Axiomatic, Parameterized, Off-Shell Quantum Field Theory
Seidewitz, Ed
2016-01-01
Axiomatic QFT attempts to provide a rigorous mathematical foundation for QFT, and it is the basis for proving some important general results, such as the well-known spin-statistics theorem. Free-field QFT meets the axioms of axiomatic QFT, showing they are consistent. Nevertheless, even after more than 50 years, there is still no known non-trivial theory of quantum fields with interactions in four-dimensional Minkowski spacetime that meets the same axioms. This paper provides a similar axiomatic basis for parameterized QFT, in which an invariant, fifth path parameter is added to the usual four spacetime position arguments of quantum fields. Dynamic evolution is in terms of the path parameter rather than the frame-dependent time coordinate. Further, the states of the theory are allowed to be off shell. Particles are therefore fundamentally "virtual" during interaction but, in the appropriate non-interacting, large-time limit, they dynamically tend towards "physical", on-shell states. Unlike traditional QFT, it...
Suppes, Patrick
1972-01-01
This clear and well-developed approach to axiomatic set theory is geared toward upper-level undergraduates and graduate students. It examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers, and other subjects. 1960 edition.
Quantum field theory on curved spacetimes: Axiomatic framework and examples
Fredenhagen, Klaus; Rejzner, Kasia
2016-03-01
In this review article, we want to expose a systematic development of quantum field theory on curved spacetimes. The leading principle is the emphasis on local properties. It turns out that this requires a reformulation of the QFT framework which also yields a new perspective for the theories on Minkowski space. The aim of the present work is to provide an almost self-contained introduction into the framework, which should be accessible for both mathematical physicists and mathematicians.
Takeuti, Gaisi
1973-01-01
This text deals with three basic techniques for constructing models of Zermelo-Fraenkel set theory: relative constructibility, Cohen's forcing, and Scott-Solovay's method of Boolean valued models. Our main concern will be the development of a unified theory that encompasses these techniques in one comprehensive framework. Consequently we will focus on certain funda mental and intrinsic relations between these methods of model construction. Extensive applications will not be treated here. This text is a continuation of our book, "I ntroduction to Axiomatic Set Theory," Springer-Verlag, 1971; indeed the two texts were originally planned as a single volume. The content of this volume is essentially that of a course taught by the first author at the University of Illinois in the spring of 1969. From the first author's lectures, a first draft was prepared by Klaus Gloede with the assistance of Donald Pelletier and the second author. This draft was then rcvised by the first author assisted by Hisao Tanaka. The in...
A synthetic axiomatization of Map Theory
DEFF Research Database (Denmark)
Berline, Chantal; Grue, Klaus Ebbe
2016-01-01
of ZFC set theory including the axiom of foundation are provable in Map Theory, and if one omits Hilbert's epsilon operator from Map Theory then one is left with a computer programming language. Map Theory fulfills Church's original aim of lambda calculus. Map Theory is suited for reasoning about......”. The class of wellfounded maps in Map Theory corresponds to the universe of sets in ZFC. The first axiomatization MT 0 of Map Theory had axioms which populated the class of wellfounded maps, much like the power set axiom along with others populate the universe of ZFC. The new axiomatization MT of Map Theory......This paper presents a substantially simplified axiomatization of Map Theory and proves the consistency of this axiomatization (called MT) in ZFC under the assumption that there exists an inaccessible ordinal. Map Theory axiomatizes lambda calculus plus Hilbert's epsilon operator. All theorems...
Introduction to axiomatic set theory
Takeuti, Gaisi
1971-01-01
In 1963, the first author introduced a course in set theory at the Uni versity of Illinois whose main objectives were to cover G6del's work on the consistency of the axiom of choice (AC) and the generalized con tinuum hypothesis (GCH), and Cohen's work on the independence of AC and the GCH. Notes taken in 1963 by the second author were the taught by him in 1966, revised extensively, and are presented here as an introduction to axiomatic set theory. Texts in set theory frequently develop the subject rapidly moving from key result to key result and suppressing many details. Advocates of the fast development claim at least two advantages. First, key results are highlighted, and second, the student who wishes to master the sub ject is compelled to develop the details on his own. However, an in structor using a "fast development" text must devote much class time to assisting his students in their efforts to bridge gaps in the text. We have chosen instead a development that is quite detailed and complete. F...
Directory of Open Access Journals (Sweden)
Stefan Hollands
2009-09-01
Full Text Available In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are ''associativity'' or ''factorization'' conditions on the operator product expansion (OPE of the theory, and are proposed to be the defining property of any quantum field theory. Our framework is presented in the Euclidean setting, and is applicable in principle to any quantum field theory, including non-conformal ones. In our framework, we obtain a characterization of perturbations of a given quantum field theory in terms of a certain cohomology ring of Hochschild-type. We illustrate our framework by the free field, but our constructions are general and apply also to interacting quantum field theories. For such theories, we propose a new scheme to construct the OPE which is based on the use of non-linear quantized field equations.
On the Axiomatic Theory of Multistate Coherent Structures.
1981-10-01
ONR Contract N00014-76-C-0839. * S On leave from the Institute de Matematica e Estatistica, Universidade de Sao Paulo, Sao Paulo, Brasil. 01 1882 017 ON...THE AXIOMATIC THEORY OF MULTISTATE COHERENT STRUCTURES Wagner de Souza Borges and Fl~vio Wagner Rodrigues Instituto de Matematica e Estatistica
Elementary process theory axiomatic introduction and applications
Cabbolet, Marcoen J T F
2011-01-01
Modern physics lacks a unitary theory that applies to all four fundamental interactions. This PhD thesis is a proposal for a single, complete, and coherent scheme of mathematically formulated elementary laws of nature. While the first chapter presents the general background, the second chapter addresses the method by which the main result has been developed. The next three chapters rigorously introduce the Elementary Process Theory, its mathematical foundations, and its applications to physics, cosmology and philosophy of mind. The final two chapters discuss the results and present the conclusions. Summarizing, the Elementary Process Theory is a scheme of seven well-formed closed expressions, written in the mathematical language of set matrix theory – a generalization of Zermelo-Fraenkel set theory. In the physical world, these seven expressions can be interpreted as elementary principles governing the universe at supersmall scale. The author critically confronts the theory with Quantum Mechanics and Genera...
Dependency through Axiomatic Approach On Rough Set Theory
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Nilaratna Kalia
2010-03-01
Full Text Available The idea of rough set consist the approximation of a set by pair of sets called the lower and the upper approximation of the set. In fact, these approximations are interior and closer operations in acertain topology generated by available data about elements of theset. The rough set is based on knowledge of an agent about somereality and his ability to discern some phenomenon processes etc.Thus this approach is based on the ability to classify data obtainedfrom observation, measurement, etc. In this paper we define thedependency of knowledge through the axiomatic approach instead ofthe traditional (Pawlak method of rough set.
Axiomatic unsharp quantum theory (From Mackey to Ludwig and Piron)
Cattaneo, Gianpiero; Laudisa, Federico
1994-05-01
On the basis of Mackey's axiomatic approach to quantum physics or, equivalently, of a “state-event-probability” (SEVP) structure, using a quite standard “fuzzification” procedure, a set of unsharp events (or “effects”) is constructed and the corresponding “state-effect-probability” (SEFP) structure is introduced. The introduction of some suitable axioms gives rise to a partially ordered structure of quantum Brouwer-Zadeh (BZ) poset; i.e., a poset endowed with two nonusual orthocomplementation mappings, a fuzzy-like orthocomplementation, and an intuitionistic-like orthocomplementation, whose set of sharp elements is an orthomodular complete lattice. As customary, by these orthocomplementations the two modal-like necessity and possibility operators are introduced, and it is shown that Ludwig's and Jauch-Piron's approaches to quantum physics are “interpreted” in complete SEFP. As a marginal result, a standard procedure to construct a lot of unsharp realizations starting from any sharp realization of a fixed observable is given, and the relationship among sharp and corresponding unsharp realizations is studied.
Wettasinghe, C M; Koh, T H
2008-11-01
This paper explores a novel approach to instructional planning using the axiomatic design theory to create an optimized curriculum. First, an existing piece of curriculum is analyzed by axiomatic design approach and design matrices are made to check whether the independence axiom is satisfied or not. Second, functional requirements (FRs) are derived from the FRs of the existing curriculums developed through conventional methods. Constraints (Cs) are defined considering the time and subject. Design parameters (DPs) are conceived in physical domain to satisfy these specified FRs and Cs, and two alternative DPs for one FR are proposed. One of these alternatives having the least information content is selected by defining FRs as the minimization of the irrelevant subjects/topics and time. Also feasibility is estimated by comparing the information content of the redesigned curriculum with that of other curriculums in consideration of costs-involved, time, and subjects-relevance.
FuzzySTAR: Fuzzy set theory of axiomatic design review
Huang, GQ; Jiang, Z
2002-01-01
Product development involves multiple phases. Design review (DR) is an essential activity formally conducted to ensure a smooth transition from one phase to another. Such a formal DR is usually a multicriteria decision problem, involving multiple disciplines. This paper proposes a systematic framework for DR using fuzzy set theory. This fuzzy approach to DR is considered particularly relevant for several reasons. First, information available at early design phases is often incomplete and impr...
Integration of axiomatic design and theory of inventive problem solving for conceptual design
Institute of Scientific and Technical Information of China (English)
TIAN Qi-hua; XIAO Ren-bin; ZHONG Yi-fang; DU Yi-xian; YANG Hong-mei
2009-01-01
Axiomatic design (AD) and theory of inventive problem solving (TRIZ) are widely used in conceptual design. Both of them have limitations, however. We presented an integrated model of these two methods to increase the efficiency and quality of the problem solving process for conceptual design. AD is used for systematically defining and structuring a problem into a hierarchy. Sometimes, the design matrix is coupled in AD which indicates the functional requirements are coupled. TRIZ separation principles can be used to separate non-independent design parameters, which provide innovative solutions at each hierarchical level. We applied the integrated model to the heating and drying equipment of bitumen reproduction device. The result verifies that the integrated model can work very well in conceptual design.
A pragmatic basis for judging models and theories in health psychology: the axiomatic method.
Smedslund, G
2000-03-01
Psychology and its subfield of health psychology suffer from a lack of standardized terminology and a unified theoretical framework for the prediction and explanation of health behaviour. Hence, it is difficult to establish whether a given theory is logically consistent and to compare different theories. Science involves both empirical and conceptual issues. It is asserted that psychology has overemphasized the former and underemphasized the latter. Empirical psychology needs an explicit, shared conceptual system in order to develop its theories. An example of an axiomatic method (Psycho-Logic; see e.g. J. Smedslund.Psychological Inquiry 1991a; 2: 325-338) is applied to show how the Health Belief Model,the Theory of Planned Behaviour and Social Cognitive Theory all conform to the a priori conditions of acting. One implication is that studies of the predictive power of theories stated as definitional truths only assess auxiliary hypotheses, i.e. the extent to which the measuring instruments are reliable and valid. On the other hand, the introduction of logic into health psychology can facilitate genuine empirical studies by helping to avoid so-called 'pseudoempirical' work (Smedslund, J. In Smith, Harré & Van Langenhove (Eds.) Rethinking psychology, 1995). Systems such as Psycho-Logic can also enhance conceptual integration by using logic to explicate and demonstrate intuitive relations. Implications for practitioners are discussed briefly.
Axiomatic Characterizations of Information Measures
Directory of Open Access Journals (Sweden)
Imre CsiszÃƒÂ¡r
2008-09-01
Full Text Available Axiomatic characterizations of Shannon entropy, Kullback I-divergence, and some generalized information measures are surveyed. Three directions are treated: (A Characterization of functions of probability distributions suitable as information measures. (B Characterization of set functions on the subsets of {1; : : : ;N} representable by joint entropies of components of an N-dimensional random vector. (C Axiomatic characterization of MaxEnt and related inference rules. The paper concludes with a brief discussion of the relevance of the axiomatic approach for information theory.
Axiomatic Characterizations of the Choquet Integral
DEFF Research Database (Denmark)
Groes, Ebbe; Whitta-Jacobsen, Hans Jørgen; Sloth, Birgitte;
The Choquet integral is an integral part of recent advances in decision theory involving non-additive measures. In this article we present two new axiomatic characterizations of this functional......The Choquet integral is an integral part of recent advances in decision theory involving non-additive measures. In this article we present two new axiomatic characterizations of this functional...
Flores, J C
2016-03-01
This work applies the competitive exclusion principle and the concept of potential competitors as simple axiomatic tools to generalized situations in ecology. These tools enable apparent competition and its dual counterpart to be explicitly evaluated in poorly understood ecological systems. Within this set-theory framework we explore theoretical symmetries and invariances, De Morgan's laws, frozen evolutionary diversity and virtual processes. In particular, we find that the exclusion principle compromises the geometrical growth of the number of species. By theoretical extending this principle, we can describe interspecific depredation in the dual case. This study also briefly considers the debated situation of intraspecific competition. The ecological consequences of our findings are discussed; particularly, the use of our framework to reinterpret coupled mathematical differential equations describing certain ecological processes.
