alternating time-dependent, and space-dependent electric fields are considered and discussed. (orig.)

  9. Realization of Cohen-Glashow very special relativity on noncommutative space-time.

    Science.gov (United States)

    Sheikh-Jabbari, M M; Tureanu, A

    2008-12-31

    We show that the Cohen-Glashow very special relativity (VSR) theory [A. G. Cohen and S. L. Glashow, Phys. Rev. Lett. 97, 021601 (2006)] can be realized as the part of the Poincaré symmetry preserved on a noncommutative Moyal plane with lightlike noncommutativity. Moreover, we show that the three subgroups relevant to VSR can also be realized in the noncommutative space-time setting. For all of these three cases, the noncommutativity parameter theta(mu upsilon) should be lightlike (theta(mu upsilon) theta mu upsilon = 0). We discuss some physical implications of this realization of the Cohen-Glashow VSR.

  10. Reasoning with Causal Cycles

    Science.gov (United States)

    Rehder, Bob

    2017-01-01

    This article assesses how people reason with categories whose features are related in causal cycles. Whereas models based on causal graphical models (CGMs) have enjoyed success modeling category-based judgments as well as a number of other cognitive phenomena, CGMs are only able to represent causal structures that are acyclic. A number of new…

  11. Noncommutative geometry inspired black holes in Rastall gravity

    Energy Technology Data Exchange (ETDEWEB)

    Ma, Meng-Sen [Shanxi Datong University, Institute of Theoretical Physics, Datong (China); Shanxi Datong University, Department of Physics, Datong (China); Zhao, Ren [Shanxi Datong University, Institute of Theoretical Physics, Datong (China)

    2017-09-15

    Under two different metric ansatzes, the noncommutative geometry inspired black holes (NCBH) in the framework of Rastall gravity are derived and analyzed. We consider the fluid-type matter with the Gaussian-distribution smeared mass density. Taking a Schwarzschild-like metric ansatz, it is shown that the noncommutative geometry inspired Schwarzschild black hole (NCSBH) in Rastall gravity, unlike its counterpart in general relativity (GR), is not a regular black hole. It has at most one event horizon. After showing a finite maximal temperature, the black hole will leave behind a point-like massive remnant at zero temperature. Considering a more general metric ansatz and a special equation of state of the matter, we also find a regular NCBH in Rastall gravity, which has a similar geometric structure and temperature to that of NCSBH in GR. (orig.)

  12. Chirality Quantum Phase Transition in Noncommutative Dirac Oscillator

    International Nuclear Information System (INIS)

    Wang Shao-Hua; Hou Yu-Long; Jing Jian; Wang Qing; Long Zheng-Wen

    2014-01-01

    The charged Dirac oscillator on a noncommutative plane coupling to a uniform perpendicular magnetic held is studied in this paper. We map the noncommutative plane to a commutative one by means of Bopp shift and study this problem on the commutative plane. We find that this model can be mapped onto a quantum optics model which contains Anti—Jaynes—Cummings (AJC) or Jaynes—Cummings (JC) interactions when a dimensionless parameter ζ (which is the function of the intensity of the magnetic held) takes values in different regimes. Furthermore, this model behaves as experiencing a chirality quantum phase transition when the dimensionless parameter ζ approaches the critical point. Several evidences of the chirality quantum phase transition are presented. We also study the non-relativistic limit of this model and find that a similar chirality quantum phase transition takes place in its non-relativistic limit. (physics of elementary particles and fields)

  13. Quantum aspects of the noncommutative Sine-Gordon model

    International Nuclear Information System (INIS)

    Kuerkcueoglu

    2007-01-01

    In this talk, I will first present some of the quantum field theoretical aspects of the integrable noncommutative sine-Gordon model proposed in [hep-th/0406065] using standard semi-classical methods. In particular, I will discuss the fluctuations at quadratic order around the static kink solution using the background field method. I will argue that at 0(θ 2 ) the spectrum of fluctuations remains essentially the same as that of the corresponding commutative theory. A brief analysis of one-loop two-point functions will also be presented and it will be followed by some remarks on the obstacles in determining the noncommutativity corrections to the quantum mass of the kink. (author)

  14. Non-commuting variations in mathematics and physics a survey

    CERN Document Server

    Preston, Serge

    2016-01-01

    This text presents and studies the method of so –called noncommuting variations in Variational Calculus. This method was pioneered by Vito Volterra who noticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanics and suggested to modify the basic rule used in Variational Calculus. This book presents a survey of Variational Calculus with non-commutative variations and shows that most basic properties of conventional Euler-Lagrange Equations are, with some modifications, preserved for EL-equations with K-twisted (defined by K)-variations. Most of the book can be understood by readers without strong mathematical preparation (some knowledge of Differential Geometry is necessary). In order to make the text more accessible the definitions and several necessary results in Geometry are presented separately in Appendices I and II Furthermore in Appendix III a short presentation of the Noether Theorem describing the relation between the symmetries of the differential equa...

  15. Dolan Grady relations and noncommutative quasi-exactly solvable systems

    Science.gov (United States)

    Klishevich, Sergey M.; Plyushchay, Mikhail S.

    2003-11-01

    We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the {\\mathfrak{su}}(2) and {\\mathfrak{sl}}(2,{\\bb {R}}) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems.

  16. The shear viscosity of the non-commutative plasma

    International Nuclear Information System (INIS)

    Landsteiner, Karl; Mas, Javier

    2007-01-01

    We compute the shear viscosity of the non-commutative N = 4 super Yang-Mills quantum field theory at strong coupling using the dual supergravity background. Special interest derives from the fact that the background presents an intrinsic anisotropy in space through the distinction of commutative and non-commutative directions. Despite this anisotropy the analysis exhibits the ubiquitous result η/s = 1/4π for two different shear channels. In order to derive this result, we show that the boundary energy momentum tensor must couple to the open string metric. As a byproduct we compute the renormalised holographic energy momentum tensor and show that it coincides with one in the commutative theory

  17. Noncommutative differential forms on the kappa-deformed space

    International Nuclear Information System (INIS)

    Meljanac, Stjepan; Kresic-Juric, Sasa

    2009-01-01

    We construct a differential algebra of forms on the kappa-deformed space. For a given realization of noncommutative coordinates as formal power series in the Weyl algebra we find an infinite family of one-forms and nilpotent exterior derivatives. We derive explicit expressions for the exterior derivative and one-forms in covariant and noncovariant realizations. We also introduce higher order forms and show that the exterior derivative satisfies the graded Leibniz rule. The differential forms are generally not graded commutative, but they satisfy the graded Jacobi identity. We also consider the star-product of classical differential forms. The star-product is well defined if the commutator between the noncommutative coordinates and one-forms is closed in the space of one-forms alone. In addition, we show that in certain realizations the exterior derivative acting on the star-product satisfies the undeformed Leibniz rule.

  18. Stability of a non-commutative Jackiw-Teitelboim gravity

    Energy Technology Data Exchange (ETDEWEB)

    Vassilevich, D.V. [Universitaet Leipzig, Institut fuer Theoretische Physik, Postfach 100 920, Leipzig (Germany); St. Petersburg University, V.A. Fock Institute of Physics, St. Petersburg (Russian Federation); Fresneda, R.; Gitman, D.M. [Sao Paulo Univ. (Brazil). Inst. de Fisica

    2006-07-15

    We start with a non-commutative version of the Jackiw-Teitelboim gravity in two dimensions which has a linear potential for the dilaton fields. We study whether it is possible to deform this model by adding quadratic terms to the potential but preserving the number of gauge symmetries. We find that no such deformation exists (provided one does not twist the gauge symmetries). (orig.)

  19. Semiclassical and quantum motions on the non-commutative plane

    International Nuclear Information System (INIS)

    Baldiotti, M.C.; Gazeau, J.P.; Gitman, D.M.

    2009-01-01

    We study the canonical and the coherent state quantizations of a particle moving in a magnetic field on the non-commutative plane. Using a θ-modified action, we perform the canonical quantization and analyze the gauge dependence of the theory. We compare coherent states quantizations obtained through Malkin-Man'ko states and circular squeezed states. The relation between these states and the 'classical' trajectories is investigated, and we present numerical explorations of some semiclassical quantities.

  20. Semiclassical and quantum motions on the non-commutative plane

    Energy Technology Data Exchange (ETDEWEB)

    Baldiotti, M.C., E-mail: baldiott@fma.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil); Gazeau, J.P., E-mail: gazeau@apc.univ-paris7.f [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil); Gitman, D.M., E-mail: gitman@dfn.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil)

    2009-10-19

    We study the canonical and the coherent state quantizations of a particle moving in a magnetic field on the non-commutative plane. Using a theta-modified action, we perform the canonical quantization and analyze the gauge dependence of the theory. We compare coherent states quantizations obtained through Malkin-Man'ko states and circular squeezed states. The relation between these states and the 'classical' trajectories is investigated, and we present numerical explorations of some semiclassical quantities.

  1. Clifford algebras, noncommutative tori and universal quantum computers

    OpenAIRE

    Vlasov, Alexander Yu.

    2001-01-01

    Recently author suggested [quant-ph/0010071] an application of Clifford algebras for construction of a "compiler" for universal binary quantum computer together with later development [quant-ph/0012009] of the similar idea for a non-binary base. The non-binary case is related with application of some extension of idea of Clifford algebras. It is noncommutative torus defined by polynomial algebraic relations of order l. For l=2 it coincides with definition of Clifford algebra. Here is presente...

  2. Commutative and Non-commutative Parallelogram Geometry: an Experimental Approach

    OpenAIRE

    Bertram, Wolfgang

    2013-01-01

    By "parallelogram geometry" we mean the elementary, "commutative", geometry corresponding to vector addition, and by "trapezoid geometry" a certain "non-commutative deformation" of the former. This text presents an elementary approach via exercises using dynamical software (such as geogebra), hopefully accessible to a wide mathematical audience, from undergraduate students and high school teachers to researchers, proceeding in three steps: (1) experimental geometry, (2) algebra (linear algebr...

  3. Euler Polynomials and Identities for Non-Commutative Operators

    OpenAIRE

    De Angelis, V.; Vignat, C.

    2015-01-01

    Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt, expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, due to J.-C. Pain, links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Fig...

  4. Group theoretical construction of planar noncommutative phase spaces

    Energy Technology Data Exchange (ETDEWEB)

    Ngendakumana, Ancille, E-mail: nancille@yahoo.fr; Todjihoundé, Leonard, E-mail: leonardt@imsp.uac.org [Institut de Mathématiques et des Sciences Physiques (IMSP), Porto-Novo (Benin); Nzotungicimpaye, Joachim, E-mail: kimpaye@kie.ac.rw [Kigali Institute of Education (KIE), Kigali (Rwanda)

    2014-01-15

    Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally abelian extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given.

  5. Group theoretical construction of planar noncommutative phase spaces

    International Nuclear Information System (INIS)

    Ngendakumana, Ancille; Todjihoundé, Leonard; Nzotungicimpaye, Joachim

    2014-01-01

    Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally abelian extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given

  6. Noncommutative geometry inspired Einstein–Gauss–Bonnet black holes

    Science.gov (United States)

    Ghosh, Sushant G.

    2018-04-01

    Low energy limits of a string theory suggests that the gravity action should include quadratic and higher-order curvature terms, in the form of dimensionally continued Gauss–Bonnet densities. Einstein–Gauss–Bonnet is a natural extension of the general relativity to higher dimensions in which the first and second-order terms correspond, respectively, to general relativity and Einstein–Gauss–Bonnet gravity. We obtain five-dimensional (5D) black hole solutions, inspired by a noncommutative geometry, with a static spherically symmetric, Gaussian mass distribution as a source both in the general relativity and Einstein–Gauss–Bonnet gravity cases, and we also analyzes their thermodynamical properties. Owing the noncommutative corrected black hole, the thermodynamic quantities have also been modified, and phase transition is shown to be achievable. The phase transitions for the thermodynamic stability, in both the theories, are characterized by a discontinuity in the specific heat at r_+=rC , with the stable (unstable) branch for r ) rC . The metric of the noncommutative inspired black holes smoothly goes over to the Boulware–Deser solution at large distance. The paper has been appended with a calculation of black hole mass using holographic renormalization.

  7. On Born's deformed reciprocal complex gravitational theory and noncommutative gravity

    International Nuclear Information System (INIS)

    Castro, Carlos

    2008-01-01

    Born's reciprocal relativity in flat spacetimes is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born's theory to the case of curved spacetimes and construct a deformed Born reciprocal general relativity theory in curved spacetimes (without the need to introduce star products) as a local gauge theory of the deformed Quaplectic group that is given by the semi-direct product of U(1,3) with the deformed (noncommutative) Weyl-Heisenberg group corresponding to noncommutative generators [Z a ,Z b ]≠0. The Hermitian metric is complex-valued with symmetric and nonsymmetric components and there are two different complex-valued Hermitian Ricci tensors R μν ,S μν . The deformed Born's reciprocal gravitational action linear in the Ricci scalars R,S with Torsion-squared terms and BF terms is presented. The plausible interpretation of Z μ =E μ a Z a as noncommuting p-brane background complex spacetime coordinates is discussed in the conclusion, where E μ a is the complex vielbein associated with the Hermitian metric G μν =g (μν) +ig [μν] =E μ a E-bar ν b η ab . This could be one of the underlying reasons why string-theory involves gravity

  8. Non-topological non-commutativity in string theory

    International Nuclear Information System (INIS)

    Guttenberg, S.; Herbst, M.; Kreuzer, M.; Rashkov, R.

    2008-01-01

    Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum field theory. Appositely, open string diagrams provided the inspiration for Kontsevich's solution of the long-standing problem of quantization of Poisson geometry by virtue of his formality theorem. In the context of D-brane physics non-commutativity is not limited, however, to the topological sector. We show that non-commutative effective actions still make sense when associativity is lost and establish a generalized Connes-Flato-Sternheimer condition through second order in a derivative expansion. The measure in general curved backgrounds is naturally provided by the Born-Infeld action and reduces to the symplectic measure in the topological limit, but remains non-singular even for degenerate Poisson structures. Analogous superspace deformations by RR-fields are also discussed. (Abstract Copyright [2008], Wiley Periodicals, Inc.)

  9. Causal imprinting in causal structure learning.

    Science.gov (United States)

    Taylor, Eric G; Ahn, Woo-Kyoung

    2012-11-01

    Suppose one observes a correlation between two events, B and C, and infers that B causes C. Later one discovers that event A explains away the correlation between B and C. Normatively, one should now dismiss or weaken the belief that B causes C. Nonetheless, participants in the current study who observed a positive contingency between B and C followed by evidence that B and C were independent given A, persisted in believing that B causes C. The authors term this difficulty in revising initially learned causal structures "causal imprinting." Throughout four experiments, causal imprinting was obtained using multiple dependent measures and control conditions. A Bayesian analysis showed that causal imprinting may be normative under some conditions, but causal imprinting also occurred in the current study when it was clearly non-normative. It is suggested that causal imprinting occurs due to the influence of prior knowledge on how reasoners interpret later evidence. Consistent with this view, when participants first viewed the evidence showing that B and C are independent given A, later evidence with only B and C did not lead to the belief that B causes C. Copyright © 2012 Elsevier Inc. All rights reserved.