Axiomatic differential geometry II-2 - differential forms
Nishimura, Hirokazu
2013-01-01
We refurbish our axiomatics of differential geometry introduced in [Mathematics for Applications,, 1 (2012), 171-182]. Then the notion of Euclideaness can naturally be formulated. The principal objective in this paper is to present an adaptation of our theory of differential forms developed in [International Journal of Pure and Applied Mathematics, 64 (2010), 85-102] to our present axiomatic framework.
Axiomatic Differential Geometry Ⅱ-2: Differential Forms
Nishimura, Hirokazu
2013-01-01
We refurbish our axiomatics of differential geometry introduced in [arXiv 1203.3911]. Then the notion of Euclideaness can naturally be formulated. The principal objective in this paper is to present an adaptation of our theory of differential forms developed in [International Journal of Pure and Applied Mathematics, 64 (2010), 85-102] to our present axiomatic framework.
Haag's theorem in renormalised quantum field theories
Klaczynski, Lutz
2016-01-01
We review a package of no-go results in axiomatic quantum field theory with Haag's theorem at its centre. Since the concept of operator-valued distributions in this framework comes very close to what we believe canonical quantum fields are about, these results are of consequence to quantum field theory: they suggest the seeming absurdity that this highly victorious theory is incapable of describing interactions. We single out unitarity of the interaction picture's intertwiner as the most salient provision of Haag's theorem and critique canonical perturbation theory to argue that renormalisation bypasses Haag's theorem by violating this very assumption.
Roman, Steven
2006-01-01
Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. The book concludes with a chapter on families of binomials - the Kummer theory. This new edition has been completely rewritten in order to improve the pedagogy and to make the text more accessible to graduate students. The exercises have also been im
Mathematical aspects of quantum field theories
Strobl, Thomas
2015-01-01
Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homolo...
Axiomatizing GSOS with Predicates
Aceto, Luca; Goriac, Eugen-Ioan; Ingolfsdottir, Anna; 10.4204/EPTCS.62.1
2011-01-01
In this paper, we introduce an extension of the GSOS rule format with predicates such as termination, convergence and divergence. For this format we generalize the technique proposed by Aceto, Bloom and Vaandrager for the automatic generation of ground-complete axiomatizations of bisimilarity over GSOS systems. Our procedure is implemented in a tool that receives SOS specifications as input and derives the corresponding axiomatizations automatically. This paves the way to checking strong bisimilarity over process terms by means of theorem-proving techniques.
Jost-Lehmann-Dyson representation in higher dimensional field theories
Maharana, Jnanadeva
2017-01-01
The Jost-Lehmann-Dyson representation is derived for massive scalar field theories in higher spacetime dimensions, D > 4, for the four point scattering amplitude. The representation is very crucial to investigate the analyticity properties of the amplitude. The axiomatic approach of Lehmann-Symanzik-Zimmermann is adopted to show the existence of such a representation. Consequently, a host of interesting results will follow from derivation of JLD representation such as proof of analyticity properties and asymptotic behavior of the amplitude.
Quantum cellular automata and free quantum field theory
D'Ariano, Giacomo Mauro; Perinotti, Paolo
2017-02-01
In a series of recent papers [1-4] it has been shown how free quantum field theory can be derived without using mechanical primitives (including space-time, special relativity, quantization rules, etc.), but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic information-theoretic derivation of the quantum theory of abstract systems [5, 6] to include quantum field theory. The inherent discrete nature of the informational axiomatization leads to an extension of quantum field theory to a quantum cellular automata theory, where the usual field theory is recovered in a regime where the discrete structure of the automata cannot be probed. A simple heuristic argument sets the scale of discreteness to the Planck scale, and the customary physical regime where discreteness is not visible is the relativistic one of small wavevectors. In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space (where the group resorts to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit. We conclude with some perspectives towards the more general scenario of non-linear automata for interacting quantum field theory.
Complete axiomatizations for XPath fragments
ten Cate, B.; Litak, T.; Marx, M.
2010-01-01
We provide complete axiomatizations for several fragments of Core XPath, the navigational core of XPath 1.0 introduced by Gottlob, Koch and Pichler. A complete axiomatization for a given fragment is a set of equivalences from which every other valid equivalence is derivable; equivalences can be thou
Unconventional Algorithms: Complementarity of Axiomatics and Construction
Directory of Open Access Journals (Sweden)
Gordana Dodig Crnkovic
2012-10-01
Full Text Available In this paper, we analyze axiomatic and constructive issues of unconventional computations from a methodological and philosophical point of view. We explain how the new models of algorithms and unconventional computations change the algorithmic universe, making it open and allowing increased flexibility and expressive power that augment creativity. At the same time, the greater power of new types of algorithms also results in the greater complexity of the algorithmic universe, transforming it into the algorithmic multiverse and demanding new tools for its study. That is why we analyze new powerful tools brought forth by local mathematics, local logics, logical varieties and the axiomatic theory of algorithms, automata and computation. We demonstrate how these new tools allow efficient navigation in the algorithmic multiverse. Further work includes study of natural computation by unconventional algorithms and constructive approaches.
Banks, Tom
2008-09-01
1. Introduction; 2. Quantum theory of free scalar fields; 3. Interacting field theory; 4. Particles of spin one, and gauge invariance; 5. Spin 1/2 particles and Fermi statistics; 6. Massive quantum electrodynamics; 7. Symmetries, Ward identities and Nambu Goldstone bosons; 8. Non-abelian gauge theory; 9. Renormalization and effective field theory; 10. Instantons and solitons; 11. Concluding remarks; Appendices; References; Index.
Peli, G; Masuch, M
1997-01-01
As a part of a larger effort to apply formal logic to organization science, we axiomatize the theory of propagation strategies (life history strategies) of Organization Ecology. We provide an axiomatic system in first-order logic that derives the theory's predictions as theorems from a set of underl
Renormalizable Tensor Field Theories
Geloun, Joseph Ben
2016-01-01
Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in any dimension and therefore form an interesting class of models for studying quantum gravity. We review the class of perturbatively renormalizable tensor field theories and some of their features.
Advanced classical field theory
Giachetta, Giovanni; Sardanashvily, Gennadi
2009-01-01
Contemporary quantum field theory is mainly developed as quantization of classical fields. Therefore, classical field theory and its BRST extension is the necessary step towards quantum field theory. This book aims to provide a complete mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. Based on the standard geometric formulation of theory of nonlinear differential operators, Lagrangian field theory is treated in a very general setting. Reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifold are considered. The second Noether theorems generalized to these theories and formulated in the homology terms provide the strict mathematical formulation of BRST extended classical field theory
Jost–Lehmann–Dyson representation in higher dimensional field theories
Directory of Open Access Journals (Sweden)
Jnanadeva Maharana
2017-01-01
Full Text Available The Jost–Lehmann–Dyson representation is derived for massive scalar field theories in higher spacetime dimensions, D>4, for the four point scattering amplitude. The representation is very crucial to investigate the analyticity properties of the amplitude. The axiomatic approach of Lehmann–Symanzik–Zimmermann is adopted to show the existence of such a representation. Consequently, a host of interesting results will follow from derivation of JLD representation such as proof of analyticity properties and asymptotic behavior of the amplitude.
Balanced Topological Field Theories
Dijkgraaf, R.; Moore, G.
We describe a class of topological field theories called ``balanced topological field theories''. These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces. We show that these theories are closely related to the geometry and equivariant cohomology of ``iterated superspaces'' that carry two differentials. We find the most general action for these theories, which turns out to define Morse theory on field space. We illustrate the constructions with numerous examples. Finally, we relate these theories to topological sigma-models twisted using an isometry of the target space.
Balanced Topological Field Theories
Dijkgraaf, R
1997-01-01
We describe a class of topological field theories called ``balanced topological field theories.'' These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces. We show that these theories are closely related to the geometry and equivariant cohomology of ``iterated superspaces'' that carry two differentials. We find the most general action for these theories, which turns out to define Morse theory on field space. We illustrate the constructions with numerous examples. Finally, we relate these theories to topological sigma-models twisted using an isometry of the target space.
Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory
Maroun, Michael Anthony
This dissertation is divided into two main topics. The first is the generalization of quantum dynamics when the Schrodinger partial differential equation is not defined even in the weak mathematical sense because the potential function itself is a distribution in the spatial variable, the same variable that is used to define the kinetic energy operator, i.e. the Laplace operator. The procedure is an extension and broadening of the distributional calculus and offers spectral results as an alternative to the only other two known methods to date, namely a) the functional calculi; and b) non-standard analysis. Furthermore, the generalizations of quantum dynamics presented within give a resolution to the time asymmetry paradox created by multi-particle quantum mechanics due to the time evolution still being unitary. A consequence is the randomization of phases needed for the fundamental justification Pauli master equation. The second topic is foundations of the quantum theory of fields. The title is phrased as ``foundations'' to emphasize that there is no claim of uniqueness but rather a proposal is put forth, which is markedly different than that of constructive or axiomatic field theory. In particular, the space of fields is defined as a space of generalized functions with involutive symmetry maps (the CPT invariance) that affect the topology of the field space. The space of quantum fields is then endowed the Frechet property and interactions change the topology in such a way as to cause some field spaces to be incompatible with others. This is seen in the consequences of the Haag theorem. Various examples and discussions are given that elucidate a new view of the quantum theory of fields and its (lack of) mathematical structure.
Nonlocal continuum field theories
2002-01-01
Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unif...
Enßlin, Torsten
2013-01-01
Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms even for non-linear and non-Gaussian signal inference problems. IFT algorithms exploit spatial correlations of the signal fields and b...
Superspace conformal field theory
Energy Technology Data Exchange (ETDEWEB)
Quella, Thomas [Koeln Univ. (Germany). Inst. fuer Theoretische Physik; Schomerus, Volker [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-07-15
Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and developments, including the general construction of WZW models on type I supergroups, the classification of conformal sigma models and their embedding into string theory.
Boundary Conformal Field Theory
Cardy, J L
2004-01-01
Boundary conformal field theory (BCFT) is simply the study of conformal field theory (CFT) in domains with a boundary. It gains its significance because, in some ways, it is mathematically simpler: the algebraic and geometric structures of CFT appear in a more straightforward manner; and because it has important applications: in string theory in the physics of open strings and D-branes, and in condensed matter physics in boundary critical behavior and quantum impurity models. In this article, however, I describe the basic ideas from the point of view of quantum field theory, without regard to particular applications nor to any deeper mathematical formulations.
Energy Technology Data Exchange (ETDEWEB)
Sadovskii, Michael V.
2013-06-01
This book discusses the main concepts of the Standard Model of elementary particles in a compact and straightforward way. The work illustrates the unity of modern theoretical physics by combining approaches and concepts of the quantum field theory and modern condensed matter theory. The inductive approach allows a deep understanding of ideas and methods used for solving problems in this field.
Bergshoeff, Eric A; Penas, Victor A; Riccioni, Fabio
2016-01-01
We present the dual formulation of double field theory at the linearized level. This is a classically equivalent theory describing the duals of the dilaton, the Kalb-Ramond field and the graviton in a T-duality or O(D,D) covariant way. In agreement with previous proposals, the resulting theory encodes fields in mixed Young-tableau representations, combining them into an antisymmetric 4-tensor under O(D,D). In contrast to previous proposals, the theory also requires an antisymmetric 2-tensor and a singlet, which are not all pure gauge. The need for these additional fields is analogous to a similar phenomenon for "exotic" dualizations, and we clarify this by comparing with the dualizations of the component fields. We close with some speculative remarks on the significance of these observations for the full non-linear theory yet to be constructed.
Baden Fuller, A J
2014-01-01
Engineering Field Theory focuses on the applications of field theory in gravitation, electrostatics, magnetism, electric current flow, conductive heat transfer, fluid flow, and seepage.The manuscript first ponders on electric flux, electrical materials, and flux function. Discussions focus on field intensity at the surface of a conductor, force on a charged surface, atomic properties, doublet and uniform field, flux tube and flux line, line charge and line sink, field of a surface charge, field intensity, flux density, permittivity, and Coulomb's law. The text then takes a look at gravitation
Mandl, Franz
2010-01-01
Following on from the successful first (1984) and revised (1993) editions, this extended and revised text is designed as a short and simple introduction to quantum field theory for final year physics students and for postgraduate students beginning research in theoretical and experimental particle physics. The three main objectives of the book are to: Explain the basic physics and formalism of quantum field theory To make the reader proficient in theory calculations using Feynman diagrams To introduce the reader to gauge theories, which play a central role in elementary particle physic
Covariantizing Classical Field Theories
López, Marco Castrillón
2010-01-01
We show how to enlarge the covariance group of any classical field theory in such a way that the resulting "covariantized" theory is 'essentially equivalent' to the original. In particular, our technique will render any classical field theory generally covariant, that is, the covariantized theory will be spacetime diffeomorphism-covariant and free of absolute objects. Our results thus generalize the well-known parametrization technique of Dirac and Kucha\\v{r}. Our constructions apply equally well to internal covariance groups, in which context they produce natural derivations of both the Utiyama minimal coupling and St\\"uckelberg tricks.
Perturbative Topological Field Theory
Dijkgraaf, Robbert
We give a review of the application of perturbative techniques to topological quantum field theories, in particular three-dimensional Chern-Simons-Witten theory and its various generalizations. To this end we give an introduction to graph homology and homotopy algebras and the work of Vassiliev and Kontsevich on perturbative knot invariants.
de Wit, Bernard
1990-01-01
After a brief and practical introduction to field theory and the use of Feynman diagram, we discuss the main concept in gauge theories and their application in elementary particle physics. We present all the ingredients necessary for the construction of the standard model.
Covariant Hamiltonian field theory
Giachetta, G; Sardanashvily, G
1999-01-01
We study the relationship between the equations of first order Lagrangian field theory on fiber bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. The main peculiarity of these Hamilton equations lies in the fact that, for degenerate systems, they contain additional gauge fixing conditions. We develop the BRST extension of the covariant Hamiltonian formalism, characterized by a Lie superalgebra of BRST and anti-BRST symmetries.
Axiomatization of Special Relativity in First Order Logic
Luo, Yi-Chen; Chen, Lei; He, Wan-Ting; Ma, Yong-Ge; Zhang, Xin-Yu
2016-07-01
The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecRel for special relativity proposed recently by Andréka et al. is not enough to explain all the main results in the theory, including the twin paradox and energy-mass relation. In this paper, from a four-dimensional space-time perspective, we introduce the concepts of world-line, proper time and four-momentum to our axiomatic system SpecRel+. Then we introduce an axiom of mass (AxMass) and take four-momentum conservation as an axiom (AxCFM) in SpecRel+. It turns out that the twin paradox and energy-mass relation can be derived from SpecRel+ logically. Hence, as an extension of SpecRel, SpecRel+ is a suitable first-order axiomatic system to describe the kinematics and dynamics of special relativity. Supported by the National Science Foundation of China under Grant Nos. 11235003 and 11475023, National Social Sciences Foundation of China under Grant No. 14BZX078 and the Research Fund for the Doctoral Program of Higher Education of China, and the Undergraduate Training Program of Beijing
Wentzel, Gregor
2003-01-01
A prominent figure in twentieth-century physics, Gregor Wentzel made major contributions to the development of quantum field theory, first in Europe and later at the University of Chicago. His Quantum Theory of Fields offers a knowledgeable view of the original literature of elementary quantum mechanics and helps make these works accessible to interested readers.An introductory volume rather than an all-inclusive account, the text opens with an examination of general principles, without specification of the field equations of the Lagrange function. The following chapters deal with particular
Theory of electromagnetic fields
Wolski, Andrzej
2011-01-01
We discuss the theory of electromagnetic fields, with an emphasis on aspects relevant to radiofrequency systems in particle accelerators. We begin by reviewing Maxwell's equations and their physical significance. We show that in free space, there are solutions to Maxwell's equations representing the propagation of electromagnetic fields as waves. We introduce electromagnetic potentials, and show how they can be used to simplify the calculation of the fields in the presence of sources. We derive Poynting's theorem, which leads to expressions for the energy density and energy flux in an electromagnetic field. We discuss the properties of electromagnetic waves in cavities, waveguides and transmission lines.
THE AESTHETIC AXIOMATIC: DECONSTRUCTION
Directory of Open Access Journals (Sweden)
IRINA VASKES SANTCHES
2007-08-01
Full Text Available Resumen: El presente trabajo contribuye al debate sobre la actualidad estética, abordando diferentes enfoques del polémico concepto de deconstrucción, introducido por Jacques Derrida. Esta categoría es de referencia casi obligatoriacuando se habla sobre teoría estética contemporánea, forma parte de su nuevo aparato conceptual y expresa bien la nueva realidad que no tiene análogos históricos en lo que antes llamaban arte, estética y cultura. La elaboracióndel concepto de deconstrucción, el análisis de cómo funciona esa nueva forma del pensamiento crítico, y el método creativo de la interpretación y de la producción del texto artístico, nos permite entrar en el código de muchas obras artísticas actuales donde el espacio entre arte y teoría del arte es cada vez más incierto, especialmente en las diversas formas de arte conceptual o “performance art”.Abstract: Tackling polemic concept of deconstruction, introduced by Jacqes Derrida, from different approaches this article contributes to the debate on aesthetic current issues. This category is of almost obligatory reference when discussing about contemporary aesthetic theory. Deconstruction belongs to its new conceptual apparatus, and expresses well new reality that does not have historical analogy with what before was called art, aesthetics and culture. The elaboration of the concept of deconstruction, and the analysis of how this new form of strategical “procedure” of interpretation and production of the text (as textual reading is functioning allow us to enter the code of many current art works where the space between art and theory of the art is more and more uncertain, specially in the diverse forms of conceptual art or “performance art“.
Zeidler, Eberhard
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. The book tries to bridge the existing gap between the different languages used by mathematicians and physicists. For students of mathematics it is shown that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which is beyond the usual curriculum in physics. It is the author's goal to present the state of the art of realizing Einstein's dream of a unified theory for the four fundamental forces in the universe (gravitational, electromagnetic, strong, and weak interaction). From the reviews: "… Quantum field theory is one of the great intellectual edifices in the history of human thought. … This volume differs from othe...
Eringen, A Cemal
1999-01-01
Microcontinuum field theories constitute an extension of classical field theories -- of elastic bodies, deformations, electromagnetism, and the like -- to microscopic spaces and short time scales. Material bodies are here viewed as collections of large numbers of deformable particles, much as each volume element of a fluid in statistical mechanics is viewed as consisting of a large number of small particles for which statistical laws are valid. Classical continuum theories are valid when the characteristic length associated with external forces or stimuli is much larger than any internal scale of the body under consideration. When the characteristic lengths are comparable, however, the response of the individual constituents becomes important, for example, in considering the fluid or elastic properties of blood, porous media, polymers, liquid crystals, slurries, and composite materials. This volume is concerned with the kinematics of microcontinua. It begins with a discussion of strain, stress tensors, balanc...
Gurau, R; Rivasseau, V
2008-01-01
We propose a new formalism for quantum field theory which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes correlation functions through convergent rather than divergent expansions. It applies both to Fermionic and Bosonic theories. It is compatible with the renormalization group, and it allows to define non-perturbatively {\\it differential} renormalization group equations. It accommodates any general stable polynomial Lagrangian. It can equally well treat noncommutative models or matrix models such as the Grosse-Wulkenhaar model. Perhaps most importantly it removes the space-time background from its central place in QFT, paving the way for a nonperturbative definition of field theory in noninteger dimension.
Invariants from classical field theory
Diaz, Rafael
2007-01-01
We introduce a method that generates invariant functions from classical field theories depending on external parameters. We apply our method to several field theories such as abelian BF, Chern-Simons and 2-dimensional Yang-Mills theory.
An overview of the fuzzy axiomatic systems and characterizations proposed at Ghent University
ETIENNE E. KERRE; Lynn D´eer; Bart Van Gasse
2016-01-01
During the past 40 years of fuzzy research at the Fuzziness and Uncertainty Modeling research unit of Ghent University several axiomatic systems and characterizations have been introduced. In this paper we highlight some of them. The main purpose of this paper consists of an invitation to continue research on these first attempts to axiomatize important concepts and systems in fuzzy set theory. Currently, these attempts are spread over many journals; with this paper they are now collected in ...
Personnel Selection Using Fuzzy Axiomatic Design Principles
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Anant V. Khandekar
2016-09-01
Full Text Available Overall competency of the working personnel is often observed to ultimately affect the productivity of an organization. The globalised competitive atmosphere coupled with technological improvements demands for efficient and specialized manpower for the industrial operations. A set of typical technological skills and attitudes is thus demanded for every job profile. Most often, these skills and attitudes are expressed imprecisely and hence, necessitating the support of fuzzy sets for their effective understanding and further processing. In this paper, a method based on fuzzy axiomatic design principles is applied for solving the personnel selection problems. Selecting a middle management staff of a service department for a large scale organization is demonstrated here as a real life example. Five shortlisted candidates are assessed with respect to a set of 18 evaluation criteria, and the selection committee with experts from the related fields also realizes the outcome of the adopted approach to be quite appropriate, befitting and in agreement with their expectations.
Aminov, G; Levin, A; Olshanetsky, M; Zotov, A
2013-01-01
We propose multidimensional versions of the Painleve VI equation and its degenerations. These field theories are related to the isomonodromy problems of flat holomorphic infinite rank bundles over elliptic curves and take the form of non-autonomous Hamiltonian equations. The modular parameter of curves plays the role of "time". Reduction of the field equations to the zero modes leads to SL(N,C) monodromy preserving equations. The latter coincide with the Painleve VI equation for N=2. We consider two types of the bundles. In the first one the group of automorphisms is the centrally and cocentrally extended loop group L(SL(N,C)) or some multiloop group. In the case of the Painleve VI field theory in D=1+1 four constants of the Painleve VI equation become dynamical fields. The second type of bundles are defined by the group of automorphisms of the noncommutative torus. They lead to the equations in dimension 2+1. In both cases we consider trigonometric, rational and scaling limits of the theories. Generically (e...
Free Quantum Field Theory from Quantum Cellular Automata
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
2015-10-01
After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).
CERN. Geneva; CERN. Geneva
2001-01-01
Starting from the notion of path integrals as developed by Feynman, we discuss field theory in zero spacetime dimensions. The concepts of perturbation expansions, connected amplitudes, Feynman diagrams, classical solutions, renormalization and the effective action are developed. The model is extended to four spacetime dimensions, and the full Feynman rules for relativisitc scalar theory derived. The S matrix and the concept of unitarity are discussed, leading to the amputation rules for S matrix elements from considerations of unitarity. The rules are extended to include particles with spin-1/2 and spin-1. The high-energy behaviour of the theory is discussed as a method to derive the gauge symmetry of the various models.
Frampton, Paul H
2008-01-01
This third edition on the classic Gauge Field Theories is an ideal reference for researchers starting work with the Large Hadron Collider and the future International Linear Collider. This latest title continues to offer an up to date reference containing revised chapters on electroweak interactions and model building including a completely new chapter on conformality. Within this essential reference logical organization of the material on gauge invariance, quantization, and renormalization is also discussed providing necessary reading for Cosmologists and Particle Astrophysicists
Axiomatic design in large systems complex products, buildings and manufacturing systems
Suh, Nam
2016-01-01
This book provides a synthesis of recent developments in Axiomatic Design theory and its application in large complex systems. Introductory chapters provide concise tutorial materials for graduate students and new practitioners, presenting the fundamentals of Axiomatic Design and relating its key concepts to those of model-based systems engineering. A mathematical exposition of design axioms is also provided. The main body of the book, which represents a concentrated treatment of several applications, is divided into three parts covering work on: complex products; buildings; and manufacturing systems. The book shows how design work in these areas can benefit from the scientific and systematic underpinning provided by Axiomatic Design, and in so doing effectively combines the state of the art in design research with practice. All contributions were written by an international group of leading proponents of Axiomatic Design. The book concludes with a call to action motivating further research into the engineeri...
Energy Technology Data Exchange (ETDEWEB)
Sugama, H. [National Inst. for Fusion Science, Toki, Gifu (Japan)
1999-08-01
The Lagrangian formulation of the gyrokinetic theory is generalized in order to describe the particles' dynamics as well as the self-consistent behavior of the electromagnetic fields. The gyrokinetic equation for the particle distribution function and the gyrokinetic Maxwell's equations for the electromagnetic fields are both derived from the variational principle for the Lagrangian consisting of the parts of particles, fields, and their interaction. In this generalized Lagrangian formulation, the energy conservation property for the total nonlinear gyrokinetic system of equations is directly shown from the Noether's theorem. This formulation can be utilized in order to derive the nonlinear gyrokinetic system of equations and the rigorously conserved total energy for fluctuations with arbitrary frequency. (author)
Geometries from field theories
Aoki, Sinya; Kikuchi, Kengo; Onogi, Tetsuya
2015-10-01
We propose a method to define a d+1-dimensional geometry from a d-dimensional quantum field theory in the 1/N expansion. We first construct a d+1-dimensional field theory from the d-dimensional one via the gradient-flow equation, whose flow time t represents the energy scale of the system such that trArr 0 corresponds to the ultraviolet and trArr infty to the infrared. We then define the induced metric from d+1-dimensional field operators. We show that the metric defined in this way becomes classical in the large-N limit, in the sense that quantum fluctuations of the metric are suppressed as 1/N due to the large-N factorization property. As a concrete example, we apply our method to the O(N) nonlinear σ model in two dimensions. We calculate the 3D induced metric, which is shown to describe an anti-de Sitter space in the massless limit. Finally, we discuss several open issues for future studies.