  10. Factors Influencing Nonabsolute Indications for Surgery in Patients With Lower Urinary Tract Symptoms Suggestive of Benign Prostatic Hyperplasia: Analysis Using Causal Bayesian Networks

    Directory of Open Access Journals (Sweden)

    Myong Kim

    2014-12-01

    Full Text Available Purpose To identify the factors affecting the surgical decisions of experienced physicians when treating patients with lower urinary tract symptoms that are suggestive of benign prostatic hyperplasia (LUTS/BPH. Methods Patients with LUTS/BPH treated by two physicians between October 2004 and August 2013 were included in this study. The causal Bayesian network (CBN model was used to analyze factors influencing the surgical decisions of physicians and the actual performance of surgery. The accuracies of the established CBN models were verified using linear regression (LR analysis. Results A total of 1,108 patients with LUTS/BPH were analyzed. The mean age and total prostate volume (TPV were 66.2 (±7.3, standard deviation years and 47.3 (±25.4 mL, respectively. Of the total 1,108 patients, 603 (54.4% were treated by physician A and 505 (45.6% were treated by physician B. Although surgery was recommended to 699 patients (63.1%, 589 (53.2% actually underwent surgery. Our CBN model showed that the TPV (R=0.432, treating physician (R=0.370, bladder outlet obstruction (BOO on urodynamic study (UDS (R=0.324, and International Prostate Symptom Score (IPSS question 3 (intermittency; R=0.141 were the factors directly influencing the surgical decision. The transition zone volume (R=0.396, treating physician (R=0.340, and BOO (R=0.300 directly affected the performance of surgery. Compared to the LR model, the area under the receiver operating characteristic curve of the CBN surgical decision model was slightly compromised (0.803 vs. 0.847, P<0.001, whereas that of the actual performance of surgery model was similar (0.801 vs. 0.820, P=0.063 to the LR model. Conclusions The TPV, treating physician, BOO on UDS, and the IPSS item of intermittency were factors that directly influenced decision-making in physicians treating patients with LUTS/BPH.

  11. Granger Causality Testing with Intensive Longitudinal Data.

    Science.gov (United States)

    Molenaar, Peter C M

    2018-06-01

    The availability of intensive longitudinal data obtained by means of ambulatory assessment opens up new prospects for prevention research in that it allows the derivation of subject-specific dynamic networks of interacting variables by means of vector autoregressive (VAR) modeling. The dynamic networks thus obtained can be subjected to Granger causality testing in order to identify causal relations among the observed time-dependent variables. VARs have two equivalent representations: standard and structural. Results obtained with Granger causality testing depend upon which representation is chosen, yet no criteria exist on which this important choice can be based. A new equivalent representation is introduced called hybrid VARs with which the best representation can be chosen in a data-driven way. Partial directed coherence, a frequency-domain statistic for Granger causality testing, is shown to perform optimally when based on hybrid VARs. An application to real data is provided.

  12. Repeated causal decision making.

    Science.gov (United States)

    Hagmayer, York; Meder, Björn

    2013-01-01

    Many of our decisions refer to actions that have a causal impact on the external environment. Such actions may not only allow for the mere learning of expected values or utilities but also for acquiring knowledge about the causal structure of our world. We used a repeated decision-making paradigm to examine what kind of knowledge people acquire in such situations and how they use their knowledge to adapt to changes in the decision context. Our studies show that decision makers' behavior is strongly contingent on their causal beliefs and that people exploit their causal knowledge to assess the consequences of changes in the decision problem. A high consistency between hypotheses about causal structure, causally expected values, and actual choices was observed. The experiments show that (a) existing causal hypotheses guide the interpretation of decision feedback, (b) consequences of decisions are used to revise existing causal beliefs, and (c) decision makers use the experienced feedback to induce a causal model of the choice situation even when they have no initial causal hypotheses, which (d) enables them to adapt their choices to changes of the decision problem. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

  13. On the Lie symmetry group for classical fields in noncommutative space

    Energy Technology Data Exchange (ETDEWEB)

    Pereira, Ricardo Martinho Lima Santiago [Universidade Federal da Bahia (UFBA), BA (Brazil); Instituto Federal da Bahia (IFBA), BA (Brazil); Ressureicao, Caio G. da [Universidade Federal da Bahia (UFBA), BA (Brazil). Inst. de Fisica; Vianna, Jose David M. [Universidade Federal da Bahia (UFBA), BA (Brazil); Universidade de Brasilia (UnB), DF (Brazil)

    2011-07-01

    Full text: An alternative way to include effects of noncommutative geometries in field theory is based on the concept of noncommutativity among degrees of freedom of the studied system. In this context it is reasonable to consider that, in the multiparticle noncommutative quantum mechanics (NCQM), the noncommutativity among degrees of freedom to discrete system with N particles is also verified. Further, an analysis of the classical limit of the single particle NCQM leads to a deformed Newtonian mechanics where the Newton's second law is modified in order to include the noncommutative parameter {theta}{sub {iota}j} and, for a one-dimensional discrete system with N particles, the dynamical evolution of each particle is given by this modified Newton's second law. Hence, applying the continuous limit to this multiparticle classical system it is possible to obtain a noncommutative extension of two -dimensional field theory in a noncommutative space. In the present communication we consider a noncommutative extension of the scalar field obtained from this approach and we analyze the Lie symmetries in order to compare the Lie group of this field with the usual scalar field in the commutative space. (author)

  14. Seiberg–Witten map and quantum phase effects for neutral Dirac particle on noncommutative plane

    Directory of Open Access Journals (Sweden)

    Kai Ma

    2016-05-01

    Full Text Available We provide a new approach to study the noncommutative effects on the neutral Dirac particle with anomalous magnetic or electric dipole moment on the noncommutative plane. The advantages of this approach are demonstrated by investigating the noncommutative corrections on the Aharonov–Casher and He–McKellar–Wilkens effects. This approach is based on the effective U(1 gauge symmetry for the electrodynamics of spin on the two dimensional space. The Seiberg–Witten map for this symmetry is then employed when we study the noncommutative corrections. Because the Seiberg–Witten map preserves the gauge symmetry, the noncommutative corrections can be defined consistently with the ordinary phases. Based on this approach we find the noncommutative corrections on the Aharonov–Casher and He–McKellar–Wilkens phases consist of two terms. The first one depends on the beam particle velocity and consistence with the previous results. However the second term is velocity-independent and then completely new. Therefore our results indicate it is possible to investigate the noncommutative space by using ultra-cold neutron interferometer in which the velocity-dependent term is negligible. Furthermore, both these two terms are proportional to the ratio between the noncommutative parameter θ and the cross section Ae/m of the electrical/magnetic charged line enclosed by the trajectory of beam particles. Therefore the experimental sensitivity can be significantly enhanced by reducing the cross section of the charge line Ae/m.

  15. Relativistic Equations for Spin Particles: What can We Learn from Noncommutativity?

    International Nuclear Information System (INIS)

    Dvoeglazov, V. V.

    2009-01-01

    We derive relativistic equations for charged and neutral spin particles. The approach for higher-spin particles is based on generalizations of the Bargmann-Wigner formalism. Next, we study, what new physical information can give the introduction of non-commutativity. Additional non-commutative parameters can provide a suitable basis for explanation of the origin of mass.

  16. Quadratic algebras and noncommutative integration of Klein-Gordon equations in non-steckel Riemann spaces

    International Nuclear Information System (INIS)

    Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.; Shirokov, I.V.

    1995-01-01

    The method of noncommutative integration of linear partial differential equations is used to solve the Klein-Gordon equations in Riemann space, in the case when the set of noncommutating symmetry operators of this equation for a quadratic algebra consists of one second-order operator and several first-order operators. Solutions that do not permit variable separation are presented

  17. Dirac-Kahler fermion with noncommutative differential forms on a lattice

    International Nuclear Information System (INIS)

    Kanamori, I.; Kawamoto, N.

    2004-01-01

    Noncommutativity between a differential form and a function allows us to define differential operator satisfying Leibniz's rule on a lattice. We propose a new associative Clifford product defined on the lattice by introducing the noncommutative differential forms. We show that this Clifford product naturally leads to the Dirac-Kaehler fermion on the lattice

  18. Quantum Field Theory with a Minimal Length Induced from Noncommutative Space

    International Nuclear Information System (INIS)

    Lin Bing-Sheng; Chen Wei; Heng Tai-Hua

    2014-01-01

    From the inspection of noncommutative quantum mechanics, we obtain an approximate equivalent relation for the energy dependence of the Planck constant in the noncommutative space, which means a minimal length of the space. We find that this relation is reasonable and it can inherit the main properties of the noncommutative space. Based on this relation, we derive the modified Klein—Gordon equation and Dirac equation. We investigate the scalar field and ϕ 4 model and then quantum electrodynamics in our theory, and derive the corresponding Feynman rules. These results may be considered as reasonable approximations to those of noncommutative quantum field theory. Our theory also shows a connection between the space with a minimal length and the noncommutative space. (physics of elementary particles and fields)

  19. Open Wilson lines and generalized star product in noncommutative scalar field theories

    International Nuclear Information System (INIS)

    Kiem, Youngjai; Sato, Haru-Tada; Rey, Soo-Jong; Yee, Jung-Tay

    2002-01-01

    Open Wilson line operators and a generalized star product have been studied extensively in noncommutative gauge theories. We show that they also show up in noncommutative scalar field theories as universal structures. We first point out that the dipole picture of noncommutative geometry provides an intuitive argument for the robustness of the open Wilson lines and generalized star products therein. We calculate the one-loop effective action of noncommutative scalar field theory with a cubic self-interaction and show explicitly that the generalized star products arise in the nonplanar part. It is shown that, at the low-energy, large noncommutativity limit, the nonplanar part is expressible solely in terms of the scalar open Wilson line operator and descendants

  20. On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs

    Energy Technology Data Exchange (ETDEWEB)

    Amini, Nina H. [Stanford University, Edward L. Ginzton Laboratory, Stanford, CA (United States); CNRS, Laboratoire des Signaux et Systemes (L2S) CentraleSupelec, Gif-sur-Yvette (France); Miao, Zibo; Pan, Yu; James, Matthew R. [Australian National University, ARC Centre for Quantum Computation and Communication Technology, Research School of Engineering, Canberra, ACT (Australia); Mabuchi, Hideo [Stanford University, Edward L. Ginzton Laboratory, Stanford, CA (United States)

    2015-12-15

    The purpose of this paper is to study the problem of generalizing the Belavkin-Kalman filter to the case where the classical measurement signal is replaced by a fully quantum non-commutative output signal. We formulate a least mean squares estimation problem that involves a non-commutative system as the filter processing the non-commutative output signal. We solve this estimation problem within the framework of non-commutative probability. Also, we find the necessary and sufficient conditions which make these non-commutative estimators physically realizable. These conditions are restrictive in practice. (orig.)

  1. The pivotal role of causality in local quantum physics

    International Nuclear Information System (INIS)

    Schroer, Bert

    1999-04-01

    In this article an attempt is made to present very recent conceptual and computational developments in QFT as new manifestation of old well established physical principles. The vehicle for converting the quantum-algebraic aspects of local quantum physics into more classical geometric structures is the modular theory of Tomita. As the above named laureate together with his collaborator showed for the first time, in sufficient generality, its use in physics goes through Einstein causality. This line of research recently gained momentum when it was realized that it is not only of great structural and conceptual innovative power (see section 4), but also promises a new computational road into nonperturbative QFT (section 5) which, picturesquely speaking, enters the subject on the extreme opposite (noncommutative) side relative to (Lagrangian) quantization. (author)

  2. On the UV renormalizability of noncommutative field theories

    International Nuclear Information System (INIS)

    Sarkar, Swarnendu

    2002-01-01

    UV/IR mixing is one of the most important features of noncommutative field theories. As a consequence of this coupling of the UV and IR sectors, the configuration of fields at the zero momentum limit in these theories is a very singular configuration. We show that the renormalization conditions set at a particular momentum configuration with a fixed number of zero momenta, renormalizes the Green's functions for any general momenta only when this configuration has same set of zero momenta. Therefore only when renormalization conditions are set at a point where all the external momenta are nonzero, the quantum theory is renormalizable for all values of nonzero momentum. This arises as a result of different scaling behaviors of Green's functions with respect to the UV cutoff (Λ) for configurations containing different set of zero momenta. We study this in the noncommutative φ 4 theory and analyse similar results for the Gross-Neveu model at one loop level. We next show this general feature using Wilsonian RG of Polchinski in the globally O(N) symmetric scalar theory and prove the renormalizability of the theory to all orders with an infrared cutoff. In the context of spontaneous symmetry breaking (SSB) in noncommutative scalar theory, it is essential to note the different scaling behaviors of Green's functions with respect to Λ for different set of zero momenta configurations. We show that in the broken phase of the theory the Ward identities are satisfied to all orders only when one keeps an infrared regulator by shifting to a nonconstant vacuum. (author)

  3. Noncommutativity and Duality through the Symplectic Embedding Formalism

    Directory of Open Access Journals (Sweden)

    Everton M.C. Abreu

    2010-07-01

    Full Text Available This work is devoted to review the gauge embedding of either commutative and noncommutative (NC theories using the symplectic formalism framework. To sum up the main features of the method, during the process of embedding, the infinitesimal gauge generators of the gauge embedded theory are easily and directly chosen. Among other advantages, this enables a greater control over the final Lagrangian and brings some light on the so-called ''arbitrariness problem''. This alternative embedding formalism also presents a way to obtain a set of dynamically dual equivalent embedded Lagrangian densities which is obtained after a finite number of steps in the iterative symplectic process, oppositely to the result proposed using the BFFT formalism. On the other hand, we will see precisely that the symplectic embedding formalism can be seen as an alternative and an efficient procedure to the standard introduction of the Moyal product in order to produce in a natural way a NC theory. In order to construct a pedagogical explanation of the method to the nonspecialist we exemplify the formalism showing that the massive NC U(1 theory is embedded in a gauge theory using this alternative systematic path based on the symplectic framework. Further, as other applications of the method, we describe exactly how to obtain a Lagrangian description for the NC version of some systems reproducing well known theories. Naming some of them, we use the procedure in the Proca model, the irrotational fluid model and the noncommutative self-dual model in order to obtain dual equivalent actions for these theories. To illustrate the process of noncommutativity introduction we use the chiral oscillator and the nondegenerate mechanics.

  4. Noncommutative Geometry in M-Theory and Conformal Field Theory

    Energy Technology Data Exchange (ETDEWEB)

    Morariu, Bogdan [Univ. of California, Berkeley, CA (United States)

    1999-05-01

    In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of Uq(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Funq (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.

  5. Noncommutative Geometry in M-Theory and Conformal Field Theory

    International Nuclear Information System (INIS)

    Morariu, Bogdan

    1999-01-01

    In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U q (SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun q (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models

  6. Space-Time Diffeomorphisms in Noncommutative Gauge Theories

    Directory of Open Access Journals (Sweden)

    L. Román Juarez

    2008-07-01

    Full Text Available In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007, 10367–10382] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchar K.V., Ann. Physics 164 (1985, 288–315, 316–333]. Nonetheless, such an homomorphic mapping can be recuperated by first modifying the original action and then adding additional constraints in the formalism in order to retrieve the original theory, as shown by Kuchar and Stone for the case of the parametrized Maxwell field in [Kuchar K.V., Stone S.L., Classical Quantum Gravity 4 (1987, 319–328]. Making use of a combination of all of these ideas, we are therefore able to apply our canonical reparametrization approach in order to derive the deformed Lie algebra of the noncommutative space-time diffeomorphisms as well as to consider how gauge transformations act on the twisted algebras of gauge and particle fields. Thus, hopefully, adding clarification on some outstanding issues in the literature concerning the symmetries for gauge theories in noncommutative space-times.