Axiomatic of Fuzzy Complex Numbers
Directory of Open Access Journals (Sweden)
Angel Garrido
2012-04-01
Full Text Available Fuzzy numbers are fuzzy subsets of the set of real numbers satisfying some additional conditions. Fuzzy numbers allow us to model very difficult uncertainties in a very easy way. Arithmetic operations on fuzzy numbers have also been developed, and are based mainly on the crucial Extension Principle. When operating with fuzzy numbers, the results of our calculations strongly depend on the shape of the membership functions of these numbers. Logically, less regular membership functions may lead to very complicated calculi. Moreover, fuzzy numbers with a simpler shape of membership functions often have more intuitive and more natural interpretations. But not only must we apply the concept and the use of fuzzy sets, and its particular case of fuzzy number, but also the new and interesting mathematical construct designed by Fuzzy Complex Numbers, which is much more than a correlate of Complex Numbers in Mathematical Analysis. The selected perspective attempts here that of advancing through axiomatic descriptions.
Alternative Axiomatic Characterizations of the Grey Shapley Value
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Sirma Zeynep Alparslan Gok
2014-05-01
Full Text Available The Shapley value, one of the most common solution concepts of cooperative game theory is defined and axiomatically characterized in different game-theoretic models. Certainly, the Shapley value can be used in interesting sharing cost/reward problems in the Operations Research area such as connection, routing, scheduling, production and inventory situations. In this paper, we focus on the Shapley value for cooperative games, where the set of players is finite and the coalition values are interval grey numbers. The central question in this paper is how to characterize the grey Shapley value. In this context, we present two alternative axiomatic characterizations. First, we characterize the grey Shapley value using the properties of efficiency, symmetry and strong monotonicity. Second, we characterize the grey Shapley value by using the grey dividends.
Vizgin, Vladimir P
2011-01-01
Despite the rapidly expanding ambit of physical research and the continual appearance of new branches of physics, the main thrust in its development has been the attempt at a theoretical synthesis of the entire body of physical knowledge. Vladimir Vizgin's work presents perhaps the first systematic historico-scientific study of the formation and development of the unified field theories in the general context of 20th century physics. Concentrating on the first three decades of the century and drawing extensively on Russian sources, the author analyses the first successes, failures and paths of
Higgs Effective Field Theories
2016-01-01
The main focus of this meeting is to present new theoretical advancements related to effective field theories, evaluate the impact of initial results from the LHC Run2, and discuss proposals for data interpretation/presentation during Run2. A crucial role of the meeting is to bring together theorists from different backgrounds and with different viewpoints and to extend bridges towards the experimental community. To this end, we would like to achieve a good balance between senior and junior speakers, enhancing the visibility of younger scientists while keeping some overview talks.
Karpilovsky, G
1989-01-01
This monograph gives a systematic account of certain important topics pertaining to field theory, including the central ideas, basic results and fundamental methods.Avoiding excessive technical detail, the book is intended for the student who has completed the equivalent of a standard first-year graduate algebra course. Thus it is assumed that the reader is familiar with basic ring-theoretic and group-theoretic concepts. A chapter on algebraic preliminaries is included, as well as a fairly large bibliography of works which are either directly relevant to the text or offer supplementary material of interest.
Lectures on Matrix Field Theory
Ydri, Badis
The subject of matrix field theory involves matrix models, noncommutative geometry, fuzzy physics and noncommutative field theory and their interplay. In these lectures, a lot of emphasis is placed on the matrix formulation of noncommutative and fuzzy spaces, and on the non-perturbative treatment of the corresponding field theories. In particular, the phase structure of noncommutative $\\phi^4$ theory is treated in great detail, and an introduction to noncommutative gauge theory is given.
A Finite Axiomatization of G-Dependence
Paolini, Gianluca
2015-01-01
We show that a form of dependence known as G-dependence (originally introduced by Grelling) admits a very natural finite axiomatization, as well as Armstrong relations. We also give an explicit translation between functional dependence and G-dependence.
Logarithmic conformal field theory
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more
A sound and complete axiomatization for Dynamic Topological Logic
Duque, David Fernández
2012-01-01
Dynamic Topological Logic (DTL) is a multimodal system for reasoning about dynamical systems. It is defined semantically and, as such, most of the work done in the field has been model-theoretic. In particular, the problem of finding a complete axiomatization for the full language of DTL over the class of all dynamical systems has proven to be quite elusive. Here we propose to enrich the language to include a polyadic topological modality, originally introduced by Dawar and Otto in a different context. We then provide a sound axiomatization for DTL over this extended language, and prove that it is complete. The polyadic modality is used in an essential way in our proof.
Theory of interacting quantum fields
Rebenko, Alexei L
2012-01-01
This monograph is devoted to the systematic and encyclopedic presentation of the foundations of quantum field theory. It represents mathematical problems of the quantum field theory with regardto the new methods of the constructive and Euclidean field theory formed for the last thirty years of the 20th century on the basis of rigorous mathematical tools of the functional analysis, the theory of operators, and the theory of generalized functions. The book is useful for young scientists who desire to understand not only the formal structure of the quantum field theory but also its basic concepts and connection with classical mechanics, relativistic classical field theory, quantum mechanics, group theory, and the theory of functional integration.
Khoury, Justin
2013-01-01
Chameleons are light scalar fields with remarkable properties. Through the interplay of self-interactions and coupling to matter, chameleon particles have a mass that depends on the ambient matter density. The manifestation of the fifth force mediated by chameleons therefore depends sensitively on their environment, which makes for a rich phenomenology. In this article, we review two recent results on chameleon phenomenology. The first result a pair of no-go theorems limiting the cosmological impact of chameleons and their generalizations: i) the range of the chameleon force at cosmological density today can be at most ~Mpc; ii) the conformal factor relating Einstein- and Jordan-frame scale factors is essentially constant over the last Hubble time. These theorems imply that chameleons have negligible effect on the linear growth of structure, and cannot account for the observed cosmic acceleration except as some form of dark energy. The second result pertains to the quantum stability of chameleon theories. We ...
Quantum field theory of fluids.
Gripaios, Ben; Sutherland, Dave
2015-02-20
The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.
Field redefinition invariance in quantum field theory
Apfeldorf, K M; Apfeldorf, Karyn M; Ordonez, Carlos
1994-01-01
We investigate the consequences of field redefinition invariance in quantum field theory by carefully performing nonlinear transformations in the path integral. We first present a ``paradox'' whereby a 1+1 freemassless scalar theory on a Minkowskian cylinder is reduced to an effectively quantum mechanical theory. We perform field redefinitions both before and after reduction to suggest that one should not ignore operator ordering issues in quantum field theory. We next employ a discretized version of the path integral for a free massless scalar quantum field in d dimensions to show that beyond the usual jacobian term, an infinite series of divergent ``extra'' terms arises in the action whenever a nonlinear field redefinition is made. The explicit forms for the first couple of these terms are derived. We evaluate Feynman diagrams to illustrate the importance of retaining the extra terms, and conjecture that these extra terms are the exact counterterms necessary to render physical quantities invariant under fie...
Axiomatic Theories of Truth on Intuitionistic Logic%直觉主义逻辑上的公理化真理论
Institute of Scientific and Technical Information of China (English)
李娜; 李晟
2015-01-01
In this paper, we investigate the disquotation scheme and the compositional axioms of truth based on the intuitionistic logic and Heyting arithmetic HA. Three intuitionistic typed theories of truth, that is, IDT, ICT and SICT, will be obtained and their basic properties will be discussed. The main results of this paper are the standard interpretation of arithmetic is suitable for all of them, IDT and SICT are both theories of truth meet adequacy conditions, and IDT is conservative over HA, but SICT not.%本文在直觉主义逻辑和海廷算术HA的基础上，重新考察了去引号模式和组合真公理，得到了三种直觉主义的类型真理论：IDT、ICT和SICT，并探讨了它们的一些基本性质。本文证明了三者都满足对算术的标准解释，并且IDT和SICT是实质上充分的真理论，而ICT不是。在保守性方面，本文证明了IDT是HA的算术保守扩充理论，而SICT是非保守扩充。
Kwak, Seung Ki
The existence of momentum and winding modes of closed string on a torus leads to a natural idea that the field theoretical approach of string theory should involve winding type coordinates as well as the usual space-time coordinates. Recently developed double field theory is motivated from this idea and it implements T-duality manifestly by doubling the coordinates. In this thesis we will mainly focus on the double field theory formulation of different string theories in its low energy limit: bosonic, heterotic, type II and its massive extensions, and N = 1 supergravity theory. In chapter 2 of the thesis we study the equivalence of different formulations of double field theory. There are three different formulations of double field theory: background field E formulation, generalized metric H formulation, and frame field EAM formulation. Starting from the frame field formalism and choosing an appropriate gauge, the equivalence of the three formulations of bosonic theory are explicitly verified. In chapter 3 we construct the double field theory formulation of heterotic strings. The global symmetry enlarges to O( D, D + n) for heterotic strings and the enlarged generalized metric features this symmetry. The structural form of bosonic theory can directly be applied to the heterotic theory with the enlarged generalized metric. In chapter 4 we develop a unified framework of double field theory for type II theories. The Ramond-Ramond potentials fit into spinor representations of the duality group O( D, D) and the theory displays Spin+( D, D) symmetry with its self-duality relation. For a specific form of RR 1-form the theory reduces to the massive deformation of type IIA theory due to Romans. In chapter 5 we formulate the N = 1 supersymmetric extension of double field theory including the coupling to n abelian vector multiplets. This theory features a local O(1, 9 + n) x O(1, 9) tangent space symmetry under which the fermions transform. (Copies available exclusively from
5d Field Theories and M Theory
Kol, Barak
1997-01-01
5-brane configurations describing 5d field theories are promoted to an M theory description a la Witten in terms of polynomials in two complex variables. The coefficients of the polynomials are the Coulomb branch. This picture resolves apparent singularities at vertices and reveals exponentially small corrections. These corrections ask to be compared to world line instanton corrections. From a different perspective this procedure may be used to define a diagrammatic representation of polynomi...
Axiomatic Design of Micro Quartz Rate Sensor
Institute of Scientific and Technical Information of China (English)
SHI Yang-he; ZHANG Hong-hai; LIU Sheng
2007-01-01
Quartz rate sensors (QRS) made out of one single piece of quartz crystal are inertial devices which can be used for general rate control, stabilization, automotive and aerospace/defense markets,etc. The mechanical design of the QRS has been investigated based on axiomatic design. The axiomatic design matrix of the mechanical structure of Coriolis Vibratory Gyroscopes (CVG) has been proposed. The mechanical function of QRS is divided into three Function Requirements ( FR ) , i. e. , FR1 is the drive mode, FR2 is the sense mode, FR3 is a coupled connection where the Coriolis force can couple the two modes with a term proportional to the rotational rate. A new QRS which is easy to be fabricated has been put forward. Furthermore, the new QRS indicated that the axiomatic design is a help to functional design of products.
Axiomatic Relation between Thermodynamic and Information-Theoretic Entropies
Weilenmann, Mirjam; Kraemer, Lea; Faist, Philippe; Renner, Renato
2016-12-01
Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [E. H. Lieb and J. Yngvason Proc. R. Soc. 469, 20130408 (2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalization to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in nonequilibrium thermodynamics correspond to entropies used in one-shot information theory.
Properties of double field theory
Penas, Victor Alejandro
2016-01-01
In this thesis we study several aspects of Double Field Theory (DFT). In general, Double Field Theory is subject to the so-called strong constraint. By using the Flux Formulation of DFT, we explore to what extent one can deal with the gauge consistency constraints of DFT without imposing the strong
Resolving Witten's Superstring Field Theory
Erler, Theodore; Sachs, Ivo
2014-01-01
We regulate Witten's open superstring field theory by replacing the picture-changing insertion at the midpoint with a contour integral of picture changing insertions over the half-string overlaps of the cubic vertex. The resulting product between string fields is non-associative, but we provide a solution to the $A_\\infty$ relations defining all higher vertices. The result is an explicit covariant superstring field theory which by construction satisfies the classical BV master equation.
The Nonlinear Field Space Theory
Energy Technology Data Exchange (ETDEWEB)
Mielczarek, Jakub, E-mail: jakub.mielczarek@uj.edu.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Trześniewski, Tomasz, E-mail: tbwbt@ift.uni.wroc.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Institute for Theoretical Physics, University of Wrocław, pl. Borna 9, 50-204 Wrocław (Poland)
2016-08-10
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
The Nonlinear Field Space Theory
Directory of Open Access Journals (Sweden)
Jakub Mielczarek
2016-08-01
Full Text Available In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity, as well as in condensed matter physics (e.g. continuous spin chains, and can shed new light on the issue of divergences in quantum field theories.
The Nonlinear Field Space Theory
Mielczarek, Jakub; Trześniewski, Tomasz
2016-08-01
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the "Principle of finiteness" of physical theories, which once motivated the Born-Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
Lectures on quantum field theory
Das, Ashok
2008-01-01
This book consists of the lectures for a two-semester course on quantum field theory, and as such is presented in a quite informal and personal manner. The course starts with relativistic one-particle systems, and develops the basics of quantum field theory with an analysis of the representations of the Poincaré group. Canonical quantization is carried out for scalar, fermion, Abelian and non-Abelian gauge theories. Covariant quantization of gauge theories is also carried out with a detailed description of the BRST symmetry. The Higgs phenomenon and the standard model of electroweak interactio
An Overview of the Fuzzy Axiomatic Systems and Characterizations Proposed at Ghent University
Directory of Open Access Journals (Sweden)
Etienne E. Kerre
2016-06-01
Full Text Available During the past 40 years of fuzzy research at the Fuzziness and Uncertainty Modeling research unit of Ghent University several axiomatic systems and characterizations have been introduced. In this paper we highlight some of them. The main purpose of this paper consists of an invitation to continue research on these first attempts to axiomatize important concepts and systems in fuzzy set theory. Currently, these attempts are spread over many journals; with this paper they are now collected in a neat overview. In the literature, many axiom systems have been introduced, but as far as we know the axiomatic system of Huntington concerning a Boolean algebra has been the only one where the axioms have been proven independent. Another line of further research could be with respect to the simplification of these systems, in discovering redundancies between the axioms.