  7. Repeated Causal Decision Making

    Science.gov (United States)

    Hagmayer, York; Meder, Bjorn

    2013-01-01

    Many of our decisions refer to actions that have a causal impact on the external environment. Such actions may not only allow for the mere learning of expected values or utilities but also for acquiring knowledge about the causal structure of our world. We used a repeated decision-making paradigm to examine what kind of knowledge people acquire in…

  8. Viscous causal cosmologies

    International Nuclear Information System (INIS)

    Novello, M.; Salim, J.M.; Torres, J.; Oliveira, H.P. de

    1989-01-01

    A set of spatially homogeneous and isotropic cosmological geometries generated by a class of non-perfect is investigated fluids. The irreversibility if this system is studied in the context of causal thermodynamics which provides a useful mechanism to conform to the non-violation of the causal principle. (author) [pt

  9. Causal Analysis After Haavelmo

    Science.gov (United States)

    Heckman, James; Pinto, Rodrigo

    2014-01-01

    Haavelmo's seminal 1943 and 1944 papers are the first rigorous treatment of causality. In them, he distinguished the definition of causal parameters from their identification. He showed that causal parameters are defined using hypothetical models that assign variation to some of the inputs determining outcomes while holding all other inputs fixed. He thus formalized and made operational Marshall's (1890) ceteris paribus analysis. We embed Haavelmo's framework into the recursive framework of Directed Acyclic Graphs (DAGs) used in one influential recent approach to causality (Pearl, 2000) and in the related literature on Bayesian nets (Lauritzen, 1996). We compare the simplicity of an analysis of causality based on Haavelmo's methodology with the complex and nonintuitive approach used in the causal literature of DAGs—the “do-calculus” of Pearl (2009). We discuss the severe limitations of DAGs and in particular of the do-calculus of Pearl in securing identification of economic models. We extend our framework to consider models for simultaneous causality, a central contribution of Haavelmo. In general cases, DAGs cannot be used to analyze models for simultaneous causality, but Haavelmo's approach naturally generalizes to cover them. PMID:25729123

  10. Causality in Classical Electrodynamics

    Science.gov (United States)

    Savage, Craig

    2012-01-01

    Causality in electrodynamics is a subject of some confusion, especially regarding the application of Faraday's law and the Ampere-Maxwell law. This has led to the suggestion that we should not teach students that electric and magnetic fields can cause each other, but rather focus on charges and currents as the causal agents. In this paper I argue…

  11. Noncommutative spectral geometry, Bogoliubov transformations and neutrino oscillations

    International Nuclear Information System (INIS)

    Gargiulo, Maria Vittoria; Vitiello, Giuseppe; Sakellariadou, Mairi

    2015-01-01

    In this report we show that neutrino mixing is intrinsically contained in Connes’ noncommutatives pectral geometry construction, thanks to the introduction of the doubling of algebra, which is connected to the Bogoliubov transformation. It is known indeed that these transformations are responsible for the mixing, turning the mass vacuum state into the flavor vacuum state, in such a way that mass and flavor vacuum states are not unitary equivalent. There is thus a red thread that binds the doubling of algebra of Connes’ model to the neutrino mixing. (paper)

  12. Strong limit theorems in noncommutative L2-spaces

    CERN Document Server

    Jajte, Ryszard

    1991-01-01

    The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.

  13. Non-commutative geometry inspired charged black holes

    International Nuclear Information System (INIS)

    Ansoldi, Stefano; Nicolini, Piero; Smailagic, Anais; Spallucci, Euro

    2007-01-01

    We find a new, non-commutative geometry inspired, solution of the coupled Einstein-Maxwell field equations describing a variety of charged, self-gravitating objects, including extremal and non-extremal black holes. The metric smoothly interpolates between de Sitter geometry, at short distance, and Reissner-Nordstrom geometry far away from the origin. Contrary to the ordinary Reissner-Nordstrom spacetime there is no curvature singularity in the origin neither 'naked' nor shielded by horizons. We investigate both Hawking process and pair creation in this new scenario

  14. Noncommutative configuration space. Classical and quantum mechanical aspects

    OpenAIRE

    Vanhecke, F. J.; Sigaud, C.; da Silva, A. R.

    2005-01-01

    In this work we examine noncommutativity of position coordinates in classical symplectic mechanics and its quantisation. In coordinates $\\{q^i,p_k\\}$ the canonical symplectic two-form is $\\omega_0=dq^i\\wedge dp_i$. It is well known in symplectic mechanics {\\bf\\cite{Souriau,Abraham,Guillemin}} that the interaction of a charged particle with a magnetic field can be described in a Hamiltonian formalism without a choice of a potential. This is done by means of a modified symplectic two-form $\\ome...

  15. Samples of noncommutative products in certain differential equations

    International Nuclear Information System (INIS)

    Legare, M

    2010-01-01

    A set of associative noncommutative products is considered in different differential equations of the ordinary and partial types. A method of separation of variables is considered for a large set of those systems. The products involved include for example some * products and some products based on Nijenhuis tensors, which are embedded in the differential equations of the Laplace/Poisson, Lax and Schroedinger styles. A comment on the *-products of Reshetikhin-Jambor-Sykora type is also given in relation to *-products of Vey type.

  16. Can non-commutativity resolve the big-bang singularity?

    Energy Technology Data Exchange (ETDEWEB)

    Maceda, M.; Madore, J. [Laboratoire de Physique Theorique, Universite de Paris-Sud, Batiment 211, 91405, Orsay (France); Manousselis, P. [Department of Engineering Sciences, University of Patras, 26110, Patras (Greece); Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens (Greece); Zoupanos, G. [Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens (Greece); Theory Division, CERN, 1211, Geneva 23 (Switzerland)

    2004-08-01

    A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has non-commutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a modification of the Kasner metric is constructed which is commutative only at large time scales. At small time scales, near the singularity, the commutation relations among the space coordinates diverge. We interpret this result as meaning that the singularity has been completely delocalized. (orig.)

  17. Quantum thetas on noncommutative Td with general embeddings

    International Nuclear Information System (INIS)

    Chang-Young, Ee; Kim, Hoil

    2008-01-01

    In this paper, we construct quantum theta functions over noncommutative T d with general embeddings. Manin has constructed quantum theta functions from the lattice embedding into vector space x finite group. We extend Manin's construction of quantum thetas to the case of general embedding of vector space x lattice x torus. It turns out that only for the vector space part of the embedding there exists the holomorphic theta vector, while for the lattice part there does not. Furthermore, the so-called quantum translations from embedding into the lattice part become non-additive, while those from the vector space part are additive

  18. Quantum Thetas on Noncommutative T^d with General Embeddings

    OpenAIRE

    Chang-Young, Ee; Kim, Hoil

    2007-01-01

    In this paper we construct quantum theta functions over noncommutative T^d with general embeddings. Manin has constructed quantum theta functions from the lattice embedding into vector space x finite group. We extend Manin's construction of quantum thetas to the case of general embedding of vector space x lattice x torus. It turns out that only for the vector space part of the embedding there exists the holomorphic theta vector, while for the lattice part there does not. Furthermore, the so-c...

  19. Non-commutative field theory with twistor-like coordinates

    International Nuclear Information System (INIS)

    Taylor, Tomasz R.

    2007-01-01

    We consider quantum field theory in four-dimensional Minkowski spacetime, with the position coordinates represented by twistors instead of the usual world-vectors. Upon imposing canonical commutation relations between twistors and dual twistors, quantum theory of fields described by non-holomorphic functions of twistor variables becomes manifestly non-commutative, with Lorentz symmetry broken by a time-like vector. We discuss the free field propagation and its impact on the short- and long-distance behavior of physical amplitudes in perturbation theory. In the ultraviolet limit, quantum field theories in twistor space are generically less divergent than their commutative counterparts. Furthermore, there is no infrared-ultraviolet mixing problem

  20. Causality in Europeanization Research

    DEFF Research Database (Denmark)

    Lynggaard, Kennet

    2012-01-01

    to develop discursive institutional analytical frameworks and something that comes close to the formulation of hypothesis on the effects of European Union (EU) policies and institutions on domestic change. Even if these efforts so far do not necessarily amount to substantive theories or claims of causality......Discourse analysis as a methodology is perhaps not readily associated with substantive causality claims. At the same time the study of discourses is very much the study of conceptions of causal relations among a set, or sets, of agents. Within Europeanization research we have seen endeavours......, it suggests that discourse analysis and the study of causality are by no means opposites. The study of Europeanization discourses may even be seen as an essential step in the move towards claims of causality in Europeanization research. This chapter deals with the question of how we may move from the study...

  1. Agency, time and causality

    Directory of Open Access Journals (Sweden)

    Thomas eWidlok

    2014-11-01

    Full Text Available Cognitive Scientists interested in causal cognition increasingly search for evidence from non-WEIRD people but find only very few cross-cultural studies that specifically target causal cognition. This article suggests how information about causality can be retrieved from ethnographic monographs, specifically from ethnographies that discuss agency and concepts of time. Many apparent cultural differences with regard to causal cognition dissolve when cultural extensions of agency and personhood to non-humans are taken into account. At the same time considerable variability remains when we include notions of time, linearity and sequence. The article focuses on ethnographic case studies from Africa but provides a more general perspective on the role of ethnography in research on the diversity and universality of causal cognition.

  2. Non-Causal Computation

    Directory of Open Access Journals (Sweden)

    Ämin Baumeler

    2017-07-01

    Full Text Available Computation models such as circuits describe sequences of computation steps that are carried out one after the other. In other words, algorithm design is traditionally subject to the restriction imposed by a fixed causal order. We address a novel computing paradigm beyond quantum computing, replacing this assumption by mere logical consistency: We study non-causal circuits, where a fixed time structure within a gate is locally assumed whilst the global causal structure between the gates is dropped. We present examples of logically consistent non-causal circuits outperforming all causal ones; they imply that suppressing loops entirely is more restrictive than just avoiding the contradictions they can give rise to. That fact is already known for correlations as well as for communication, and we here extend it to computation.

  3. Explaining quantum correlations through evolution of causal models

    Science.gov (United States)

    Harper, Robin; Chapman, Robert J.; Ferrie, Christopher; Granade, Christopher; Kueng, Richard; Naoumenko, Daniel; Flammia, Steven T.; Peruzzo, Alberto

    2017-04-01

    We propose a framework for the systematic and quantitative generalization of Bell's theorem using causal networks. We first consider the multiobjective optimization problem of matching observed data while minimizing the causal effect of nonlocal variables and prove an inequality for the optimal region that both strengthens and generalizes Bell's theorem. To solve the optimization problem (rather than simply bound it), we develop a genetic algorithm treating as individuals causal networks. By applying our algorithm to a photonic Bell experiment, we demonstrate the trade-off between the quantitative relaxation of one or more local causality assumptions and the ability of data to match quantum correlations.

  4. Causality and headache triggers

    Science.gov (United States)

    Turner, Dana P.; Smitherman, Todd A.; Martin, Vincent T.; Penzien, Donald B.; Houle, Timothy T.

    2013-01-01

    Objective The objective of this study was to explore the conditions necessary to assign causal status to headache triggers. Background The term “headache trigger” is commonly used to label any stimulus that is assumed to cause headaches. However, the assumptions required for determining if a given stimulus in fact has a causal-type relationship in eliciting headaches have not been explicated. Methods A synthesis and application of Rubin’s Causal Model is applied to the context of headache causes. From this application the conditions necessary to infer that one event (trigger) causes another (headache) are outlined using basic assumptions and examples from relevant literature. Results Although many conditions must be satisfied for a causal attribution, three basic assumptions are identified for determining causality in headache triggers: 1) constancy of the sufferer; 2) constancy of the trigger effect; and 3) constancy of the trigger presentation. A valid evaluation of a potential trigger’s effect can only be undertaken once these three basic assumptions are satisfied during formal or informal studies of headache triggers. Conclusions Evaluating these assumptions is extremely difficult or infeasible in clinical practice, and satisfying them during natural experimentation is unlikely. Researchers, practitioners, and headache sufferers are encouraged to avoid natural experimentation to determine the causal effects of headache triggers. Instead, formal experimental designs or retrospective diary studies using advanced statistical modeling techniques provide the best approaches to satisfy the required assumptions and inform causal statements about headache triggers. PMID:23534872

  5. Causality re-established.

    Science.gov (United States)

    D'Ariano, Giacomo Mauro

    2018-07-13

    Causality has never gained the status of a 'law' or 'principle' in physics. Some recent literature has even popularized the false idea that causality is a notion that should be banned from theory. Such misconception relies on an alleged universality of the reversibility of the laws of physics, based either on the determinism of classical theory, or on the multiverse interpretation of quantum theory, in both cases motivated by mere interpretational requirements for realism of the theory. Here, I will show that a properly defined unambiguous notion of causality is a theorem of quantum theory, which is also a falsifiable proposition of the theory. Such a notion of causality appeared in the literature within the framework of operational probabilistic theories. It is a genuinely theoretical notion, corresponding to establishing a definite partial order among events, in the same way as we do by using the future causal cone on Minkowski space. The notion of causality is logically completely independent of the misidentified concept of 'determinism', and, being a consequence of quantum theory, is ubiquitous in physics. In addition, as classical theory can be regarded as a restriction of quantum theory, causality holds also in the classical case, although the determinism of the theory trivializes it. I then conclude by arguing that causality naturally establishes an arrow of time. This implies that the scenario of the 'block Universe' and the connected 'past hypothesis' are incompatible with causality, and thus with quantum theory: they are both doomed to remain mere interpretations and, as such, are not falsifiable, similar to the hypothesis of 'super-determinism'.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

  6. A non-commutative formula for the isotropic magneto-electric response

    International Nuclear Information System (INIS)

    Leung, Bryan; Prodan, Emil

    2013-01-01

    A non-commutative formula for the isotropic magneto-electric response of disordered insulators under magnetic fields is derived using the methods of non-commutative geometry. Our result follows from an explicit evaluation of the Ito derivative with respect to the magnetic field of the non-commutative formula for the electric polarization reported in Schulz-Baldes and Teufel (2012 arXiv:1201.4812v1). The quantization, topological invariance and connection to a second Chern number of the magneto-electric response are discussed in the context of three-dimensional, disordered, time-reversal or inversion symmetric topological insulators. (paper)

  7. Non-commutative gauge Gravity: Second- order Correction and Scalar Particles Creation

    International Nuclear Information System (INIS)

    Zaim, S.

    2009-01-01

    A noncommutative gauge theory for a charged scalar field is constructed. The invariance of this model under local Poincare and general coordinate transformations is verified. Using the general modified field equation, a general Klein-Gordon equation up to the second order of the noncommu- tativity parameter is derived. As an application, we choose the Bianchi I universe. Using the Seiberg-Witten maps, the deformed noncommutative metric is obtained and a particle production process is studied. It is shown that the noncommutativity plays the same role as an electric field, gravity and chemical potential.

  8. On the classical dynamics of charges in non-commutative QED

    International Nuclear Information System (INIS)

    Fatollahi, A.H.; Mohammadzadeh, H.

    2004-01-01

    Following Wong's approach to formulating the classical dynamics of charged particles in non-Abelian gauge theories, we derive the classical equations of motion of a charged particle in U(1) gauge theory on non-commutative space, the so-called non-commutative QED. In the present use of the procedure, it is observed that the definition of the mechanical momenta should be modified. The derived equations of motion manifest the previous statement about the dipole behavior of the charges in non-commutative space. (orig.)

  9. Statistical mechanics of free particles on space with Lie-type noncommutativity

    Energy Technology Data Exchange (ETDEWEB)

    Shariati, Ahmad; Khorrami, Mohammad; Fatollahi, Amir H, E-mail: shariati@mailaps.or, E-mail: mamwad@mailaps.or, E-mail: ahfatol@gmail.co [Department of Physics, Alzahra University, Tehran 1993891167 (Iran, Islamic Republic of)

    2010-07-16

    Effects of Lie-type noncommutativity on thermodynamic properties of a system of free identical particles are investigated. A definition for finite volume of the configuration space is given, and the grandcanonical partition function in the thermodynamic limit is calculated. Two possible definitions for the pressure are discussed, which are equivalent when the noncommutativity vanishes. The thermodynamic observables are extracted from the partition function. Different limits are discussed where either the noncommutativity or the quantum effects are important. Finally, specific cases are discussed where the group is SU(2) or SO(3), and the partition function of a nondegenerate gas is calculated.