Quantum Field Theory, Revised Edition
Mandl, F.; Shaw, G.
1994-01-01
Quantum Field Theory Revised Edition F. Mandl and G. Shaw, Department of Theoretical Physics, The Schuster Laboratory, The University, Manchester, UK When this book first appeared in 1984, only a handful of W± and Z° bosons had been observed and the experimental investigation of high energy electro-weak interactions was in its infancy. Nowadays, W± bosons and especially Z° bosons can be produced by the thousand and the study of their properties is a precise science. We have revised the text of the later chapters to incorporate these developments and discuss their implications. We have also taken this opportunity to update the references throughout and to make some improvements in the treatment of dimen-sional regularization. Finally, we have corrected some minor errors and are grateful to various people for pointing these out. This book is designed as a short and simple introduction to quantum field theory for students beginning research in theoretical and experimental physics. The three main objectives are to explain the basic physics and formalism of quantum field theory, to make the reader fully proficient in theory calculations using Feynman diagrams, and to introduce the reader to gauge theories, which play such a central role in elementary particle physics. The theory is applied to quantum electrodynamics (QED), where quantum field theory had its early triumphs, and to weak interactions where the standard electro-weak theory has had many impressive successes. The treatment is based on the canonical quantization method, because readers will be familiar with this, because it brings out lucidly the connection between invariance and conservation laws, and because it leads directly to the Feynman diagram techniques which are so important in many branches of physics. In order to help inexperienced research students grasp the meaning of the theory and learn to handle it confidently, the mathematical formalism is developed from first principles, its physical
Fuzzy Entropy： Axiomatic Definition and Neural Networks Model
Institute of Scientific and Technical Information of China (English)
QINGMing; CAOYue; HUANGTian-min
2004-01-01
The measure of uncertainty is adopted as a measure of information. The measures of fuzziness are known as fuzzy information measures. The measure of a quantity of fuzzy information gained from a fuzzy set or fuzzy system is known as fuzzy entropy. Fuzzy entropy has been focused and studied by many researchers in various fields. In this paper, firstly, the axiomatic definition of fuzzy entropy is discussed. Then, neural networks model of fuzzy entropy is proposed, based on the computing capability of neural networks. In the end, two examples are discussed to show the efficiency of the model.
An Axiomatic Representation of System Dynamics
Baianu, I
2004-01-01
An axiomatic representation of system dynamics is introduced in terms of categories, functors, organismal supercategories, limits and colimits of diagrams. Specific examples are considered in Complex Systems Biology, such as ribosome biogenesis and Hormonal Control in human subjects. "Fuzzy" Relational Structures are also proposed for flexible representations of biological system dynamics and organization.
Axiomatic Characterizations of IVF Rough Approximation Operators
Directory of Open Access Journals (Sweden)
Guangji Yu
2014-01-01
Full Text Available This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.
Lectures on matrix field theory
Ydri, Badis
2017-01-01
These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries. The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last chapter offers a general introduction to non-commutative gauge theories, while two appendices round out the text. Primarily written as a self-study guide for postgraduate students – with the aim of pedagogically introducing them to key analytical and numerical tools, as well as useful physical models in applications – these lecture notes will also benefit experienced researchers by providing a reference guide to the fundamentals of non-commutative field theory with an emphasis on matrix models and fuzzy geometries.
Quantum field theory competitive models
Tolksdorf, Jürgen; Zeidler, Eberhard
2009-01-01
For more than 70 years, quantum field theory (QFT) can be seen as a driving force in the development of theoretical physics. Equally fascinating is the fruitful impact which QFT had in rather remote areas of mathematics. The present book features some of the different approaches, different physically viewpoints and techniques used to make the notion of quantum field theory more precise. For example, the present book contains a discussion including general considerations, stochastic methods, deformation theory and the holographic AdS/CFT correspondence. It also contains a discussion of more recent developments like the use of category theory and topos theoretic methods to describe QFT. The present volume emerged from the 3rd 'Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: 'To bring together outstanding experts working in...
Maxfield, Travis; Robbins, Daniel; Sethi, Savdeep
2016-11-01
Studying a quantum field theory involves a choice of space-time manifold and a choice of background for any global symmetries of the theory. We argue that many more choices are possible when specifying the background. In the context of branes in string theory, the additional data corresponds to a choice of supergravity tensor fluxes. We propose the existence of a landscape of field theory backgrounds, characterized by the space-time metric, global symmetry background and a choice of tensor fluxes. As evidence for this landscape, we study the supersymmetric six-dimensional (2, 0) theory compactified to two dimensions. Different choices of metric and flux give rise to distinct two-dimensional theories, which can preserve differing amounts of supersymmetry.
Maxfield, Travis; Sethi, Savdeep
2015-01-01
Studying a quantum field theory involves a choice of space-time manifold and a choice of background for any global symmetries of the theory. We argue that many more choices are possible when specifying the background. In the context of branes in string theory, the additional data corresponds to a choice of supergravity tensor fluxes. We propose the existence of a landscape of field theory backgrounds, characterized by the space-time metric, global symmetry background and a choice of tensor fluxes. As evidence for this landscape, we study the supersymmetric six-dimensional (2,0) theory compactified to two dimensions. Different choices of metric and flux give rise to distinct two-dimensional theories, which can preserve differing amounts of supersymmetry.
The Theory of Conceptual Fields
Vergnaud, Gerard
2009-01-01
The theory of conceptual fields is a developmental theory. It has two aims: (1) to describe and analyse the progressive complexity, on a long- and medium-term basis, of the mathematical competences that students develop inside and outside school, and (2) to establish better connections between the operational form of knowledge, which consists in…
Neural fields theory and applications
Graben, Peter; Potthast, Roland; Wright, James
2014-01-01
With this book, the editors present the first comprehensive collection in neural field studies, authored by leading scientists in the field - among them are two of the founding-fathers of neural field theory. Up to now, research results in the field have been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. Starting with a tutorial for novices in neural field studies, the book comprises chapters on emergent patterns, their phase transitions and evolution, on stochastic approaches, cortical development, cognition, robotics and computation, large-scale numerical simulations, the coupling of neural fields to the electroencephalogram and phase transitions in anesthesia. The intended readership are students and scientists in applied mathematics, theoretical physics, theoretical biology, and computational neuroscience. Neural field theory and its applications have a long-standing tradition in the mathematical and computational ...
Solutions in Exceptional Field Theory
Energy Technology Data Exchange (ETDEWEB)
Rudolph, Felix J. [Queen Mary University of London, Centre for Research in String Theory, School of Physics, London (United Kingdom)
2016-04-15
Exceptional Field Theory employs an extended spacetime to make supergravity fully covariant under the U-duality groups of M-theory. This allows for the wave and monopole solutions to be combined into a single solution which obeys a twisted self-duality relation. All fundamental, solitonic and Dirichlet branes of ten- and eleven-dimensonal supergravity may be extracted from this single solution in Exceptional Field Theory. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Lectures on Conformal Field Theory
Qualls, Joshua D
2015-01-01
These lectures notes are based on courses given at National Taiwan University, National Chiao-Tung University, and National Tsing Hua University in the spring term of 2015. Although the course was offered primarily for graduate students, these lecture notes have been prepared for a more general audience. They are intended as an introduction to conformal field theories in various dimensions, with applications related to topics of particular interest: topics include the conformal bootstrap program, boundary conformal field theory, and applications related to the AdS/CFT correspondence. We assume the reader to be familiar with quantum mechanics at the graduate level and to have some basic knowledge of quantum field theory. Familiarity with string theory is not a prerequisite for this lectures, although it can only help.
Nonlocal and quasilocal field theories
Tomboulis, E. T.
2015-12-01
We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasilocal (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasilocal kernels all acausal effects are confined within the compact support regions. We briefly discuss the extension to other types of fields and prospects of such theories.
Background Independent String Field Theory
Bars, Itzhak
2014-01-01
We develop a new background independent Moyal star formalism in bosonic open string field theory. The new star product is formulated in a half-phase-space, and because phase space is independent of any background fields, the interactions are background independent. In this basis there is a large amount of symmetry, including a supersymmetry OSp(d|2) that acts on matter and ghost degrees of freedom, and simplifies computations. The BRST operator that defines the quadratic kinetic term of string field theory may be regarded as the solution of the equation of motion A*A=0 of a purely cubic background independent string field theory. We find an infinite number of non-perturbative solutions to this equation, and are able to associate them to the BRST operator of conformal field theories on the worldsheet. Thus, the background emerges from a spontaneous-type breaking of a purely cubic highly symmetric theory. The form of the BRST field breaks the symmetry in a tractable way such that the symmetry continues to be us...
SELF-ORGANIZED SEMANTIC FEATURE EVOLUTION FOR AXIOMATIC DESIGN
Institute of Scientific and Technical Information of China (English)
HAO He; FENG Yixiong; TAN Jianrong; XUE Yang
2008-01-01
Aiming at the problem existing in the computer aided design process that how to express the design intents with high-level engineering terminologies, a mechanical product self-organized semantic feature evolution technology for axiomatic design is proposed, so that the constraint relations between mechanical parts could be expressed in a semantic form which is more suitable for designers. By describing the evolution rules for semantic constraint information, the abstract expression of design semantics in mechanical product evolution process is realized and the constraint relations between parts are mapped to the geometric level from the semantic level; With semantic feature relation graph, the abstract semantic description, the semantic relative structure and the semantic constraint information are linked together; And the methods of semantic feature self-organized evolution are classified. Finally, combining a design example of domestic high-speed elevator, how to apply the theory to practical product development is illustrated and this method and its validity is described and verified. According to the study results, the designers are able to represent the design intents at an advanced semantic level in a more intuitional and natural way and the automation, recursion and visualization for mechanical product axiomatic design are also realized.
Electromagnetic field theories for engineering
Salam, Md Abdus
2014-01-01
A four year Electrical and Electronic engineering curriculum normally contains two modules of electromagnetic field theories during the first two years. However, some curricula do not have enough slots to accommodate the two modules. This book, Electromagnetic Field Theories, is designed for Electrical and Electronic engineering undergraduate students to provide fundamental knowledge of electromagnetic fields and waves in a structured manner. A comprehensive fundamental knowledge of electric and magnetic fields is required to understand the working principles of generators, motors and transformers. This knowledge is also necessary to analyze transmission lines, substations, insulator flashover mechanism, transient phenomena, etc. Recently, academics and researches are working for sending electrical power to a remote area by designing a suitable antenna. In this case, the knowledge of electromagnetic fields is considered as important tool.
Applying the V Model and Axiomatic Design in the Domain of IT Architecture Practice
Tarenskeen, Debbie; Bakker, René; Joosten, Stef
2015-01-01
This paper applies and discusses the principles of Axiomatic Design for changing IT architecture in health care. It presents three case studies positioned in the field of Enterprise architecture that explore how IT architects, as professionals, manage change and re-design the structure of the IT sys
Currents in supersymmetric field theories
Derendinger, Jean-Pierre
2016-01-01
A general formalism to construct and improve supercurrents and source or anomaly superfields in two-derivative N=1 supersymmetric theories is presented. It includes arbitrary gauge and chiral superfields and a linear superfield coupled to gauge fields. These families of supercurrent structures are characterized by their energy-momentum tensors and R currents and they display a specific relation to the dilatation current of the theory. The linear superfield is introduced in order to describe the gauge coupling as a background (or propagating) field. Supersymmetry does not constrain the dependence on this gauge coupling field of gauge kinetic terms and holomorphicity restrictions are absent. Applying these results to an effective (Wilson) description of super-Yang-Mills theory, matching or cancellation of anomalies leads to an algebraic derivation of the all-order NSVZ beta function.
Phenomenology of Noncommutative Field Theories
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.
Bosonic colored group field theory
Energy Technology Data Exchange (ETDEWEB)
Ben Geloun, Joseph [Universite Paris XI, Laboratoire de Physique Theorique, Orsay Cedex (France); University of Abomey-Calavi, Cotonou (BJ). International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair); Universite Cheikh Anta Diop, Departement de Mathematiques et Informatique, Faculte des Sciences et Techniques, Dakar (Senegal); Magnen, Jacques [Ecole Polytechnique, Centre de Physique Theorique, Palaiseau Cedex (France); Rivasseau, Vincent [Universite Paris XI, Laboratoire de Physique Theorique, Orsay Cedex (France)
2010-12-15
Bosonic colored group field theory is considered. Focusing first on dimension four, namely the colored Ooguri group field model, the main properties of Feynman graphs are studied. This leads to a theorem on optimal perturbative bounds of Feynman amplitudes in the ''ultraspin'' (large spin) limit. The results are generalized in any dimension. Finally, integrating out two colors we write a new representation, which could be useful for the constructive analysis of this type of models. (orig.)
Unitarity of superstring field theory
Sen, Ashoke
2016-12-01
We complete the proof of unitarity of (compactified) heterotic and type II string field theories by showing that in the cut diagrams only physical states appear in the sum over intermediate states. This analysis takes into account the effect of mass and wave-function renormalization, and the possibility that the true vacuum may be related to the perturbative vacuum by small shifts in the string fields.
Unitarity of Superstring Field Theory
Sen, Ashoke
2016-01-01
We complete the proof of unitarity of (compactified) heterotic and type II string field theories by showing that in the cut diagrams only physical states appear in the sum over intermediate states. This analysis takes into account the effect of mass and wave-function renormalization, and the possibility that the true vacuum may be related to the perturbative vacuum by small shifts in the string fields.
Fields, meadows and abstract data types
Bergstra, J.; Hirschfeld, Y.; Tucker, J.; Avron, A.; Dershowitz, N.; Rabinovich, A.
2008-01-01
Fields and division rings are not algebras in the sense of "Universal Algebra", as inverse is not a total function. Mending the inverse by any definition of 0(-1) will not suffice to axiomatize the axiom of inverse x(-1) · x = 1, by an equation. In particular the theory of fields cannot be used for
Bohmian mechanics and quantum field theory.
Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino
2004-08-27
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.
Field Analysis and Potential Theory
1985-06-01
T T T 430 FIELD ANALYSIS AND POTENTIAL THEORY [Sec.5.7 But V2f [ dT - Z j V2 Jxdr T T hence V c2at 7- dT _- J2 (J2 dT T TT whence dalf [13 dT " 0 (5.7...8) at exterior points or dal pot [2] - O (5.7-8(a)) Similarly, dalf r dS - 0 (5.7-9) dal [y] ds - 0 (5.7-10) r Sec.5.7] RETARDED POTENTIAL THEORY 431
Einstein's theory of unified fields
Tonnelat, Marie Antoinette
2014-01-01
First published in1966, here is presented a comprehensive overview of one of the most elusive scientific speculations by the pre-eminent genius of the 20th century. The theory is viewed by some scientists with deep suspicion, by others with optimism, but all agree that it represents an extreme challenge. As the author herself affirms, this work is not intended to be a complete treatise or 'didactic exposition' of the theory of unified fields, but rather a tool for further study, both by students and professional physicists. Dealing with all the major areas of research whic
Baal, Pierre Van
2014-01-01
""… a pleasant novelty that manages the impossible: a full course in field theory from a derivation of the Dirac equation to the standard electroweak theory in less than 200 pages. Moreover, the final chapter consists of a careful selection of assorted problems, which are original and either anticipate or detail some of the topics discussed in the bulk of the chapters. Instead of building a treatise out of a collection of lecture notes, the author took the complementary approach and constructed a course out of a number of well-known and classic treatises. The result is fresh and useful. … the
Field reparametrization in effective field theories
Passarino, Giampiero
2016-01-01
Debate topic for Effective Field Theory (EFT) is the choice of a "basis" for $\\mrdim = 6$ operators Clearly all bases are equivalent as long as they are a "basis", containing a minimal set of operators after the use of equations of motion and respecting gauge invariance. From a more formal point of view a basis is characterized by its closure with respect to renormalization. Equivalence of bases should always be understood as a statement for the S-matrix and not for the Lagrangian, as dictated by the equivalence theorem. Any phenomenological approach that misses one of these ingredients is still acceptable for a preliminar analysis, as long as it does not pretend to be an EFT. Here we revisit the equivalence theorem and its consequences for EFT when two sets of higher dimensional operators are connected by a set of non-linear, noninvariant, field reparametrizations.
Variational methods for field theories
Energy Technology Data Exchange (ETDEWEB)
Ben-Menahem, S.
1986-09-01
Four field theory models are studied: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. Free field theory is used as a laboratory for a new variational blocking-truncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes (Boron-Oppenheimer approximation). This ''adiabatic truncation'' method gives very accurate results for ground-state energy density and correlation functions. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Euclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. The transfer-matrix method is used to find a good (non-blocking) trial ground state for the Ising model in a transverse magnetic field in (1 + 1) dimensions.
Karkheck, John; Stell, George
1981-08-01
A kinetic mean-field theory for the evolution of the one-particle distribution function is derived from maximizing the entropy. For a potential with a hard-sphere core plus tail, the resulting theory treats the hard-core part as in the revised Enskog theory. The tail, weighted by the hard-sphere pair distribution function, appears linearly in a mean-field term. The kinetic equation is accompanied by an entropy functional for which an H theorem was proven earlier. The revised Enskog theory is obtained by setting the potential tail to zero, the Vlasov equation is obtained by setting the hard-sphere diameter to zero, and an equation of the Enskog-Vlasov type is obtained by effecting the Kac limit on the potential tail. At equilibrium, the theory yields a radial distribution function that is given by the hard-sphere reference system and thus furnishes through the internal energy a thermodynamic description which is exact to first order in inverse temperature. A second natural route to thermodynamics (from the momentum flux which yields an approximate equation of state) gives somewhat different results; both routes coincide and become exact in the Kac limit. Our theory furnishes a conceptual basis for the association in the heuristically based modified Enskog theory (MET) of the contact value of the radial distribution function with the ''thermal pressure'' since this association follows from our theory (using either route to thermodynamics) and moreover becomes exact in the Kac limit. Our transport theory is readily extended to the general case of a soft repulsive core, e.g., as exhibited by the Lennard-Jones potential, via by-now-standard statistical-mechanical methods involving an effective hard-core potential, thus providing a self-contained statistical-mechanical basis for application to such potentials that is lacking in the standard versions of the MET. We obtain very good agreement with experiment for the thermal conductivity and shear viscosity of several
Vollhardt, D.; Byczuk, K.; Kollar, M.
2011-01-01
The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the ...
Symmetries in Lagrangian Field Theory
Búa, Lucia; Bucataru, Ioan; León, Manuel de; Salgado, Modesto; Vilariño, Silvia
2015-06-01
By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1π of a fiber bundle π : E → ℝk where ℝk is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.
Complete Axiomatization for the Bisimilarity Distance on Markov Chains
DEFF Research Database (Denmark)
Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim Guldstrand;
2016-01-01
In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS...
Zitterbewegung in quantum field theory
Institute of Scientific and Technical Information of China (English)
Wang Zhi-Yong; Xiong Cai-Dong
2008-01-01
Traditionally,the zitterbewegung (ZB) of the Dirac electron has just been studied at the level of quantum mechanics.Seeing the fact that an old interest in ZB has recently been rekindled by the investigations on spintronic,graphene,and superconducting systems,etc.,this paper presents a quantum-field-theory investigation on ZB and obtains the con clusion that,the ZB of an electron arises from the influence of virtual electron-positron pairs (or vacuum fluctuations)on the electron.
The place of probability in Hilbert's axiomatization of physics, ca. 1900-1928
Verburgt, Lukas M.
2016-02-01
Although it has become a common place to refer to the 'sixth problem' of Hilbert's (1900) Paris lecture as the starting point for modern axiomatized probability theory, his own views on probability have received comparatively little explicit attention. The central aim of this paper is to provide a detailed account of this topic in light of the central observation that the development of Hilbert's project of the axiomatization of physics went hand-in-hand with a redefinition of the status of probability theory and the meaning of probability. Where Hilbert first regarded the theory as a mathematizable physical discipline and later approached it as a 'vague' mathematical application in physics, he eventually understood probability, first, as a feature of human thought and, then, as an implicitly defined concept without a fixed physical interpretation. It thus becomes possible to suggest that Hilbert came to question, from the early 1920s on, the very possibility of achieving the goal of the axiomatization of probability as described in the 'sixth problem' of 1900.
Number theory arising from finite fields analytic and probabilistic theory
Knopfmacher, John
2001-01-01
""Number Theory Arising from Finite Fields: Analytic and Probabilistic Theory"" offers a discussion of the advances and developments in the field of number theory arising from finite fields. It emphasizes mean-value theorems of multiplicative functions, the theory of additive formulations, and the normal distribution of values from additive functions. The work explores calculations from classical stages to emerging discoveries in alternative abstract prime number theorems.
A Naturally Renormalized Quantum Field Theory
2006-01-01
It was shown that quantum metric fluctuations smear out the singularities of Green's functions on the light cone [1], but it does not remove other ultraviolet divergences of quantum field theory. We have proved that the quantum field theory in Krein space, {\\it i.e.} indefinite metric quantization, removes all divergences of quantum field theory with exception of the light cone singularity [2,3]. In this paper, it is discussed that the combination of quantum field theory in Krein space togeth...
Inflation from string field theory
Koshelev, Alexey S; Moniz, Paulo Vargas
2016-01-01
In the framework of string field theory (SFT) a setting where the closed string dilaton is coupled to the open string tachyon at the final stage of an unstable brane or brane-anti-brane pair decay is considered. We show that this configuration can lead to viable inflation by means of the dilaton becoming a non-local (infinite-derivative) inflaton. The structure of non-locality leads to interesting inflationary scenarios. We obtain (i) a class of single field inflation with universal attractor predictions at $n_{s}\\sim0.967$ with any value of $r<0.1$, where the tensor to scalar ratio $r$ can be solely regulated by parameters of the SFT; (ii) a new class of two field conformally invariant models with a peculiar quadratic cross-product of scalar fields. We analyze a specific case where a spontaneously broken conformal invariance leads to Starobinsky like inflation plus creating an uplifted potential minimum which accounts to vacuum energy after inflation.
Field Theory of Fundamental Interactions
Wang, Shouhong; Ma, Tian
2017-01-01
First, we present two basic principles, the principle of interaction dynamics (PID) and the principle of representation invariance (PRI). Intuitively, PID takes the variation of the action under energy-momentum conservation constraint. We show that the PID is the requirement of the presence of dark matter and dark energy, the Higgs field and the quark confinement. PRI requires that the SU(N) gauge theory be independent of representations of SU(N). It is clear that PRI is the logic requirement of any gauge theory. With PRI, we demonstrate that the coupling constants for the strong and the weak interactions are the main sources of these two interactions, reminiscent of the electric charge. Second, we emphasize that symmetry principles-the principle of general relativity and the principle of Lorentz invariance and gauge invariance-together with the simplicity of laws of nature, dictate the actions for the four fundamental interactions. Finally, we show that the PID and the PRI, together with the symmetry principles give rise to a unified field model for the fundamental interactions, which is consistent with current experimental observations and offers some new physical predictions. The research is supported in part by the National Science Foundation (NSF) grant DMS-1515024, and by the Office of Naval Research (ONR) grant N00014-15-1-2662.
Effective Field Theories and Inflation
Burgess, C P; Holman, R
2003-01-01
We investigate the possible influence of very-high-energy physics on inflationary predictions focussing on whether effective field theories can allow effects which are parametrically larger than order H^2/M^2, where M is the scale of heavy physics and H is the Hubble scale at horizon exit. By investigating supersymmetric hybrid inflation models, we show that decoupling does not preclude heavy-physics having effects for the CMB with observable size even if H^2/M^2 << O(1%), although their presence can only be inferred from observations given some a priori assumptions about the inflationary mechanism. Our analysis differs from the results of hep-th/0210233, in which other kinds of heavy-physics effects were found which could alter inflationary predictions for CMB fluctuations, inasmuch as the heavy-physics can be integrated out here to produce an effective field theory description of low-energy physics. We argue, as in hep-th/0210233, that the potential presence of heavy-physics effects in the CMB does no...
Quantum Field Theory in (0 + 1) Dimensions
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
Noncommutative Dipole Field Theories And Unitarity
Chiou, D W; Chiou, Dah-Wei; Ganor, Ori J.
2004-01-01
We extend the argument of Gomis and Mehen for violation of unitarity in field theories with space-time noncommutativity to dipole field theories. In dipole field theories with a timelike dipole vector, we present 1-loop amplitudes that violate the optical theorem. A quantum mechanical system with nonlocal potential of finite extent in time also shows violation of unitarity.
Conformal field theory, boundary conditions and applications to string theory
Schweigert, C.; Fuchs, J.; Walcher, J.
2000-01-01
This is an introduction to two-dimensional conformal field theory and its applications in string theory. Modern concepts of conformal field theory are explained, and it is outlined how they are used in recent studies of D-branes in the strong curvature regime by means of CFT on surfaces with boundary.
Neutrix Calculus and Finite Quantum Field Theory
Ng, Y J
2004-01-01
In general, quantum field theories require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like QED are not convergent series, but are asymptotic series in their interaction couplings. We propose to apply neutrix calculus, developed by van der Corput and Hadamard in connection with asymptotic series, to tackle divergent integrals, yielding finite renormalizations for the parameters in quantum field theories. We observe that quantum gravity theories are rendered more manageable, and that both renormalizable field theories and effective field theories can be accommodated in the framework of neutrix calculus.