  10. Loop calculations for the non-commutative U*(1) gauge field model with oscillator term

    International Nuclear Information System (INIS)

    Blaschke, Daniel N.; Grosse, Harald; Kronberger, Erwin; Schweda, Manfred; Wohlgenannt, Michael

    2010-01-01

    Motivated by the success of the non-commutative scalar Grosse-Wulkenhaar model, a non-commutative U * (1) gauge field theory including an oscillator-like term in the action has been put forward in (Blaschke et al. in Europhys. Lett. 79:61002, 2007). The aim of the current work is to analyze whether that action can lead to a fully renormalizable gauge model on non-commutative Euclidean space. In a first step, explicit one-loop graph computations are hence presented, and their results as well as necessary modifications of the action are successively discussed. (orig.)

  11. Noncommutative Gröbner bases and filtered-graded transfer

    CERN Document Server

    Li, Huishi

    2002-01-01

    This self-contained monograph is the first to feature the intersection of the structure theory of noncommutative associative algebras and the algorithmic aspect of Groebner basis theory. A double filtered-graded transfer of data in using noncommutative Groebner bases leads to effective exploitation of the solutions to several structural-computational problems, e.g., an algorithmic recognition of quadric solvable polynomial algebras, computation of GK-dimension and multiplicity for modules, and elimination of variables in noncommutative setting. All topics included deal with algebras of (q-)differential operators as well as some other operator algebras, enveloping algebras of Lie algebras, typical quantum algebras, and many of their deformations.

  12. Non-commutative multiple-valued logic algebras

    CERN Document Server

    Ciungu, Lavinia Corina

    2014-01-01

    This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects.   A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing.   Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.

  13. Moyal noncommutative integrability and the Burgers-KdV mapping

    International Nuclear Information System (INIS)

    Sedra, M.B.

    2005-12-01

    The Moyal momentum algebra, is once again used to discuss some important aspects of NC integrable models and 2d conformal field theories. Among the results presented, we set up algebraic structures and makes useful convention notations leading to extract non trivial properties of the Moyal momentum algebra. We study also the Lax pair building mechanism for particular examples namely, the noncommutative KdV and Burgers systems. We show in a crucial step that these two systems are mapped to each other through the following crucial mapping ∂ t 2 → ∂ t 3 ≡ ∂ t 2 ∂ x + α∂ x 3 . This makes a strong constraint on the NC Burgers system which corresponds to linearizing its associated differential equation. From the CFT's point of view, this constraint equation is nothing but the analogue of the conservation law of the conformal current. We believe that the considered mapping might help to bring new insights towards understanding the integrability of noncommutative 2d-systems. (author)

  14. A View on Optimal Transport from Noncommutative Geometry

    Directory of Open Access Journals (Sweden)

    Francesco D'Andrea

    2010-07-01

    Full Text Available We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry. Starting from a remark of Rieffel on compact manifolds, we first show that on any - i.e. non-necessary compact - complete Riemannian spin manifolds, the two distances coincide. Then, on convex manifolds in the sense of Nash embedding, we provide some natural upper and lower bounds to the distance between any two probability distributions. Specializing to the Euclidean space R^n, we explicitly compute the distance for a particular class of distributions generalizing Gaussian wave packet. Finally we explore the analogy between the spectral and the Wasserstein distances in the noncommutative case, focusing on the standard model and the Moyal plane. In particular we point out that in the two-sheet space of the standard model, an optimal-transport interpretation of the metric requires a cost function that does not vanish on the diagonal. The latest is similar to the cost function occurring in the relativistic heat equation.

  15. Noncommutative unification of general relativity and quantum mechanics

    International Nuclear Information System (INIS)

    Heller, Michael; Pysiak, Leszek; Sasin, Wieslaw

    2005-01-01

    We present a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry is developed in terms of a noncommutative algebra A which is defined on a transformation groupoid Γ given by the action of a noncompact group G on the total space E of a principal fiber bundle over space-time M. The case is important since to obtain physical effects predicted by the model we should assume that G is a Lorentz group or some of its representations. We show that the generalized Einstein equation of the model has the form of the eigenvalue equation for the generalized Ricci operator, and all relevant operators in the quantum sector of the model are random operators; we study their dynamics. We also show that the model correctly reproduces general relativity and the usual quantum mechanics. It is interesting that the latter is recovered by performing the measurement of any observable. In the act of such a measurement the model 'collapses' to the usual quantum mechanics

  16. Bootstrapping non-commutative gauge theories from L∞ algebras

    Science.gov (United States)

    Blumenhagen, Ralph; Brunner, Ilka; Kupriyanov, Vladislav; Lüst, Dieter

    2018-05-01

    Non-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L∞ algebra, that governs not only the action of the symmetries but also the dynamics of the theory. Our approach is well motivated from string theory. We recall that such field theories arise in the context of branes in WZW models and briefly comment on its appearance for integrable deformations of AdS5 sigma models. For the SU(2) WZW model, we show that the earlier proposed matrix valued gauge theory on the fuzzy 2-sphere can be bootstrapped via an L∞ algebra. We then apply this approach to the construction of non-commutative Chern-Simons and Yang-Mills theories on flat and curved backgrounds with non-constant NC-structure. More concretely, up to the second order, we demonstrate how derivative and curvature corrections to the equations of motion can be bootstrapped in an algebraic way from the L∞ algebra. The appearance of a non-trivial A∞ algebra is discussed, as well.

  17. Tachyons and causal paradoxes

    International Nuclear Information System (INIS)

    Maund, J.B.

    1979-01-01

    Although the existence of tachyons is not ruled out by special relativity, it appears that causal paradoxes will arise if there are tachyons. The usual solutions to these paradoxes employ some form of the reinterpretation principle. In this paper it is argued first that, the principle is incoherent, second, that even if it is not, some causal paradoxes remain, and third, the most plausible ''solution,'' which appeals to boundary conditions of the universe, will conflict with special relativity

  18. Dynamics and causality constraints

    International Nuclear Information System (INIS)

    Sousa, Manoelito M. de

    2001-04-01

    The physical meaning and the geometrical interpretation of causality implementation in classical field theories are discussed. Causality in field theory are kinematical constraints dynamically implemented via solutions of the field equation, but in a limit of zero-distance from the field sources part of these constraints carries a dynamical content that explains old problems of classical electrodynamics away with deep implications to the nature of physicals interactions. (author)

  19. Late time acceleration in a non-commutative model of modified cosmology

    Energy Technology Data Exchange (ETDEWEB)

    Malekolkalami, B., E-mail: b.malakolkalami@uok.ac.ir [Department of Physics, University of Kurdistan, Pasdaran St., Sanandaj (Iran, Islamic Republic of); Atazadeh, K., E-mail: atazadeh@azaruniv.ac.ir [Department of Physics, Azarbaijan Shahid Madani University, 53714-161, Tabriz (Iran, Islamic Republic of); Vakili, B., E-mail: b-vakili@iauc.ac.ir [Department of Physics, Central Tehran Branch, Islamic Azad University, Tehran (Iran, Islamic Republic of)

    2014-12-12

    We investigate the effects of non-commutativity between the position–position, position–momentum and momentum–momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such non-commutativity results in a Moyal Poisson algebra between the phase space variables in which the product law between the functions is of the kind of an α-deformed product. We then transform the variables in such a way that the Poisson brackets between the dynamical variables take the form of a usual Poisson bracket but this time with a noncommutative structure. For a power law expression for the function of the Ricci scalar with which the action of the gravity model is modified, the exact solutions in the commutative and noncommutative cases are presented and compared. In terms of these solutions we address the issue of the late time acceleration in cosmic evolution.

  20. Beyond the Standard Model with noncommutative geometry, strolling towards quantum gravity

    International Nuclear Information System (INIS)

    Martinetti, Pierre

    2015-01-01

    Noncommutative geometry in its many incarnations appears at the crossroad of many researches in theoretical and mathematical physics: from models of quantum spacetime(with or without breaking of Lorentz symmetry) to loop gravity and string theory, from early considerations on UV-divergenciesin quantum field theory to recent models of gauge theories on noncommutatives pacetime, from Connes description of the standard model of elementary particles to recent Pati-Salam like extensions. We list several of these applications, emphasizing also the original point of view brought by noncommutative geometry on the nature of time. This text serves as an introduction to the volume of proceedings of the parallel session “Noncommutative geometry and quantum gravity”, as a part of the conference “Conceptual and technical challenges in quantum gravity” organized at the University of Rome La Sapienza sin September 2014. (paper)

  1. Remarks on the formulation of quantum mechanics on noncommutative phase spaces

    International Nuclear Information System (INIS)

    Muthukumar, Balasundaram

    2007-01-01

    We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and also with canonically conjugate momenta. With a postulated normalized distribution function in the quantum domain, the square of the Dirac delta density distribution in the classical case is properly realised in noncommutative phase space and it serves as the quantum condition. With only these inputs, we pull out the entire formalisms of noncommutative quantum mechanics in phase space and in Hilbert space, and elegantly establish the link between classical and quantum formalisms and between Hilbert space and phase space formalisms of noncommutative quantum mechanics. Also, we show that the distribution function in this case possesses 'twisted' Galilean symmetry

  2. Noncommutative o*(N) and usp*(2N) algebras and the corresponding gauge field theories

    International Nuclear Information System (INIS)

    Bars, I.; Sheikh-Jabbari, M.M.; Vasiliev, M.A.

    2001-03-01

    The extension of the noncommutative u * (N) Lie algebra to noncommutative orthogonal and symplectic Lie algebras is studied. Using an anti-automorphism of the star-matrix algebra, we show that the u * (N) can consistently be restricted to o * (N) and usp * (N) algebras that have new mathematical structures. We give explicit fundamental matrix representations of these algebras, through which the formulation for the corresponding noncommutative gauge field theories are obtained. In addition, we present a D-brane configuration with an orientifold which realizes geometrically our algebraic construction, thus embedding the new noncommutative gauge theories in superstring theory in the presence of a constant background magnetic field. Some algebraic generalizations that may have applications in other areas of physics are also discussed. (author)

  3. Late time acceleration in a non-commutative model of modified cosmology

    International Nuclear Information System (INIS)

    Malekolkalami, B.; Atazadeh, K.; Vakili, B.

    2014-01-01

    We investigate the effects of non-commutativity between the position–position, position–momentum and momentum–momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such non-commutativity results in a Moyal Poisson algebra between the phase space variables in which the product law between the functions is of the kind of an α-deformed product. We then transform the variables in such a way that the Poisson brackets between the dynamical variables take the form of a usual Poisson bracket but this time with a noncommutative structure. For a power law expression for the function of the Ricci scalar with which the action of the gravity model is modified, the exact solutions in the commutative and noncommutative cases are presented and compared. In terms of these solutions we address the issue of the late time acceleration in cosmic evolution

  4. Metamaterials mimicking dynamic spacetime, D-brane and noncommutativity in string theory

    International Nuclear Information System (INIS)

    Miao Rongxin; Zheng Rui; Li Miao

    2011-01-01

    We propose a scheme to mimic the expanding cosmos in 1+2 dimensions in laboratory. Furthermore, we develop a general procedure to use nonlinear metamaterials to mimic D-brane and noncommutativity in string theory.

  5. A new non-commutative representation of the Wiener and Poisson processes

    International Nuclear Information System (INIS)

    Privault, N.

    1996-01-01

    Using two different constructions of the chaotic and variational calculus on Poisson space, we show that the Wiener and Poisson processes have a non-commutative representation which is different from the one obtained by transfer of the Fock space creation and annihilation operators. We obtain in this way an extension of the non-commutative It calculus. The associated commutation relations show a link between the geometric and exponential distributions. (author). 11 refs

  6. On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere

    Science.gov (United States)

    Arnlind, Joakim; Wilson, Mitsuru

    2017-01-01

    We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization of the projective module corresponding to the space of vector fields, which allows us to formulate a Chern-Gauss-Bonnet type theorem for the noncommutative 4-sphere.

  7. Time-dependent transitions with time–space noncommutativity and its implications in quantum optics

    International Nuclear Information System (INIS)

    Chandra, Nitin

    2012-01-01

    We study the time-dependent transitions of a quantum-forced harmonic oscillator in noncommutative R 1,1 perturbatively to linear order in the noncommutativity θ. We show that the Poisson distribution gets modified, and that the vacuum state evolves into a ‘squeezed’ state rather than a coherent state. The time evolutions of uncertainties in position and momentum in vacuum are also studied and imply interesting consequences for modeling nonlinear phenomena in quantum optics. (paper)

  8. LAPLACE-RUNGE-LENZ VECTOR IN QUANTUM MECHANICS IN NONCOMMUTATIVE SPACE

    Directory of Open Access Journals (Sweden)

    Peter Prešnajder

    2014-04-01

    Full Text Available The object under scrutiny is the dynamical symmetry connected with conservation of the Laplace-Runge-Lenz vector (LRL in the hydrogen atom problem solved by means of noncommutative quantum mechanics (NCQM. The considered noncommutative configuration space has such a “fuzzy”structure that the rotational invariance is not spoilt. An analogy with the LRL vector in the NCQM is brought to provide our results and also a comparison with the standard QM predictions.

  9. UV/IR mixing and the Goldstone theorem in noncommutative field theory

    International Nuclear Information System (INIS)

    Ruiz Ruiz, F.

    2002-01-01

    Noncommutative IR singularities and UV/IR mixing in relation with the Goldstone theorem for complex scalar field theory are investigated. The classical model has two coupling constants, λ 1 and λ 2 , associated to the two noncommutative extensions phi*starphistarphi* starphi and phistarphi*starphistarphi of the interaction term vertical bar phi vertical bar 4 on commutative spacetime. It is shown that the symmetric phase is one-loop renormalizable for all λ 1 and λ 2 compatible with perturbation theory, whereas the broken phase is proved to exist at one loop only if λ 2 =0, a condition required by the Ward identities for global U(1) invariance. Explicit expressions for the noncommutative IR singularities in the 1PI Green functions of both phases are given. They show that UV/IR duality does not hold for any of the phases and that the broken phase is free of quadratic noncommutative IR singularities. More remarkably, the pion selfenergy does not have noncommutative IR singularities at all, which proves essential to formulate the Goldstone theorem at one loop for all values of the spacetime noncommutativity parameter θ

  10. Unusual high-energy phenomenology of Lorentz-invariant noncommutative field theories

    International Nuclear Information System (INIS)

    Carone, Christopher D.; Kwee, Herry J.

    2006-01-01

    It has been suggested that one may construct a Lorentz-invariant noncommutative field theory by extending the coordinate algebra to additional, fictitious coordinates that transform nontrivially under the Lorentz group. Integration over these coordinates in the action produces a four-dimensional effective theory with Lorentz invariance intact. Previous applications of this approach, in particular, to a specific construction of noncommutative QED, have been studied only in a low-momentum approximation. Here we discuss Lorentz-invariant field theories in which the relevant physics can be studied without requiring an expansion in the inverse scale of noncommutativity. Qualitatively, we find that tree-level scattering cross sections are dramatically suppressed as the center-of-mass energy exceeds the scale of noncommutativity, that cross sections that are isotropic in the commutative limit can develop a pronounced angular dependence, and that nonrelativistic potentials (for example, the Coloumb potential) become nonsingular at the origin. We consider a number of processes in noncommutative QED that may be studied at a future linear collider. We also give an example of scattering via a four-fermion operator in which the noncommutative modifications of the interaction can unitarize the tree-level amplitude, without requiring any other new physics in the ultraviolet

  11. Causality discovery technology

    Science.gov (United States)

    Chen, M.; Ertl, T.; Jirotka, M.; Trefethen, A.; Schmidt, A.; Coecke, B.; Bañares-Alcántara, R.

    2012-11-01

    Causality is the fabric of our dynamic world. We all make frequent attempts to reason causation relationships of everyday events (e.g., what was the cause of my headache, or what has upset Alice?). We attempt to manage causality all the time through planning and scheduling. The greatest scientific discoveries are usually about causality (e.g., Newton found the cause for an apple to fall, and Darwin discovered natural selection). Meanwhile, we continue to seek a comprehensive understanding about the causes of numerous complex phenomena, such as social divisions, economic crisis, global warming, home-grown terrorism, etc. Humans analyse and reason causality based on observation, experimentation and acquired a priori knowledge. Today's technologies enable us to make observations and carry out experiments in an unprecedented scale that has created data mountains everywhere. Whereas there are exciting opportunities to discover new causation relationships, there are also unparalleled challenges to benefit from such data mountains. In this article, we present a case for developing a new piece of ICT, called Causality Discovery Technology. We reason about the necessity, feasibility and potential impact of such a technology.

  12. Winter School on Operator Spaces, Noncommutative Probability and Quantum Groups

    CERN Document Server

    2017-01-01

    Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems.  A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions.  The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory of Banach spaces to quantum information. The l...

  13. Feynman's operational calculus and beyond noncommutativity and time-ordering

    CERN Document Server

    Johnson, George W; Nielsen, Lance

    2015-01-01

    This book is aimed at providing a coherent, essentially self-contained, rigorous and comprehensive abstract theory of Feynman's operational calculus for noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and time-ordering rules in his seminal 1951 paper An operator calculus having applications in quantum electrodynamics, as will be made abundantly clear in the introduction (Chapter 1) and elsewhere in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work. Hence, the second part of the main title of this book. The basic properties of the operational calculus are developed and certain algebraic and analytic properties of the operational calculus are explored. Also, the operational calculus will be seen to possess some pleasant stability properties. Furthermore, an evolution equation and a generalized integral equation obeyed by the operational calculus are discussed and connections wi...

  14. Essay on physics and non-commutative geometry

    International Nuclear Information System (INIS)

    Connes, A.

    1990-01-01

    Our aim, in this article, is to try to discover what physics would be like if the space in which it took place was not a set of points, but a non-commutative space. We shall not go very far in this direction, and the consequences of this investigation are for the moment either mathematical or only applied to a commutative space-time. It is clear, however, that a tool as remarkable as the Dixmier trace for analyzing logarithmic divergences should be useful to physicists. Moreover we have been able to show that a small modification of our picture of space-time gives a conceptual explanation of the Higgs fields and of the way they appear in the Weinberg-Salam model. This should allow us to make at the classical level explicit predictions of the Higgs mass: a very crude one is discussed. (author)

  15. Aspects of noncommutative (1+1)-dimensional black holes

    International Nuclear Information System (INIS)

    Mureika, Jonas R.; Nicolini, Piero

    2011-01-01

    We present a comprehensive analysis of the spacetime structure and thermodynamics of (1+1)-dimensional black holes in a noncommutative framework. It is shown that a wider variety of solutions are possible than the commutative case considered previously in the literature. As expected, the introduction of a minimal length √(θ) cures singularity pathologies that plague the standard two-dimensional general relativistic case, where the latter solution is recovered at large length scales. Depending on the choice of input parameters (black hole mass M, cosmological constant Λ, etc.), black hole solutions with zero, up to six, horizons are possible. The associated thermodynamics allows for the either complete evaporation, or the production of black hole remnants.

  16. Accretion onto a noncommutative geometry inspired black hole

    Energy Technology Data Exchange (ETDEWEB)

    Kumar, Rahul [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); Ghosh, Sushant G. [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); Jamia Millia Islamia, Multidisciplinary Centre for Advanced Research and Studies (MCARS), New Delhi (India); University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)

    2017-09-15

    The spherically symmetric accretion onto a noncommutative (NC) inspired Schwarzschild black hole is treated for a polytropic fluid. The critical accretion rate M, sonic speed a{sub s} and other flow parameters are generalized for the NC inspired static black hole and compared with the results obtained for the standard Schwarzschild black holes. Also explicit expressions for gas compression ratios and temperature profiles below the accretion radius and at the event horizon are derived. This analysis is a generalization of Michel's solution to the NC geometry. Owing to the NC corrected black hole, the accretion flow parameters also have been modified. It turns out that M ∼ M{sup 2} is still achievable but r{sub s} seems to be substantially decreased due to the NC effects. They in turn do affect the accretion process. (orig.)

  17. Noncommutative geometry and its application to the standard model

    Energy Technology Data Exchange (ETDEWEB)

    Martinetti, Pierre [Georg-August Universitaet, Goettingen (Germany)

    2009-07-01

    We give an overview of the description of the standard model of particle physics minimally coupled to gravity within the framework of noncommutative geometry. Especially we study in detail the metric structure of spacetime that emerges from the spectral triple recently proposed by Chamseddine, Connes and Marcolli. Within this framework points of spacetime acquire an internal structure inherited from the gauge group of the standard model. A distance is defined on this generalized spacetime which is fully encoded by the Yang-Mills gauge fields together with the Higgs field. We focus on some explicit examples, underlying the link between this distance and other distances well known by physicists and mathematicians, such has the Carnot-Caratheodory horizontal distance or the Monge-Kantorovitch transport distance.

  18. Constraining the noncommutative spectral action via astrophysical observations.

    Science.gov (United States)

    Nelson, William; Ochoa, Joseph; Sakellariadou, Mairi

    2010-09-03

    The noncommutative spectral action extends our familiar notion of commutative spaces, using the data encoded in a spectral triple on an almost commutative space. Varying a rather simple action, one can derive all of the standard model of particle physics in this setting, in addition to a modified version of Einstein-Hilbert gravity. In this Letter we use observations of pulsar timings, assuming that no deviation from general relativity has been observed, to constrain the gravitational sector of this theory. While the bounds on the coupling constants remain rather weak, they are comparable to existing bounds on deviations from general relativity in other settings and are likely to be further constrained by future observations.

  19. Noncommutative U(1) gauge theory from a worldline perspective

    Energy Technology Data Exchange (ETDEWEB)

    Ahmadiniaz, Naser [Facultad de Ciencias en Física y Matemáticas, Universidad Autónoma de Chiapas,Ciudad Universitaria, Tuxtla Gutiérrez 29050 (Mexico); Corradini, Olindo [Facultad de Ciencias en Física y Matemáticas, Universidad Autónoma de Chiapas,Ciudad Universitaria, Tuxtla Gutiérrez 29050 (Mexico); Dipartimento di Scienze Fisiche, Informatiche e Matematiche,Università di Modena e Reggio Emilia,Via Campi 213/A, I-41125 Modena (Italy); D’Ascanio, Daniela [Instituto de Física La Plata - CONICET, Universidad Nacional de La Plata,CC 67 (1900), La Plata (Argentina); Estrada-Jiménez, Sendic [Facultad de Ciencias en Física y Matemáticas, Universidad Autónoma de Chiapas,Ciudad Universitaria, Tuxtla Gutiérrez 29050 (Mexico); Pisani, Pablo [Instituto de Física La Plata - CONICET, Universidad Nacional de La Plata,CC 67 (1900), La Plata (Argentina)

    2015-11-10

    We study pure noncommutative U(1) gauge theory representing its one-loop effective action in terms of a phase space worldline path integral. We write the quadratic action using the background field method to keep explicit gauge invariance, and then employ the worldline formalism to write the one-loop effective action, singling out UV-divergent parts and finite (planar and non-planar) parts, and study renormalization properties of the theory. This amounts to employ worldline Feynman rules for the phase space path integral, that nicely incorporate the Fadeev-Popov ghost contribution and efficiently separate planar and non-planar contributions. We also show that the effective action calculation is independent of the choice of the worldline Green’s function, that corresponds to a particular way of factoring out a particle zero-mode. This allows to employ homogeneous string-inspired Feynman rules that greatly simplify the computation.

  20. Relativistic differential-difference momentum operators and noncommutative differential calculus

    International Nuclear Information System (INIS)

    Mir-Kasimov, R.M.

    2011-01-01

    Full text: (author)The relativistic kinetic momentum operators are introduced in the framework of the Quantum Mechanics in the relativistic configuration space (RCS). These operators correspond to the half of the non-Euclidean distance in the Lobachevsky momentum space. In terms of kinetic momentum operators the relativistic kinetic energy is separated from the total Hamiltonian. The role of the plane wave (wave function of the motion with definite value of momentum and energy) plays the generation function for the matrix elements of the unitary irreps of Lorentz group (generalized Jacobi polynomials). The kinetic momentum operators are the interior derivatives in the framework of the non-commutative differential calculus over the commutative algebra generated by the coordinate functions over the RCS

  1. Structural aspects of quantum field theory and noncommutative geometry

    CERN Document Server

    Grensing, Gerhard

    2013-01-01

    This book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation. The first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a r...

  2. Euler polynomials and identities for non-commutative operators

    Science.gov (United States)

    De Angelis, Valerio; Vignat, Christophe

    2015-12-01

    Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt [Phys. Rev. D 54(12), 7710-7723 (1996)], expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, by Pain [J. Phys. A: Math. Theor. 46, 035304 (2013)], links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Figuieira de Morisson and Fring [J. Phys. A: Math. Gen. 39, 9269 (2006)] in the context of non-Hermitian Hamiltonian systems. In each case, we provide several proofs and extensions of these identities that highlight the role of Euler and Bernoulli polynomials.

  3. The noncommutative family Atiyah-Patodi-Singer index theorem

    Science.gov (United States)

    Wang, Yong

    2016-12-01

    In this paper, we define the eta cochain form and prove its regularity when the kernel of a family of Dirac operators is a vector bundle. We decompose the eta form as a pairing of the eta cochain form with the Chern character of an idempotent matrix and we also decompose the Chern character of the index bundle for a fibration with boundary as a pairing of the family Chern-Connes character for a manifold with boundary with the Chern character of an idempotent matrix. We define the family b-Chern-Connes character and then we prove that it is entire and give its variation formula. By this variation formula, we prove another noncommutative family Atiyah-Patodi-Singer index theorem. Thus, we extend the results of Getzler and Wu to the family case.

  4. Yang-Feldman formalism on noncommutative Minkowski space

    Energy Technology Data Exchange (ETDEWEB)

    Doescher, C.

    2006-12-15

    We examine quantum field theory on noncummutative spacetime. For this we choose an approach which lives explicitly on the noncommutative Minkowski space, namely the Yang-Feldman formalism. Here the ansatz is to try to solve the field equation of the quantum fields. In this setting we first take a look at an additional mass term, and use this to discuss possible IR cutoffs. We find classes of IR cutoffs which indeed yield the expected limit. Furthermore, we look at interacting models, namely the {phi}{sup 3} model in four and six dimensions, the {phi}{sup 4} model and the Wess-Zumino model. For these we calculate dispersion relations. We see that there exist huge differences in the orders of magnitude between logarithmically and quadratically divergent models. Integrals which are made finite by twisting factors are calculated rigorously in the sense of the theory of oscillatory integrals. (orig.)

  5. Quantum thetas on noncommutative T4 from embeddings into lattice

    International Nuclear Information System (INIS)

    Chang-Young, Ee; Kim, Hoil

    2007-01-01

    In this paper, we investigate the theta vector and quantum theta function over noncommutative T 4 from the embedding of RxZ 2 . Manin has constructed the quantum theta functions from the lattice embedding into vector space (x finite group). We extend Manin's construction of the quantum theta function to the embedding of vector space x lattice case. We find that the holomorphic theta vector exists only over the vector space part of the embedding, and over the lattice part we can only impose the condition for the Schwartz function. The quantum theta function built on this partial theta vector satisfies the requirement of the quantum theta function. However, two subsequent quantum translations from the embedding into the lattice part are nonadditive, contrary to the additivity of those from the vector space part

  6. A quantum causal discovery algorithm

    Science.gov (United States)

    Giarmatzi, Christina; Costa, Fabio

    2018-03-01

    Finding a causal model for a set of classical variables is now a well-established task—but what about the quantum equivalent? Even the notion of a quantum causal model is controversial. Here, we present a causal discovery algorithm for quantum systems. The input to the algorithm is a process matrix describing correlations between quantum events. Its output consists of different levels of information about the underlying causal model. Our algorithm determines whether the process is causally ordered by grouping the events into causally ordered non-signaling sets. It detects if all relevant common causes are included in the process, which we label Markovian, or alternatively if some causal relations are mediated through some external memory. For a Markovian process, it outputs a causal model, namely the causal relations and the corresponding mechanisms, represented as quantum states and channels. Our algorithm opens the route to more general quantum causal discovery methods.

  7. Causal symmetric spaces

    CERN Document Server

    Olafsson, Gestur; Helgason, Sigurdur

    1996-01-01

    This book is intended to introduce researchers and graduate students to the concepts of causal symmetric spaces. To date, results of recent studies considered standard by specialists have not been widely published. This book seeks to bring this information to students and researchers in geometry and analysis on causal symmetric spaces.Includes the newest results in harmonic analysis including Spherical functions on ordered symmetric space and the holmorphic discrete series and Hardy spaces on compactly casual symmetric spacesDeals with the infinitesimal situation, coverings of symmetric spaces, classification of causal symmetric pairs and invariant cone fieldsPresents basic geometric properties of semi-simple symmetric spacesIncludes appendices on Lie algebras and Lie groups, Bounded symmetric domains (Cayley transforms), Antiholomorphic Involutions on Bounded Domains and Para-Hermitian Symmetric Spaces

  8. Is Host-Based Anomaly Detection + Temporal Correlation = Worm Causality

    National Research Council Canada - National Science Library

    Sekar, Vyas; Xie, Yinglian; Reiter, Michael K; Zhang, Hui

    2007-01-01

    Epidemic-spreading attacks (e.g., worm and botnet propagation) have a natural notion of attack causality - a single network flow causes a victim host to get infected and subsequently spread the attack...

  9. The noncommutative standard model. Construction beyond leading order in θ and collider phenomenology

    International Nuclear Information System (INIS)

    Alboteanu, A.M.

    2007-01-01

    Within this work we study the phenomenological consequences of a possible realization of QFT on noncommutative space-time. In the first part we performed a phenomenological analysis of the hadronic process pp → Z γ → l + l - γ at the LHC and of electron-positron pair annihilation into a Z boson and a photon at the International Linear Collider (ILC). The noncommutative extension of the SM considered within this work relies on two building blocks: the Moyal-Weyl *-product of functions on ordinary space-time and the Seiberg-Witten maps. A consequence of the noncommutativity of space-time is the violation of rotational invariance with respect to the beam axis. This effect shows up in the azimuthal dependence of cross sections, which is absent in the SM as well as in other models beyond the SM. We have found this dependence to be best suited for deriving the sensitivity bounds on the noncommutative scale NC. By studying pp→Z γ →l + l - γ to first order in the noncommutative parameter θ, we show in the first part of this work that measurements at the LHC are sensitive to noncommutative effects only in certain cases, giving bounds on the noncommutative scale of Λ NC >or similar 1.2 TeV. By means of e + e - → Z γ → l + l - γ to O(θ) we have shown that ILC measurements are complementary to LHC measurements of the noncommutative parameters. In addition, the bounds on Λ NC derived from the ILC are significantly higher and reach Λ NC >or similar 6 TeV. In the second part of this work we expand the neutral current sector of the noncommutative SM to second order in θ. We found that, against the general expectation, the theory must be enlarged by additional parameters. The new parameters enter the theory as ambiguities of the Seiberg-Witten maps. The latter are not uniquely determined and differ by homogeneous solutions of the gauge equivalence equations. The expectation was that the ambiguities correspond to field redefinitions and therefore should

  10. The noncommutative standard model. Construction beyond leading order in {theta} and collider phenomenology

    Energy Technology Data Exchange (ETDEWEB)

    Alboteanu, A.M.