Axiomatic nonextensive statistics at NICA energies
Energy Technology Data Exchange (ETDEWEB)
Nasser Tawfik, Abdel [Modern University for Technology and Information (MTI), Egyptian Center for Theoretical Physics (ECTP), Cairo (Egypt); World Laboratory for Cosmology And Particle Physics (WLCAPP), Cairo (Egypt); Network for Nuclear Sciences (NNS), Academy for Scientific Research and Technology (ASRT), Cairo (Egypt)
2016-08-15
We discuss the possibility of implementing axiomatic nonextensive statistics, where it is conjectured that the phase-space volume determines the (non)extensive entropy, on the particle production at NICA energies. Both Boltzmann-Gibbs and Tsallis statistics are very special cases of this generic (non)extensivity. We conclude that the lattice thermodynamics is ab initio extensive and additive and thus the nonextensive approaches including Tsallis statistics categorically are not matching with them, while the particle production, for instance the particle ratios at various center-of-mass energies, is likely a nonextensive process but certainly not of Tsallis type. The resulting freezeout parameters, the temperature and the chemical potentials, are approximately compatible with the ones deduced from Boltzmann-Gibbs statistics. (orig.)
An axiomatic approach to Maxwell's equations
Heras, José A
2016-01-01
This paper suggests an axiomatic approach to Maxwell's equations. The basis of this approach is a theorem formulated for two sets of functions localized in space and time. If each set satisfies a continuity equation then the theorem provides an integral representation for each function. A corollary of this theorem yields Maxwell's equations with magnetic monopoles. It is pointed out that the causality principle and the conservation of electric and magnetic charges are the most fundamental physical axioms underlying these equations. Another application of the corollary yields Maxwell's equations in material media. The theorem is also formulated in the Minkowski space-time and applied to obtain the covariant form of Maxwell's equations with magnetic monopoles and the covariant form of Maxwell's equations in material media. The approach makes use of the infinite-space Green function of the wave equation and is therefore suitable for an advanced course in electrodynamics.
Axiomatic nonextensive statistics at NICA energies
Tawfik, Abdel Nasser
2016-01-01
We discuss the possibility of implementing axiomatic nonextensive statistics, where it is conjectured that the phase-space volume determines the (non)extensive entropy, on the particle production at NICA energies. Both Boltzmann-Gibbs and Tsallis statistics are very special cases of this generic (non)extensivity. We conclude that the lattice thermodynamics is {\\it ab initio} extensive and additive and thus the nonextensive approaches including Tsallis statistics categorically are not matching with them, while the particle production, for instance the particle ratios at various center-of-mass energies, is likely a nonextensive process but certainly not of Tsallis type. The resulting freezeout parameters, the temperature and the chemical potentials, are approximately compatible with the ones deduced from Boltzmann-Gibbs statistics.
Encoding field theories into gravities
Aoki, Sinya; Onogi, Tetsuya
2016-01-01
We propose a method to give a $d+1$ geometry from a $d$ dimensional quantum field theory in the large N expansion. We first construct a $d+1$ dimensional field from the $d$ dimensional one using the gradient flow equation, whose flow time $t$ represents the energy scale of the system such that $t\\rightarrow 0$ corresponds to the ultra-violet (UV) while $t\\rightarrow\\infty$ to the infra-red (IR). We define the induced metric using $d+1$ dimensional field operators. We show that the metric defined in this way becomes classical in the large N limit: quantum fluctuations of the metric are suppressed as 1/N due to the large $N$ factorization property. As a concrete example, we apply our method to the O(N) non-linear $\\sigma$ model in two dimensions. We calculate the three dimensional induced metric, which describes an AdS space in the massless limit. We finally discuss several open issues for future investigations.
Quantum Field Theory A Modern Perspective
Parameswaran Nair, V
2005-01-01
Quantum field theory, which started with Paul Dirac’s work shortly after the discovery of quantum mechanics, has produced an impressive and important array of results. Quantum electrodynamics, with its extremely accurate and well-tested predictions, and the standard model of electroweak and chromodynamic (nuclear) forces are examples of successful theories. Field theory has also been applied to a variety of phenomena in condensed matter physics, including superconductivity, superfluidity and the quantum Hall effect. The concept of the renormalization group has given us a new perspective on field theory in general and on critical phenomena in particular. At this stage, a strong case can be made that quantum field theory is the mathematical and intellectual framework for describing and understanding all physical phenomena, except possibly for a quantum theory of gravity. Quantum Field Theory: A Modern Perspective presents Professor Nair’s view of certain topics in field theory loosely knit together as it gr...
Quantum Mechanics and Quantum Field Theory
Dimock, Jonathan
2011-02-01
Introduction; Part I. Non-relativistic: 1. Mathematical prelude; 2. Classical mechanics; 3. Quantum mechanics; 4. Single particle; 5. Many particles; 6. Statistical mechanics; Part II. Relativistic: 7. Relativity; 8. Scalar particles and fields; 9. Electrons and photons; 10. Field theory on a manifold; Part III. Probabilistic Methods: 11. Path integrals; 12. Fields as random variables; 13. A nonlinear field theory; Appendices; References; Index.
Families and degenerations of conformal field theories
Energy Technology Data Exchange (ETDEWEB)
Roggenkamp, D.
2004-09-01
In this work, moduli spaces of conformal field theories are investigated. In the first part, moduli spaces corresponding to current-current deformation of conformal field theories are constructed explicitly. For WZW models, they are described in detail, and sigma model realizations of the deformed WZW models are presented. The second part is devoted to the study of boundaries of moduli spaces of conformal field theories. For this purpose a notion of convergence of families of conformal field theories is introduced, which admits certain degenerated conformal field theories to occur as limits. To such a degeneration of conformal field theories, a degeneration of metric spaces together with additional geometric structures can be associated, which give rise to a geometric interpretation. Boundaries of moduli spaces of toroidal conformal field theories, orbifolds thereof and WZW models are analyzed. Furthermore, also the limit of the discrete family of Virasoro minimal models is investigated. (orig.)
Localisation in Quantum Field Theory
Balachandran, A P
2016-01-01
In nonrelativistic quantum mechanics , Born's principle of localisation is as follows: For a single particle, if a wave function $\\psi_K$ vanishes outside a spatial region $K$, it is said to be localised in $K$. In particular if a spatial region $K'$ is disjoint from $K$, a wave function $\\psi_{K'}$ localised in $K'$ is orthogonal to $\\psi_K$. Such a principle of localisation does not exist compatibly with relativity and causality in quantum field theory (Newton and Wigner) or interacting point particles (Currie,Jordan and Sudarshan).It is replaced by symplectic localisation of observables as shown by Brunetti, Guido and Longo, Schroer and others. This localisation gives a simple derivation of the spin-statistics theorem and the Unruh effect, and shows how to construct quantum fields for anyons and for massless particles with `continuous' spin. This review outlines the basic principles underlying symplectic localisation and shows or mentions its deep implications. In particular, it has the potential to affect...
Nuclear Dynamics with Effective Field Theories
Epelbaum, Evgeny
2013-01-01
These are the proceedings of the international workshop on "Nuclear Dynamics with Effective Field Theories" held at Ruhr-Universitaet Bochum, Germany from July 1 to 3, 2013. The workshop focused on effective field theories of low-energy QCD, chiral perturbation theory for nuclear forces as well as few- and many-body physics. Included are a short contribution per talk.
Towards an axiomatic noncommutative geometry of quantum space and time
Kiselev, Arthemy V
2013-01-01
By exploring a possible physical realisation of the geometric concept of noncommutative tangent bundle, we outline an axiomatic quantum picture of space as topological manifold and time as a count of its reconfiguration events.
Final design of a spacer grid using axiomatic design
Energy Technology Data Exchange (ETDEWEB)
Park, Gyung-Jin; Lee, Hyun-Ah; Kim, Chong-Ki [Hanyang Univ., Seoul (Korea, Republic of); Song, Gi-Nam [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2007-03-15
The spacer grid set is a component in the nuclear fuel assembly. The set supports the fuel rod safely. The spacer grid set must have enough strength to sustain external loads such as earthquake. The fretting wear occurs between the spring of the fuel rod and the spacer grid due to the flow-induced vibration after the fuel rod is inserted to the spacer grid set. Design of the spring is carried out by using the independence axiom in axiomatic design to solve the two problems. The spacer grid is divided into two parts for sustaining the impact load and reducing fretting wear based on the function requirements. The design for the impact load is performed through non-linear analysis and the homology theory is adopted to reduce fretting wear achieved for shape optimization. The objective function to be minimized ids the maximum stress and constraints are defined to increase the contact area between the fuel rod and the spring using the homology theory. In the design results, the contact area becomes large and it is conformed by nonlinear static analysis. The final design shows that larger impact loads can be sustained compared to the current model.
Design of Safety Injection Tanks Using Axiomatic Design and TRIZ
Energy Technology Data Exchange (ETDEWEB)
Heo, Gyunyoung [Kyung Hee University, 1 Seocheon-dong, Giheung-gu, Yongin-si, Gyeonggi-do, 446-701 (Korea, Republic of); Jeong, Yong Hoon [Korea Advanced Institute of Science and Technology, 373-1 Guseong-dong, Yuseong-gu, Daejeon, 305-701 (Korea, Republic of)
2008-07-01
Design can be categorized into two steps: 'synthesis' and 'analysis'. While synthesis is the process of decision-making on design parameters, analysis is the process of optimizing the parameters selected. It is known from experience that the mistakes made in the synthesis process are hardly corrected in the analysis process. 'Systematic synthesis' is, therefore, easy to overlook but an important topic. 'Systematic' is interpreted as 'minimizing' uncertainty and subjectivity. This paper will introduce the design product achieved by using Axiomatic Design (AD) and TRIZ (Theory of Inventive Problem Solving romanized acronym for Russian), which is a new design of Safety Injection Tank (SIT). In designing a large-capacity SIT which should play an important role in mitigating the large break loss of coolant accidents, there are three issues: 1) the excessively large plenum for pressurized nitrogen gas; 2) the difficulties maintaining the high initial injection flow rate; and 3) the non-condensable nitrogen gas in the coolant. This study proposes a conceptual idea for SITs that are pressurized by the chemical reaction of solid propellants. The AD theory and the principles of TRIZ enable new approach in problem-solving for those three issues in an innovative way. The paper made an effort to clarify the systematic synthesis process to reach the final design solution. (authors)
Dynamics and causality constraints in field theory
De Souza, M M
1997-01-01
We discuss the physical meaning and the geometric interpretation of causality implementation in classical field theories. Causality is normally implemented through kinematical constraints on fields but we show that in a zero-distance limit they also carry a dynamical information, which calls for a revision of our standard concepts of interacting fields. The origin of infinities and other inconsistencies in field theories is traced to fields defined with support on the lightcone; a finite and consistent field theory requires a lightcone generator as the field support.
Magnetic Backgrounds and Noncommutative Field Theory
Szabo, Richard J.
2004-01-01
This paper is a rudimentary introduction, geared at non-specialists, to how noncommutative field theories arise in physics and their applications to string theory, particle physics and condensed matter systems.
Introductory Lectures on Quantum Field Theory
Alvarez-Gaumé, Luís
2014-01-01
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String Theory.
Toward a gauge field theory of gravity.
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
Towards weakly constrained double field theory
Directory of Open Access Journals (Sweden)
Kanghoon Lee
2016-08-01
Full Text Available We show that it is possible to construct a well-defined effective field theory incorporating string winding modes without using strong constraint in double field theory. We show that X-ray (Radon transform on a torus is well-suited for describing weakly constrained double fields, and any weakly constrained fields are represented as a sum of strongly constrained fields. Using inverse X-ray transform we define a novel binary operation which is compatible with the level matching constraint. Based on this formalism, we construct a consistent gauge transform and gauge invariant action without using strong constraint. We then discuss the relation of our result to the closed string field theory. Our construction suggests that there exists an effective field theory description for massless sector of closed string field theory on a torus in an associative truncation.
Towards weakly constrained double field theory
Lee, Kanghoon
2016-08-01
We show that it is possible to construct a well-defined effective field theory incorporating string winding modes without using strong constraint in double field theory. We show that X-ray (Radon) transform on a torus is well-suited for describing weakly constrained double fields, and any weakly constrained fields are represented as a sum of strongly constrained fields. Using inverse X-ray transform we define a novel binary operation which is compatible with the level matching constraint. Based on this formalism, we construct a consistent gauge transform and gauge invariant action without using strong constraint. We then discuss the relation of our result to the closed string field theory. Our construction suggests that there exists an effective field theory description for massless sector of closed string field theory on a torus in an associative truncation.
Towards Weakly Constrained Double Field Theory
Lee, Kanghoon
2015-01-01
We show that it is possible to construct a well-defined effective field theory incorporating string winding modes without using strong constraint in double field theory. We show that X-ray (Radon) transform on a torus is well-suited for describing weakly constrained double fields, and any weakly constrained fields are represented as a sum of strongly constrained fields. Using inverse X- ray transform we define a novel binary operation which is compatible with the level matching constraint. Based on this formalism, we construct a consistent gauge transform and gauge invariant action without using strong constraint. We then discuss the relation of our result to the closed string field theory. Our construction suggests that there exists an effective field theory description for massless sector of closed string field theory on a torus in an associative truncation.