    2007-07-01

    Within this work we study the phenomenological consequences of a possible realization of QFT on noncommutative space-time. In the first part we performed a phenomenological analysis of the hadronic process pp {yields} Z{sub {gamma}} {yields} l{sup +}l{sup -}{gamma} at the LHC and of electron-positron pair annihilation into a Z boson and a photon at the International Linear Collider (ILC). The noncommutative extension of the SM considered within this work relies on two building blocks: the Moyal-Weyl *-product of functions on ordinary space-time and the Seiberg-Witten maps. A consequence of the noncommutativity of space-time is the violation of rotational invariance with respect to the beam axis. This effect shows up in the azimuthal dependence of cross sections, which is absent in the SM as well as in other models beyond the SM. We have found this dependence to be best suited for deriving the sensitivity bounds on the noncommutative scale NC. By studying pp{yields}Z{sub {gamma}} {yields}l{sup +}l{sup -}{gamma} to first order in the noncommutative parameter {theta}, we show in the first part of this work that measurements at the LHC are sensitive to noncommutative effects only in certain cases, giving bounds on the noncommutative scale of {lambda}{sub NC} >or similar 1.2 TeV. By means of e{sup +}e{sup -} {yields} Z{sub {gamma}} {yields} l{sup +}l{sup -}{gamma} to O({theta}) we have shown that ILC measurements are complementary to LHC measurements of the noncommutative parameters. In addition, the bounds on {lambda}{sub NC} derived from the ILC are significantly higher and reach {lambda}{sub NC} >or similar 6 TeV. In the second part of this work we expand the neutral current sector of the noncommutative SM to second order in {theta}. We found that, against the general expectation, the theory must be enlarged by additional parameters. The new parameters enter the theory as ambiguities of the Seiberg-Witten maps. The latter are not uniquely determined and differ by

  11. Maximally causal quantum mechanics

    International Nuclear Information System (INIS)

    Roy, S.M.

    1998-01-01

    We present a new causal quantum mechanics in one and two dimensions developed recently at TIFR by this author and V. Singh. In this theory both position and momentum for a system point have Hamiltonian evolution in such a way that the ensemble of system points leads to position and momentum probability densities agreeing exactly with ordinary quantum mechanics. (author)

  12. Causality in demand

    DEFF Research Database (Denmark)

    Nielsen, Max; Jensen, Frank; Setälä, Jari

    2011-01-01

    to fish demand. On the German market for farmed trout and substitutes, it is found that supply sources, i.e. aquaculture and fishery, are not the only determinant of causality. Storing, tightness of management and aggregation level of integrated markets might also be important. The methodological...

  13. Causality and Free Will

    Czech Academy of Sciences Publication Activity Database

    Hvorecký, Juraj

    2012-01-01

    Roč. 19, Supp.2 (2012), s. 64-69 ISSN 1335-0668 R&D Projects: GA ČR(CZ) GAP401/12/0833 Institutional support: RVO:67985955 Keywords : conciousness * free will * determinism * causality Subject RIV: AA - Philosophy ; Religion

  14. Explaining through causal mechanisms

    NARCIS (Netherlands)

    Biesbroek, Robbert; Dupuis, Johann; Wellstead, Adam

    2017-01-01

    This paper synthesizes and builds on recent critiques of the resilience literature; namely that the field has largely been unsuccessful in capturing the complexity of governance processes, in particular cause–effects relationships. We demonstrate that absence of a causal model is reflected in the

  15. Neural correlates of continuous causal word generation.

    Science.gov (United States)

    Wende, Kim C; Straube, Benjamin; Stratmann, Mirjam; Sommer, Jens; Kircher, Tilo; Nagels, Arne

    2012-09-01

    Causality provides a natural structure for organizing our experience and language. Causal reasoning during speech production is a distinct aspect of verbal communication, whose related brain processes are yet unknown. The aim of the current study was to investigate the neural mechanisms underlying the continuous generation of cause-and-effect coherences during overt word production. During fMRI data acquisition participants performed three verbal fluency tasks on identical cue words: A novel causal verbal fluency task (CVF), requiring the production of multiple reasons to a given cue word (e.g. reasons for heat are fire, sun etc.), a semantic (free association, FA, e.g. associations with heat are sweat, shower etc.) and a phonological control task (phonological verbal fluency, PVF, e.g. rhymes with heat are meat, wheat etc.). We found that, in contrast to PVF, both CVF and FA activated a left lateralized network encompassing inferior frontal, inferior parietal and angular regions, with further bilateral activation in middle and inferior as well as superior temporal gyri and the cerebellum. For CVF contrasted against FA, we found greater bold responses only in the left middle frontal cortex. Large overlaps in the neural activations during free association and causal verbal fluency indicate that the access to causal relationships between verbal concepts is at least partly based on the semantic neural network. The selective activation in the left middle frontal cortex for causal verbal fluency suggests that distinct neural processes related to cause-and-effect-relations are associated with the recruitment of middle frontal brain areas. Copyright © 2012 Elsevier Inc. All rights reserved.

  16. Optimal causal inference: estimating stored information and approximating causal architecture.

    Science.gov (United States)

    Still, Susanne; Crutchfield, James P; Ellison, Christopher J

    2010-09-01

    We introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate-distortion theory to use causal shielding--a natural principle of learning. We study two distinct cases of causal inference: optimal causal filtering and optimal causal estimation. Filtering corresponds to the ideal case in which the probability distribution of measurement sequences is known, giving a principled method to approximate a system's causal structure at a desired level of representation. We show that in the limit in which a model-complexity constraint is relaxed, filtering finds the exact causal architecture of a stochastic dynamical system, known as the causal-state partition. From this, one can estimate the amount of historical information the process stores. More generally, causal filtering finds a graded model-complexity hierarchy of approximations to the causal architecture. Abrupt changes in the hierarchy, as a function of approximation, capture distinct scales of structural organization. For nonideal cases with finite data, we show how the correct number of the underlying causal states can be found by optimal causal estimation. A previously derived model-complexity control term allows us to correct for the effect of statistical fluctuations in probability estimates and thereby avoid overfitting.

  17. Supergravity couplings to Noncommutative Branes, Open Wilson Lines and Generalised Star Products

    International Nuclear Information System (INIS)

    Das, S.R.; Trivedi, S.P.

    2001-01-01

    Noncommutative gauge theories can be constructed from ordinary U(∞) gauge theories in lower dimensions. Using this construction we identify the operators on noncommutative D-branes which couple to linearized supergravity backgrounds, from a knowledge of such couplings to lower dimensional D-branes with no B field. These operators belong to a class of gauge invariant observables involving open Wilson lines. Assuming a DBI form of the coupling we show, to second order in the gauge potential but to all orders of the noncommutativity parameter, that our proposal agrees with the operator obtained in terms of ordinary gauge fields by considering brane actions in backgrounds and then using the Seiberg-Witten map to rewrite this in terms of noncommutative gauge fields. Our result clarify why a certain commutative but non-associative 'generalized star product' appears both in the expansion of the open Wilson line, as well as in string amplitude computations of open string-closed string couplings. We outline how our procedure can be used to obtain operators in the noncommutative theory which are holographically dual to supergravity modes. (author)

  18. Light-like noncommutativity, light-front quantization and new light on UV/IR mixing

    International Nuclear Information System (INIS)

    Sheikh-Jabbari, M.M.; Tureanu, A.

    2011-01-01

    We revisit the problem of quantizing field theories on noncommutative Moyal space-time with light-like noncommutativity. To tackle the issues arising from noncommuting and hence nonlocal time, we argue that for this case light-front quantization procedure should be employed. In this appropriate quantization scheme we perform the non-planar loop analysis for the light-like noncommutative field theories. One of the important and peculiar features of light-front quantization is that the UV cutoff of the light-cone Hamiltonian manifests itself as an IR cutoff for the light-cone momentum, p + . Due to this feature, the naive results of covariant quantization for the light-like case allude to the absence of the UV/IR mixing in the light-front quantization. However, by a careful analysis of non-planar loop integrals we show that this is not the case and the UV/IR mixing persists. In addition, we argue in favour of the perturbative unitarity of light-like noncommutative field theories in the light-front quantization scheme.

  19. The theory of pseudo-differential operators on the noncommutative n-torus

    Science.gov (United States)

    Tao, J.

    2018-02-01

    The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct analogy with the theory of pseudo-differential operators on finite-dimensional real vector spaces, one may derive a similar pseudo-differential calculus on noncommutative n-tori, and with the development of this calculus came many results concerning the local differential geometry of noncommutative tori for n=2,4, as shown in the groundbreaking paper in which the Gauss-Bonnet theorem on the noncommutative two-torus is proved and later papers. Certain details of the proofs in the original derivation of the calculus were omitted, such as the evaluation of oscillatory integrals, so we make it the objective of this paper to fill in all the details. After reproving in more detail the formula for the symbol of the adjoint of a pseudo-differential operator and the formula for the symbol of a product of two pseudo-differential operators, we extend these results to finitely generated projective right modules over the noncommutative n-torus. Then we define the corresponding analog of Sobolev spaces and prove equivalents of the Sobolev and Rellich lemmas.

  20. Noncommutative generalization of SU(n)-principal fiber bundles: a review

    International Nuclear Information System (INIS)

    Masson, T

    2008-01-01

    This is an extended version of a communication made at the international conference 'Noncommutative Geometry and Physics' held at Orsay in april 2007. In this proceeding, we make a review of some noncommutative constructions connected to the ordinary fiber bundle theory. The noncommutative algebra is the endomorphism algebra of a SU(n)-vector bundle, and its differential calculus is based on its Lie algebra of derivations. It is shown that this noncommutative geometry contains some of the most important constructions introduced and used in the theory of connections on vector bundles, in particular, what is needed to introduce gauge models in physics, and it also contains naturally the essential aspects of the Higgs fields and its associated mechanics of mass generation. It permits one also to extend some previous constructions, as for instance symmetric reduction of (here noncommutative) connections. From a mathematical point of view, these geometrico-algebraic considerations highlight some new point on view, in particular we introduce a new construction of the Chern characteristic classes

  1. Operator ordering and causality

    OpenAIRE

    Plimak, L. I.; Stenholm, S. T.

    2011-01-01

    It is shown that causality violations [M. de Haan, Physica 132A, 375, 397 (1985)], emerging when the conventional definition of the time-normal operator ordering [P.L.Kelley and W.H.Kleiner, Phys.Rev. 136, A316 (1964)] is taken outside the rotating wave approximation, disappear when the amended definition [L.P. and S.S., Annals of Physics, 323, 1989 (2008)] of this ordering is used.

  2. Space, time and causality

    International Nuclear Information System (INIS)

    Lucas, J.R.

    1984-01-01

    Originating from lectures given to first year undergraduates reading physics and philosophy or mathematics and philosophy, formal logic is applied to issues and the elucidation of problems in space, time and causality. No special knowledge of relativity theory or quantum mechanics is needed. The text is interspersed with exercises and each chapter is preceded by a suggested 'preliminary reading' and followed by 'further reading' references. (U.K.)

  3. Ontology-based Vaccine and Drug Adverse Event Representation and Theory-guided Systematic Causal Network Analysis toward Integrative Pharmacovigilance Research.

    Science.gov (United States)

    He, Yongqun

    2016-06-01

    Compared with controlled terminologies ( e.g. , MedDRA, CTCAE, and WHO-ART), the community-based Ontology of AEs (OAE) has many advantages in adverse event (AE) classifications. The OAE-derived Ontology of Vaccine AEs (OVAE) and Ontology of Drug Neuropathy AEs (ODNAE) serve as AE knowledge bases and support data integration and analysis. The Immune Response Gene Network Theory explains molecular mechanisms of vaccine-related AEs. The OneNet Theory of Life treats the whole process of a life of an organism as a single complex and dynamic network ( i.e. , OneNet). A new "OneNet effectiveness" tenet is proposed here to expand the OneNet theory. Derived from the OneNet theory, the author hypothesizes that one human uses one single genotype-rooted mechanism to respond to different vaccinations and drug treatments, and experimentally identified mechanisms are manifestations of the OneNet blueprint mechanism under specific conditions. The theories and ontologies interact together as semantic frameworks to support integrative pharmacovigilance research.

  4. Situation models and memory: the effects of temporal and causal information on recall sequence.

    Science.gov (United States)

    Brownstein, Aaron L; Read, Stephen J

    2007-10-01

    Participants watched an episode of the television show Cheers on video and then reported free recall. Recall sequence followed the sequence of events in the story; if one concept was observed immediately after another, it was recalled immediately after it. We also made a causal network of the show's story and found that recall sequence followed causal links; effects were recalled immediately after their causes. Recall sequence was more likely to follow causal links than temporal sequence, and most likely to follow causal links that were temporally sequential. Results were similar at 10-minute and 1-week delayed recall. This is the most direct and detailed evidence reported on sequential effects in recall. The causal network also predicted probability of recall; concepts with more links and concepts on the main causal chain were most likely to be recalled. This extends the causal network model to more complex materials than previous research.

  5. Noncommutative D-branes from covariant AdS superstring

    International Nuclear Information System (INIS)

    Sakaguchi, Makoto; Yoshida, Kentaroh

    2008-01-01

    We study noncommutative (NC) D-branes on AdS 5 xS 5 from κ-invariance of covariant Green-Schwarz action of an open string with a non-trivial world-volume flux. Finding boundary conditions to ensure the κ-invariance, we can see possible configurations of the NC D-branes. With this method 1/4 BPS NC D-branes are discussed. The resulting NC Dp-branes are 1/4 BPS at arbitrary position other than the p=1 case. The exceptional D-string is 1/2 BPS at the origin and 1/4 BPS outside the origin. Those are reduced to possible 1/4 BPS or 1/2 BPS AdS D-branes in the commutative limit. The same analysis is applied to an open superstring in a pp-wave and leads to 1/4 BPS configurations of NC D-branes. These D-branes are consistently obtained from AdS D-branes via the Penrose limit

  6. Non-commutative solitons and strong-weak duality

    Energy Technology Data Exchange (ETDEWEB)

    Blas, Harold [Departamento de Matematica - ICET, Universidade Federal de Mato Grosso, Av. Fernando Correa, s/n, Coxipo, 78060-900, Cuiaba - MT (Brazil)]. E-mail: blas@cpd.ufmt.br; Carrion, Hector L. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro (Brazil); Rojas, Moises [Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud, 150 CEP 22290-180, Rio de Janeiro-RJ (Brazil)

    2005-03-01

    Some properties of the non-commutative versions of the sine-Gordon model (NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our method relies on the NC extension of integrable models and the master Lagrangian approach to deal with dual theories. The master lagrangians turn out to be the NC versions of the so-called affine Toda model coupled to matter fields (NCATM) associated to the group GL(2), in which the Toda field belongs to certain representations of either U(1)xU(1) or U(1){sub C} corresponding to the Lechtenfeld et al. (NCSG{sub 1}) or Grisaru-Penati (NCSG{sub 2}) proposals for the NC versions of the sine-Gordon model, respectively. Besides, the relevant NCMT{sub 1,2} models are written for two (four) types of Dirac fields corresponding to the Moyal product extension of one (two) copy(ies) of the ordinary massive Thirring model. The NCATM{sub 1,2} models share the same one-soliton (real Toda field sector of model 2) exact solutions, which are found without expansion in the NC parameter {theta} for the corresponding Toda and matter fields describing the strong-weak phases, respectively. The correspondence NCSG{sub 1} {r_reversible} NCMT{sub 1} is promising since it is expected to hold on the quantum level. (author)

  7. Noncommutative gauge theory and symmetry breaking in matrix models

    International Nuclear Information System (INIS)

    Grosse, Harald; Steinacker, Harold; Lizzi, Fedele

    2010-01-01

    We show how the fields and particles of the standard model can be naturally realized in noncommutative gauge theory. Starting with a Yang-Mills matrix model in more than four dimensions, an SU(n) gauge theory on a Moyal-Weyl space arises with all matter and fields in the adjoint of the gauge group. We show how this gauge symmetry can be broken spontaneously down to SU(3) c xSU(2) L xU(1) Q [resp. SU(3) c xU(1) Q ], which couples appropriately to all fields in the standard model. An additional U(1) B gauge group arises which is anomalous at low energies, while the trace-U(1) sector is understood in terms of emergent gravity. A number of additional fields arise, which we assume to be massive, in a pattern that is reminiscent of supersymmetry. The symmetry breaking might arise via spontaneously generated fuzzy spheres, in which case the mechanism is similar to brane constructions in string theory.

  8. Stability analysis of lower dimensional gravastars in noncommutative geometry

    Energy Technology Data Exchange (ETDEWEB)

    Banerjee, Ayan [Jadavpur University, Department of Mathematics, Kolkata (India); Hansraj, Sudan [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)

    2016-11-15

    The Banados et al. (Phys. Rev. Lett 69:1849, 1992), black hole solution is revamped from the Einstein field equations in (2 + 1)-dimensional anti-de Sitter spacetime, in a context of noncommutative geometry (Phys. Rev. D 87:084014, 2013). In this article, we explore the exact gravastar solutions in three-dimensional anti-de Sitter space given in the same geometry. As a first step we derive BTZ solution assuming the source of energy density as point-like structures in favor of smeared objects, where the particle mass M, is diffused throughout a region of linear size √(α) and is described by a Gaussian function of finite width rather than a Dirac delta function. We matched our interior solution to an exterior BTZ spacetime at a junction interface situated outside the event horizon. Furthermore, a stability analysis is carried out for the specific case when χ < 0.214 under radial perturbations about the static equilibrium solutions. To give theoretical support we are also trying to explore their physical properties and characteristics. (orig.)

  9. Weinberg-Salam theory in non-commutative geometry

    International Nuclear Information System (INIS)

    Morita, Katsusada; Okumura, Yoshitaka.

    1994-01-01

    Ordinary differential calculus on smooth manifold is generalized so as to construct gauge theory coupled to fermions on discrete space M 4 xZ 2 which is an underlying space-time in the non-commutative geometry for the standard model. We can reproduce not only the bosonic sector but also the fermionic sector of the Weinberg-Salam theory without recourse to the Dirac operator at the outset. Treatment of the fermionic sector is based on the generalized spinor one-forms from which the Dirac lagrangian is derived through taking the inner product. Two model constructions are presented using our formalism, both giving the classical mass relation m H = √2m w . The first model leaves the Weinberg angle arbitrary as usual, while the second one predicts sin 2 θ w = 1/4 in the tree level. This prediction is the same as that of Connes but we obtain it from correct hypercharge assignment of 2x2 matrix-valued Higgs field and from vanishing photon mass, thereby dispensing with Connes' 0-trace condition or the equivalent. (author)

  10. Problem of quantifying quantum correlations with non-commutative discord

    Science.gov (United States)

    Majtey, A. P.; Bussandri, D. G.; Osán, T. M.; Lamberti, P. W.; Valdés-Hernández, A.

    2017-09-01

    In this work we analyze a non-commutativity measure of quantum correlations recently proposed by Guo (Sci Rep 6:25241, 2016). By resorting to a systematic survey of a two-qubit system, we detected an undesirable behavior of such a measure related to its representation-dependence. In the case of pure states, this dependence manifests as a non-satisfactory entanglement measure whenever a representation other than the Schmidt's is used. In order to avoid this basis-dependence feature, we argue that a minimization procedure over the set of all possible representations of the quantum state is required. In the case of pure states, this minimization can be analytically performed and the optimal basis turns out to be that of Schmidt's. In addition, the resulting measure inherits the main properties of Guo's measure and, unlike the latter, it reduces to a legitimate entanglement measure in the case of pure states. Some examples involving general mixed states are also analyzed considering such an optimization. The results show that, in most cases of interest, the use of Guo's measure can result in an overestimation of quantum correlations. However, since Guo's measure has the advantage of being easily computable, it might be used as a qualitative estimator of the presence of quantum correlations.

  11. Noncommutative field theory and violation of translation invariance

    International Nuclear Information System (INIS)

    Bertolami, Orfeu; Guisado, Luis

    2003-01-01

    Noncommutative field theories with commutator of the coordinates of the form [x μ , x ν ] = i Λ μν ω x ω with nilpotent structure constants are studied and shown that a free quantum field theory is not affected. Invariance under translations is broken and the conservation of energy-momentum is violated, obeying a new law which is expressed by a Poincare-invariant equation. The resulting new kinematics is studied and applied to simple examples and to astrophysical puzzles, such as the observed violation of the GZK cutoff. The λΦ 4 quantum field theory is also considered in this context. In particular, self interaction terms violate the usual conservation of energy-momentum and, hence, the radiative correction to the propagator is altered. The correction to first order in λ is calculated. The usual UV divergent terms are still present, but a new type of term also emerges, which is IR divergent, violates momentum conservation and implies a correction to the dispersion relation. (author)

  12. Noncommutative spaces and matrix embeddings on flat ℝ{sup 2n+1}

    Energy Technology Data Exchange (ETDEWEB)

    Karczmarek, Joanna L.; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)

    2015-11-23

    We conjecture an embedding operator which assigns, to any 2n+1 hermitian matrices, a 2n-dimensional hypersurface in flat (2n+1)-dimensional Euclidean space. This corresponds to precisely defining a fuzzy D(2n)-brane corresponding to N D0-branes. Points on the emergent hypersurface correspond to zero eigenstates of the embedding operator, which have an interpretation as coherent states underlying the emergent noncommutative geometry. Using this correspondence, all physical properties of the emergent D(2n)-brane can be computed. We apply our conjecture to noncommutative flat and spherical spaces. As a by-product, we obtain a construction of a rotationally symmetric flat noncommutative space in 4 dimensions.

  13. Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces

    Science.gov (United States)

    Meljanac, Stjepan; Krešić–Jurić, Saša; Martinić, Tea

    2017-07-01

    This paper investigates bicovariant differential calculus on noncommutative spaces of the Lie algebra type. For a given Lie algebra g0, we construct a Lie superalgebra g =g0⊕g1 containing noncommutative coordinates and one-forms. We show that g can be extended by a set of generators TAB whose action on the enveloping algebra U (g ) gives the commutation relations between monomials in U (g0 ) and one-forms. Realizations of noncommutative coordinates, one-forms, and the generators TAB as formal power series in a semicompleted Weyl superalgebra are found. In the special case dim(g0 ) =dim(g1 ) , we also find a realization of the exterior derivative on U (g0 ) . The realizations of these geometric objects yield a bicovariant differential calculus on U (g0 ) as a deformation of the standard calculus on the Euclidean space.

  14. Non-Commutative Integration, Zeta Functions and the Haar State for SU{sub q}(2)

    Energy Technology Data Exchange (ETDEWEB)

    Matassa, Marco, E-mail: marco.matassa@gmail.com [SISSA (Italy)

    2015-12-15

    We study a notion of non-commutative integration, in the spirit of modular spectral triples, for the quantum group SU{sub q}(2). In particular we define the non-commutative integral as the residue at the spectral dimension of a zeta function, which is constructed using a Dirac operator and a weight. We consider the Dirac operator introduced by Kaad and Senior and a family of weights depending on two parameters, which are related to the diagonal automorphisms of SU{sub q}(2). We show that, after fixing one of the parameters, the non-commutative integral coincides with the Haar state of SU{sub q}(2). Moreover we can impose an additional condition on the zeta function, which also fixes the second parameter. For this unique choice the spectral dimension coincides with the classical dimension.

  15. Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics

    Science.gov (United States)

    Rodriguez R., Miguel E.

    2018-01-01

    Quantum mechanics in noncommutative space modifies the standard result of the Aharonov-Bohm effect for electrons and other recent quantum effects. Here we obtain the phase in noncommutative space for the Spavieri effect, a generalization of Aharonov-Bohm effect which involves a coherent superposition of particles with opposite charges moving along a single open interferometric path. By means of the experimental considerations a limit √{θ }≃(0.13TeV)-1 is achieved, improving by 10 orders of magnitude the results derived by Chaichian et al. [Phys. Lett. B 527, 149 (2002), 10.1016/S0370-2693(02)01176-0] for the Aharonov-Bohm effect. It is also shown that the noncommutative phases of the Aharonov-Casher and He-McKellar-Willkens effects are nullified in the current experimental tests.

  16. Search of wormholes in different dimensional non-commutative inspired space-times with Lorentzian distribution

    Energy Technology Data Exchange (ETDEWEB)

    Bhar, Piyali; Rahaman, Farook [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India)

    2014-12-01

    In this paper we ask whether the wormhole solutions exist in different dimensional noncommutativity-inspired spacetimes. It is well known that the noncommutativity of the space is an outcome of string theory and it replaced the usual point-like object by a smeared object. Here we have chosen the Lorentzian distribution as the density function in the noncommutativity-inspired spacetime. We have observed that the wormhole solutions exist only in four and five dimensions; however, in higher than five dimensions no wormhole exists. For five dimensional spacetime, we get a wormhole for a restricted region. In the usual four dimensional spacetime, we get a stable wormhole which is asymptotically flat. (orig.)

  17. String states, loops and effective actions in noncommutative field theory and matrix models

    Directory of Open Access Journals (Sweden)

    Harold C. Steinacker

    2016-09-01

    Full Text Available Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string states as a tool for loop computations in noncommutative field theory and matrix models. Defined in terms of coherent states, they exhibit the stringy features of noncommutative field theory. This leads to a closed form for the 1-loop effective action in position space, capturing the long-range non-local UV/IR mixing for scalar fields. The formalism applies to generic fuzzy spaces. The non-locality is tamed in the maximally supersymmetric IKKT or IIB model, where it gives rise to supergravity. The linearized supergravity interactions are obtained directly in position space at one loop using string states on generic noncommutative branes.

  18. Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry

    International Nuclear Information System (INIS)

    Alvarez, Pedro D.; Gomis, Joaquim; Kamimura, Kiyoshi; Plyushchay, Mikhail S.

    2008-01-01

    We investigate the planar anisotropic harmonic oscillator with explicit rotational symmetry as a particle model with non-commutative coordinates. It includes the exotic Newton-Hooke particle and the non-commutative Landau problem as special, isotropic and maximally anisotropic, cases. The system is described by the same (2+1)-dimensional exotic Newton-Hooke symmetry as in the isotropic case, and develops three different phases depending on the values of the two central charges. The special cases of the exotic Newton-Hooke particle and non-commutative Landau problem are shown to be characterized by additional, so(3) or so(2,1) Lie symmetry, which reflects their peculiar spectral properties

  19. Higgs production in e−e+ collisions as a probe of noncommutativity

    International Nuclear Information System (INIS)

    Ghasemkhani, M.; Goldouzian, R.; Khanpour, H.; Yanehsari, M. Khatiri; Najafabadi, M. Mohammadi

    2014-01-01

    We examine the sensitivity of the angular distribution of the Higgs boson in the process of e + e − →ZH and the total cross section in the minimal noncommutative standard model (mNCSM) framework to set a lower limit on the noncommutative characteristic scale (Λ). In contrast to the standard model case, in this process the Higgs boson tends to be emitted anisotropically in the transverse plane. Based on this fact, the profile likelihood ratio is used to set the lower limit on Λ. The lower limit is presented as a function of the integrated luminosity. We show that at a center-of-mass energy of 1.5 TeV and with 500 fb −1 of data, the noncommutative characteristic energy scale Λ can be excluded up to 1.2 TeV

  20. String states, loops and effective actions in noncommutative field theory and matrix models

    Energy Technology Data Exchange (ETDEWEB)

    Steinacker, Harold C., E-mail: harold.steinacker@univie.ac.at

    2016-09-15

    Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string states as a tool for loop computations in noncommutative field theory and matrix models. Defined in terms of coherent states, they exhibit the stringy features of noncommutative field theory. This leads to a closed form for the 1-loop effective action in position space, capturing the long-range non-local UV/IR mixing for scalar fields. The formalism applies to generic fuzzy spaces. The non-locality is tamed in the maximally supersymmetric IKKT or IIB model, where it gives rise to supergravity. The linearized supergravity interactions are obtained directly in position space at one loop using string states on generic noncommutative branes.

  1. Towards Noncommutative Topological Quantum Field Theory: New invariants for 3-manifolds

    International Nuclear Information System (INIS)

    Zois, I.P.

    2016-01-01

    We present some ideas for a possible Noncommutative Topological Quantum Field Theory (NCTQFT for short) and Noncommutative Floer Homology (NCFH for short). Our motivation is two-fold and it comes both from physics and mathematics: On the one hand we argue that NCTQFT is the correct mathematical framework for a quantum field theory of all known interactions in nature (including gravity). On the other hand we hope that a possible NCFH will apply to practically every 3-manifold (and not only to homology 3-spheres as ordinary Floer Homology currently does). The two motivations are closely related since, at least in the commutative case, Floer Homology Groups constitute the space of quantum observables of (3+1)-dim Topological Quantum Field Theory. Towards this goal we define some new invariants for 3-manifolds using the space of taut codim-1 foliations modulo coarse isotopy along with various techniques from noncommutative geometry. (paper)

  2. Non-Commutative Integration, Zeta Functions and the Haar State for SUq(2)

    International Nuclear Information System (INIS)

    Matassa, Marco

    2015-01-01

    We study a notion of non-commutative integration, in the spirit of modular spectral triples, for the quantum group SU q (2). In particular we define the non-commutative integral as the residue at the spectral dimension of a zeta function, which is constructed using a Dirac operator and a weight. We consider the Dirac operator introduced by Kaad and Senior and a family of weights depending on two parameters, which are related to the diagonal automorphisms of SU q (2). We show that, after fixing one of the parameters, the non-commutative integral coincides with the Haar state of SU q (2). Moreover we can impose an additional condition on the zeta function, which also fixes the second parameter. For this unique choice the spectral dimension coincides with the classical dimension

  3. An algebraic scheme associated with the non-commutative KP hierarchy and some of its extensions

    International Nuclear Information System (INIS)

    Dimakis, Aristophanes; Mueller-Hoissen, Folkert

    2005-01-01

    A well-known ansatz ('trace method') for soliton solutions turns the equations of the (non-commutative) KP hierarchy, and those of certain extensions, into families of algebraic sum identities. We develop an algebraic formalism, in particular involving a (mixable) shuffle product, to explore their structure. More precisely, we show that the equations of the non-commutative KP hierarchy and its extension (xncKP) in the case of a Moyal-deformed product, as derived in previous work, correspond to identities in this algebra. Furthermore, the Moyal product is replaced by a more general associative product. This leads to a new even more general extension of the non-commutative KP hierarchy. Relations with Rota-Baxter algebras are established

  4. A computational non-commutative geometry program for disordered topological insulators

    CERN Document Server

    Prodan, Emil

    2017-01-01

    This work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators. Noncommutative geometry has been originally proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, this approach has been successfully applied to topological insulators, where it facilitated many rigorous results concerning the stability of the topological invariants against disorder. In the first part of the book the notion of a homogeneous material is introduced and the class of disordered crystals defined together with the classification table, which conjectures all topological phases from this class. The manuscript continues with a discussion of electrons’ dynamics in disordered crystals and the theory of topological invariants in the presence of strong disorder is briefly reviewed. It is shown how all this can be captured in the language of noncommutative geometry using the co...

  5. Quantum theories on noncommutative spaces with nontrivial topology: Aharonov-Bohm and Casimir effects

    International Nuclear Information System (INIS)

    Chaichian, M.; Tureanu, A.; Demichev, A.; Presnajder, P.; Sheikh-Jabbari, M.M.

    2001-02-01

    After discussing the peculiarities of quantum systems on noncommutative (NC) spaces with nontrivial topology and the operator representation of the *-product on them, we consider the Aharonov-Bohm and Casimir effects for such spaces. For the case of the Aharonov-Bohm effect, we have obtained an explicit expression for the shift of the phase, which is gauge invariant in the NC sense. The Casimir energy of a field theory on a NC cylinder is divergent, while it becomes finite on a torus, when the dimensionless parameter of noncommutativity is a rational number. The latter corresponds to a well-defined physical picture. Certain distinctions from other treatments based on a different way of taking the noncommutativity into account are also discussed. (author)

  6. BOLD Granger causality reflects vascular anatomy.

    Directory of Open Access Journals (Sweden)

    J Taylor Webb

    Full Text Available A number of studies have tried to exploit subtle phase differences in BOLD time series to resolve the order of sequential activation of brain regions, or more generally the ability of signal in one region to predict subsequent signal in another region. More recently, such lag-based measures have been applied to investigate directed functional connectivity, although this application has been controversial. We attempted to use large publicly available datasets (FCON 1000, ADHD 200, Human Connectome Project to determine whether consistent spatial patterns of Granger Causality are observed in typical fMRI data. For BOLD datasets from 1,240 typically developing subjects ages 7-40, we measured Granger causality between time series for every pair of 7,266 spherical ROIs covering the gray matter and 264 seed ROIs at hubs of the brain's functional network architecture. Granger causality estimates were strongly reproducible for connections in a test and replication sample (n=620 subjects for each group, as well as in data from a single subject scanned repeatedly, both during resting and passive video viewing. The same effect was even stronger in high temporal resolution fMRI data from the Human Connectome Project, and was observed independently in data collected during performance of 7 task paradigms. The spatial distribution of Granger causality reflected vascular anatomy with a progression from Granger causality sources, in Circle of Willis arterial inflow distributions, to sinks, near large venous vascular structures such as dural venous sinuses and at the periphery of the brain. Attempts to resolve BOLD phase differences with Granger causality should consider the possibility of reproducible vascular confounds, a problem that is independent of the known regional variability of the hemodynamic response.

  7. Area-preserving diffeomorphisms in gauge theory on a non-commutative plane. A lattice study

    International Nuclear Information System (INIS)

    Bietenholz, W.; Bigarini, A.; INFN, Sezione di Perugia; Humboldt-Universitaet, Berlin; Torrielli, A.

    2007-06-01

    We consider Yang-Mills theory with the U(1) gauge group on a non-commutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2,R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and measurements of Wilson loops with the same area but with a variety of different shapes. Our results confirm the expected loss of invariance under APDs. Moreover, they strongly suggest that non-perturbatively the SL(2,R) symmetry does not persist either. (orig.)

  8. A novel noncommutative KdV-type equation, its recursion operator, and solitons

    Science.gov (United States)

    Carillo, Sandra; Lo Schiavo, Mauro; Porten, Egmont; Schiebold, Cornelia

    2018-04-01

    A noncommutative KdV-type equation is introduced extending the Bäcklund chart in Carillo et al. [Symmetry Integrability Geom.: Methods Appl. 12, 087 (2016)]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two noncommutative versions of the mKdV equations listed in Olver and Sokolov [Commun. Math. Phys. 193, 245 (1998), Theorem 3.6]. For this meta-mKdV, and its mirror counterpart, recursion operators, hierarchies, and an explicit solution class are derived.

  9. Non-commutative phase space and its space-time symmetry

    International Nuclear Information System (INIS)

    Li Kang; Dulat Sayipjamal

    2010-01-01

    First a description of 2+1 dimensional non-commutative (NC) phase space is presented, and then we find that in this formulation the generalized Bopp's shift has a symmetric representation and one can easily and straightforwardly define the star product on NC phase space. Then we define non-commutative Lorentz transformations both on NC space and NC phase space. We also discuss the Poincare symmetry. Finally we point out that our NC phase space formulation and the NC Lorentz transformations are applicable to any even dimensional NC space and NC phase space. (authors)

  10. Some homological properties of skew PBW extensions arising in non-commutative algebraic geometry

    Directory of Open Access Journals (Sweden)

    Lezama Oswaldo

    2017-06-01

    Full Text Available In this short paper we study for the skew PBW (Poincar-Birkhoff-Witt extensions some homological properties arising in non-commutative algebraic geometry, namely, Auslander-Gorenstein regularity, Cohen-Macaulayness and strongly noetherianity. Skew PBW extensions include a considerable number of non-commutative rings of polynomial type such that classical PBW extensions, quantum polynomial rings, multiplicative analogue of the Weyl algebra, some Sklyanin algebras, operator algebras, diffusion algebras, quadratic algebras in 3 variables, among many others. Parametrization of the point modules of some examples is also presented.

  11. Anomalies, Weinberg angle and a noncommutative geometric description of the standard model

    International Nuclear Information System (INIS)

    Scheck, F.

    1992-01-01

    The conditions on weak hypercharge assignments of quarks and leptons that are imposed by the absence of chiral anomalies, are identical with the supertrace conditions that appear in descriptions of the minimal standard model based on noncommutative geometry. Even though in these approaches there is no more explicit symmetry in the electroweak sector than the well-known SU(2) L xU(1), the noncommutative, graded algebra characterized by the modified exterior (Cartan and discrete) derivative is stringent enough to fix - at the classical level - the Weinberg angle. With the usual fermion content of the standard model the value typical for grand unified theories is found. (orig.)

  12. Géométrie non-commutative, théorie de jauge et renormalisation

    OpenAIRE

    De Goursac , Axel

    2009-01-01

    Thèse effectuée en cotutelle au Département de Mathématique de l'Université de Münster (Allemagne); Nowadays, noncommutative geometry is a growing domain of mathematics, which can appear as a promising framework for modern physics. Quantum field theories on "noncommutative spaces" are indeed much investigated, and suffer from a new type of divergence called the ultraviolet-infrared mixing. However, this problem has recently been solved by H. Grosse and R. Wulkenhaar by adding to the action of...

  13. Stabilization of compactification volume in a noncommutative mini-super-phase-space

    International Nuclear Information System (INIS)

    Khosravi, N.; Sepangi, H.R.; Sheikh-Jabbari, M.M.

    2007-01-01

    We consider a class of generalized FRW type metrics in the context of higher dimensional Einstein gravity in which the extra dimensions are allowed to have different scale factors. It is shown that noncommutativity between the momenta conjugate to the internal space scale factors controls the power-law behavior of the scale factors in the extra dimensions, taming it to an oscillatory behavior. Hence noncommutativity among the internal momenta of the mini-super-phase-space can be used to explain stabilization of the compactification volume of the internal space in a higher dimensional gravity theory

  14. Local field theory on κ-Minkowski space, star products and noncommutative translations

    International Nuclear Information System (INIS)

    Kosinski, P.; Maslanka, P.; Lukierski, J.

    2000-01-01

    We consider local field theory on κ-deformed Minkowski space which is an example of solvable Lie-algebraic noncommutative structure. Using integration formula over κ-Minkowski space and κ-deformed Fourier transform, we consider for deformed local fields the reality conditions as well as deformation of action functionals in standard Minkowski space. We present explicit formulas for two equivalent star products describing CBH quantization of field theory on κ-Minkowski space. We express also via star product technique the noncommutative translations in κ-Minkowski space by commutative translations in standard Minkowski space. (author)

  15. Beyond Markov: Accounting for independence violations in causal reasoning.

    Science.gov (United States)

    Rehder, Bob

    2018-06-01

    Although many theories of causal cognition are based on causal graphical models, a key property of such models-the independence relations stipulated by the Markov condition-is routinely violated by human reasoners. This article presents three new accounts of those independence violations, accounts that share the assumption that people's understanding of the correlational structure of data generated from a causal graph differs from that stipulated by causal graphical model framework. To distinguish these models, experiments assessed how people reason with causal graphs that are larger than those tested in previous studies. A traditional common cause network (Y 1 ←X→Y 2 ) was extended so that the effects themselves had effects (Z 1 ←Y 1 ←X→Y 2 →Z 2 ). A traditional common effect network (Y 1 →X←Y 2 ) was extended so that the causes themselves had causes (Z 1 →Y 1 →X←Y 2 ←Z 2 ). Subjects' inferences were most consistent with the beta-Q model in which consistent states of the world-those in which variables are either mostly all present or mostly all absent-are viewed as more probable than stipulated by the causal graphical model framework. Substantial variability in subjects' inferences was also observed, with the result that substantial minorities of subjects were best fit by one of the other models (the dual prototype or a leaky gate models). The discrepancy between normative and human causal cognition stipulated by these models is foundational in the sense that they locate the error not in people's causal reasoning but rather in their causal representations. As a result, they are applicable to any cognitive theory grounded in causal graphical models, including theories of analogy, learning, explanation, categorization, decision-making, and counterfactual reasoning. Preliminary evidence that independence violations indeed generalize to other judgment types is presented. Copyright © 2018 Elsevier Inc. All rights reserved.

  16. A Comparative Analysis and Prediction of Traffic Accident Causalities in the Sultanate of Oman using Artificial Neural Networks and Statistical methods

    Directory of Open Access Journals (Sweden)

    Galal A. Ali

    1998-12-01

    Full Text Available Traffic accidents are among the major causes of death in the Sultanate of Oman This is particularly the case in the age group of I6 to 25. Studies indicate that, in spite of Oman's high population-per-vehicle ratio, its fatality rate per l0,000 vehicles is one of the highest in the world. This alarming Situation underlines the importance of analyzing traffic accident data and predicting accident casualties. Such steps will lead to understanding the underlying causes of traffic accidents, and thereby to devise appropriate measures to reduce the number of car accidents and enhance safety standards. In this paper, a comparative study of car accident casualties in Oman was undertaken. Artificial Neural Networks (ANNs were used to analyze the data and make predictions of the number of accident casualties. The results were compared with those obtained from the analysis and predictions by regression techniques. Both approaches attempted to model accident casualties using historical  data on related factors, such as population, number of cars on the road and so on, covering the period from I976 to 1994. Forecasts for the years 1995 to 2000 were made using ANNs and regression equations. The results from ANNs provided the best fit for the data. However, it was found that ANNs gave lower forecasts relative to those obtained by the regression methods used, indicating that ANNs are suitable for interpolation but their use for extrapolation may be limited. Nevertheless, the study showed that ANNs provide a potentially powerful tool in analyzing and forecasting traffic accidents and casualties.

  17. Quantum groups, non-commutative differential geometry and applications

    International Nuclear Information System (INIS)

    Schupp, P.; California Univ., Berkeley, CA

    1993-01-01

    The topic of this thesis is the development of a versatile and geometrically motivated differential calculus on non-commutative or quantum spaces, providing powerful but easy-to-use mathematical tools for applications in physics and related sciences. A generalization of unitary time evolution is proposed and studied for a simple 2-level system, leading to non-conservation of microscopic entropy, a phenomenon new to quantum mechanics. A Cartan calculus that combines functions, forms, Lie derivatives and inner derivations along general vector fields into one big algebra is constructed for quantum groups and then extended to quantum planes. The construction of a tangent bundle on a quantum group manifold and an BRST type approach to quantum group gauge theory are given as further examples of applications. The material is organized in two parts: Part I studies vector fields on quantum groups, emphasizing Hopf algebraic structures, but also introducing a ''quantum geometric'' construction. Using a generalized semi-direct product construction we combine the dual Hopf algebras A of functions and U of left-invariant vector fields into one fully bicovariant algebra of differential operators. The pure braid group is introduced as the commutant of Δ(U). It provides invariant maps A → U and thereby bicovariant vector fields, casimirs and metrics. This construction allows the translation of undeformed matrix expressions into their less obvious quantum algebraic counter parts. We study this in detail for quasitriangular Hopf algebras, giving the determinant and orthogonality relation for the ''reflection'' matrix. Part II considers the additional structures of differential forms and finitely generated quantum Lie algebras -- it is devoted to the construction of the Cartan calculus, based on an undeformed Cartan identity

  18. Models with oscillator terms in noncommutative quantum field theory

    International Nuclear Information System (INIS)

    Kronberger, E.

    2010-01-01

    The main focus of this Ph.D. thesis is on noncommutative models involving oscillator terms in the action. The first one historically is the successful Grosse-Wulkenhaar (G.W.) model which has already been proven to be renormalizable to all orders of perturbation theory. Remarkably it is furthermore capable of solving the Landau ghost problem. In a first step, we have generalized the G.W. model to gauge theories in a very straightforward way, where the action is BRS invariant and exhibits the good damping properties of the scalar theory by using the same propagator, the so-called Mehler kernel. To be able to handle some more involved one-loop graphs we have programmed a powerful Mathematica package, which is capable of analytically computing Feynman graphs with many terms. The result of those investigations is that new terms originally not present in the action arise, which led us to the conclusion that we should better start from a theory where those terms are already built in. Fortunately there is an action containing this complete set of terms. It can be obtained by coupling a gauge field to the scalar field of the G.W. model, integrating out the latter, and thus 'inducing' a gauge theory. Hence the model is called Induced Gauge Theory. Despite the advantage that it is by construction completely gauge invariant, it contains also some unphysical terms linear in the gauge field. Advantageously we could get rid of these terms using a special gauge dedicated to this purpose. Within this gauge we could again establish the Mehler kernel as gauge field propagator. Furthermore we where able to calculate the ghost propagator, which turned out to be very involved. Thus we were able to start with the first few loop computations showing the expected behavior. The next step is to show renormalizability of the model, where some hints towards this direction will also be given. (author) [de

  19. Calculating the jet quenching parameter in the plasma of noncommutative Yang-Mills theory from gauge/gravity duality

    Science.gov (United States)

    Chakraborty, Somdeb; Roy, Shibaji

    2012-02-01

    A particular decoupling limit of the nonextremal (D1, D3) brane bound state system of type IIB string theory is known to give the gravity dual of space-space noncommutative Yang-Mills theory at finite temperature. We use a string probe in this background to compute the jet quenching parameter in a strongly coupled plasma of hot noncommutative Yang-Mills theory in (3+1) dimensions from gauge/gravity duality. We give expressions for the jet quenching parameter for both small and large noncommutativity. For small noncommutativity, we find that the value of the jet quenching parameter gets reduced from its commutative value. The reduction is enhanced with temperature as T7 for fixed noncommutativity and fixed ’t Hooft coupling. We also give an estimate of the correction due to noncommutativity at the present collider energies like in RHIC or in LHC and find it too small to be detected. We further generalize the results for noncommutative Yang-Mills theories in diverse dimensions.

  20. Causal events enter awareness faster than non-causal events

    Directory of Open Access Journals (Sweden)

    Pieter Moors

    2017-01-01

    Full Text Available Philosophers have long argued that causality cannot be directly observed but requires a conscious inference (Hume, 1967. Albert Michotte however developed numerous visual phenomena in which people seemed to perceive causality akin to primary visual properties like colour or motion (Michotte, 1946. Michotte claimed that the perception of causality did not require a conscious, deliberate inference but, working over 70 years ago, he did not have access to the experimental methods to test this claim. Here we employ Continuous Flash Suppression (CFS—an interocular suppression technique to render stimuli invisible (Tsuchiya & Koch, 2005—to test whether causal events enter awareness faster than non-causal events. We presented observers with ‘causal’ and ‘non-causal’ events, and found consistent evidence that participants become aware of causal events more rapidly than non-causal events. Our results suggest that, whilst causality must be inferred from sensory evidence, this inference might be computed at low levels of perceptual processing, and does not depend on a deliberative conscious evaluation of the stimulus. This work therefore supports Michotte’s contention that, like colour or motion, causality is an immediate property of our perception of the world.