Gauge field theories: various mathematical approaches
Jordan, François; Thierry, Masson
2014-01-01
This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe Yang-Mills-Higgs theories or gravitation theories, and each of them improves the paradigm of gauge field theories. A brief comparison between them is carried out, essentially due to the various notions of connection. However they reveal a compelling common mathematical pattern on which the paper concludes.
Conformal field theory on the plane
Ribault, Sylvain
2014-01-01
We provide an introduction to conformal field theory on the plane in the conformal bootstrap approach. We introduce the main ideas of the bootstrap approach to quantum field theory, and how they apply to two-dimensional theories with local conformal symmetry. We describe the mathematical structures which appear in such theories, from the Virasoro algebra and its representations, to the BPZ equations and their solutions. As examples, we study a number of models: Liouville theory, (generalized) minimal models, free bosonic theories, the $H_3^+$ model, and the $SU_2$ and $\\widetilde{SL}_2(\\mathbb{R})$ WZW models.
Parameterized quantum field theory without Haag's theorem
Seidewitz, Ed
2015-01-01
Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that quantum field theory can be formulated, using an invariant, fifth path parameter in addition to the usual four position parameters, in such a way that Haag's theorem no longer applies, but such that the Dyson perturbation expansion for the sc...
The problem of interaction in a dynamical theory of particles (general questions). 2
Sannikov-Proskuryakov, S S
2002-01-01
We continue the consideration of the interaction problem in the frame of a new field particle theory. Here a new correspondence principle and the connection between bilocal and usual local fields are discussed. The method of second quantization of bilocal fields is formulated and a scattering matrix is built. Explicit form of smearing operators and formfactors is found. Comparison of a new particle field theory with the old (local) axiomatic approach is given.
Killing Vector Fields and Superharmonic Field Theories
Groeger, Josua
2013-01-01
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, referred to as superharmonic action, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of the superharmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.
Duality Covariant Solutions in Extended Field Theories
Rudolph, Felix J
2016-01-01
Double field theory and exceptional field theory are formulations of supergravity that make certain dualities manifest symmetries of the action. To achieve this, the geometry is extended by including dual coordinates corresponding to winding modes of the fundamental objects. This geometrically unifies the spacetime metric and the gauge fields (and their local symmetries) in a generalized geometry. Solutions to these extended field theories take the simple form of waves and monopoles in the extended space. From a supergravity point of view they appear as 1/2 BPS objects such as the string, the membrane and the fivebrane in ordinary spacetime. In this thesis double field theory and exceptional field theory are introduced, solutions to their equations of motion are constructed and their properties are analyzed. Further it is established how isometries in the extended space give rise to duality relations between the supergravity solutions. Extensions to these core ideas include studying Goldstone modes, probing s...
Zahedi, Ramin
2015-01-01
The main idea of this article is based on my previous publications (Refs. [1], [2], [3], [4], 1997-1998). In this article we present a new axiomatic matrix approach (and subsequently constructing a linearization theory) based on the ring theory and the generalized Clifford algebra. On the basis of this (primary) mathematical approach and also the assumption of discreteness of the relativistic energy-momentum (D-momentum), by linearization (and simultaneous parameterization, as necessary algeb...
Worked examples in engineering field theory
Fuller, A J Baden
1976-01-01
Worked Examples in Engineering Field Theory is a product of a lecture course given by the author to first-year students in the Department of Engineering in the University of Leicester. The book presents a summary of field theory together with a large number of worked examples and solutions to all problems given in the author's other book, Engineering Field Theory. The 14 chapters of this book are organized into two parts. Part I focuses on the concept of flux including electric flux. This part also tackles the application of the theory in gravitation, ideal fluid flow, and magnetism. Part II d
Wavelet-Based Quantum Field Theory
Directory of Open Access Journals (Sweden)
Mikhail V. Altaisky
2007-11-01
Full Text Available The Euclidean quantum field theory for the fields $phi_{Delta x}(x$, which depend on both the position $x$ and the resolution $Delta x$, constructed in SIGMA 2 (2006, 046, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments.
Lattice methods and effective field theory
Nicholson, Amy N
2016-01-01
Lattice field theory is a non-perturbative tool for studying properties of strongly interacting field theories, which is particularly amenable to numerical calculations and has quantifiable systematic errors. In these lectures we apply these techniques to nuclear Effective Field Theory (EFT), a non-relativistic theory for nuclei involving the nucleons as the basic degrees of freedom. The lattice formulation of [1,2] for so-called pionless EFT is discussed in detail, with portions of code included to aid the reader in code development. Systematic and statistical uncertainties of these methods are discussed at length, and extensions beyond pionless EFT are introduced in the final Section.
Backgrounds in Boundary String Field Theory
Baumgartl, M
2009-01-01
We study the role of closed string backgrounds in boundary string field theory. Background independence requires the introduction of dual boundary fields, which are reminiscent of the doubled field formalism. We find a correspondence between closed string backgrounds and collective excitations of open strings described by vertex operators involving dual fields. Renormalization group flow, solutions and stability are discussed in an example.
Ostrogradsky in Theories with Multiple Fields
de Rham, Claudia
2016-01-01
We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar--Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark ene...
Quantum Field Theory in a Semiotic Perspective
Günter Dosch, Hans; Sieroka, Norman
2005-01-01
Viewing physical theories as symbolic constructions came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic field from mechanics; most notably this happened through the work of Helmholtz, Hertz, Poincaré, and later Weyl. The epistemological problems that nourished this development are today highlighted within quantum field theory. The present essay starts off with a concise and non-technical outline of the firmly based aspects of relativistic quantum field theory, i.e. the very successful description of subnuclear phenomena. The particular methods, by which these different aspects have to be accessed, then get described as distinct facets of quantum field theory. The authors show how these different facets vary with respect to the relation between quantum fields and associated particles. Thus, by emphasising the respective role of various basic concepts involved, the authors claim that only a very general epistemic approach can properly ac...
Pilot-wave theory and quantum fields
Struyve, Ward
2010-10-01
Pilot-wave theories provide possible solutions to the measurement problem. In such theories, quantum systems are not only described by the state vector but also by some additional variables. These additional variables, also called beables, can be particle positions, field configurations, strings, etc. In this paper we focus our attention on pilot-wave theories in which the additional variables are field configurations. The first such theory was proposed by Bohm for the free electromagnetic field. Since Bohm, similar pilot-wave theories have been proposed for other quantum fields. The purpose of this paper is to present an overview and further development of these proposals. We discuss various bosonic quantum field theories such as the Schrödinger field, the free electromagnetic field, scalar quantum electrodynamics and the Abelian Higgs model. In particular, we compare the pilot-wave theories proposed by Bohm and by Valentini for the electromagnetic field, finding that they are equivalent. We further discuss the proposals for fermionic fields by Holland and Valentini. In the case of Holland's model we indicate that further work is required in order to show that the model is capable of reproducing the standard quantum predictions. We also consider a similar model, which does not seem to reproduce the standard quantum predictions. In the case of Valentini's model we point out a problem that seems hard to overcome.
Noncommutative Field Theory on Homogeneous Gravitational Waves
Halliday, S; Halliday, Sam; Szabo, Richard J.
2006-01-01
We describe an algebraic approach to the time-dependent noncommutative geometry of a six-dimensional Cahen-Wallach pp-wave string background supported by a constant Neveu-Schwarz flux, and develop a general formalism to construct and analyse quantum field theories defined thereon. Various star-products are derived in closed explicit form and the Hopf algebra of twisted isometries of the plane wave is constructed. Scalar field theories are defined using explicit forms of derivative operators, traces and noncommutative frame fields for the geometry, and various physical features are described. Noncommutative worldvolume field theories of D-branes in the pp-wave background are also constructed.
Conformal Field Theory Correlators from Classical Scalar Field Theory on $AdS_{d+1}$
Mück, W; Mueck, Wolfgang
1998-01-01
We use the correspondence between scalar field theory on $AdS_{d+1}$ and a conformal field theory on $R^d$ to calculate the 3- and 4-point functions of the latter. The classical scalar field theory action is evaluated at tree level.
Matrix string theory, contact terms, and superstring field theory
Dijkgraaf, R; Dijkgraaf, Robbert; Motl, Lubos
2003-01-01
In this note, we first explain the equivalence between the interaction Hamiltonian of Green-Schwarz light-cone gauge superstring field theory and the twist field formalism known from matrix string theory. We analyze the role of the large N limit in matrix string theory, in particular in relation with conformal perturbation theory around the orbifold SCFT that reproduces light-cone string perturbation theory. We show how the scaling with N is directly related to measures on the moduli space of Riemann surfaces. The scaling dimension 3 of the Mandelstam vertex as reproduced by the twist field interaction is in this way related to the dimension 3(h-1) of the moduli space. We analyze the structure and scaling of the higher order twist fields that represent the contact terms. We find one relevant twist field at each order. More generally, the structure of string field theory seems more transparent in the twist field formalism. Finally we also investigate the modifications necessary to describe the pp-wave backgrou...
Weiss, Edwin
1998-01-01
Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate's thesis).Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract te
Resolving Witten’s superstring field theory
Energy Technology Data Exchange (ETDEWEB)
Erler, Theodore; Konopka, Sebastian; Sachs, Ivo [Arnold Sommerfeld Center, Ludwig-Maximilians University, Theresienstrasse 37, D-80333, Munich (Germany)
2014-04-24
We regulate Witten’s open superstring field theory by replacing the picture-changing insertion at the midpoint with a contour integral of picture changing insertions over the half-string overlaps of the cubic vertex. The resulting product between string fields is non-associative, but we provide a solution to the A{sub ∞} relations defining all higher vertices. The result is an explicit covariant superstring field theory which by construction satisfies the classical BV master equation.
Supergeometry in locally covariant quantum field theory
Hack, Thomas-Paul; Schenkel, Alexander
2015-01-01
In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor A : SLoc --> S*Alg to the category of super-*-algebras which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct super-quantum field theories in terms of enriched functors eA : eSLoc --> eS*Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the en...
A Field Theory with Curvature and Anticurvature
Directory of Open Access Journals (Sweden)
M. I. Wanas
2014-01-01
Full Text Available The present work is an attempt to construct a unified field theory in a space with curvature and anticurvature, the PAP-space. The theory is derived from an action principle and a Lagrangian density using a symmetric linear parameterized connection. Three different methods are used to explore physical contents of the theory obtained. Poisson’s equations for both material and charge distributions are obtained, as special cases, from the field equations of the theory. The theory is a pure geometric one in the sense that material distribution, charge distribution, gravitational and electromagnetic potentials, and other physical quantities are defined in terms of pure geometric objects of the structure used. In the case of pure gravity in free space, the spherical symmetric solution of the field equations gives the Schwarzschild exterior field. The weak equivalence principle is respected only in the case of pure gravity in free space; otherwise it is violated.
Light-Front quantization of field theory
Srivastava, P P
1996-01-01
Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincarè algebra and the LF Spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local Hamiltonian theory on the LF in view of the constraint equations on the phase space, which relate the bosonic condensates to the non-zero modes. This new ingredient is useful to describe the spontaneous symmetry breaking on the LF. The instability of the symmetric phase in two dimensional scalar theory when the coupling constant grows is shown in the LF theory renormalized to one loop order. Chern-Simons gauge theory regarded to describe excitations with fractional statistics, is quantized in the light-cone gauge and a simple LF Hamiltonian obtained which may allow us to construct renormalized theory of anyons.
Playing with QCD I: effective field theories
Energy Technology Data Exchange (ETDEWEB)
Fraga, Eduardo S. [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Inst. de Fisica
2009-07-01
The building blocks of hadrons are quarks and gluons, although color is confined into singlet states. QCD is believed to be the fundamental theory of strong interactions. Its asymptotically free nature puts the vacuum out of reach for perturbation theory. The Lagrangian of QCD and the Feynman rules associated were built by using the Gauge Principle, starting from the quark matter fields and obtaining gluons as connections. A simpler, and sometimes necessary or complementary, approach is provided by effective field theories or effective models, especially when one has to deal with the nonperturbative sector of the theory. (author)
N=2 gauge theories and degenerate fields of Toda theory
Kanno, Shoichi; Shiba, Shotaro; Tachikawa, Yuji
2009-01-01
We discuss the correspondence between degenerate fields of the W_N algebra and punctures of Gaiotto's description of the Seiberg-Witten curve of N=2 superconformal gauge theories. Namely, we find that the type of degenerate fields of the W_N algebra, with null states at level one, is classified by Young diagrams with N boxes, and that the singular behavior of the Seiberg-Witten curve near the puncture agrees with that of W_N generators. We also find how to translate mass parameters of the gauge theory to the momenta of the Toda theory.
Chaotic instantons in scalar field theory
Addazi, Andrea
2016-01-01
We consider a new class of instantons in context of quantum field theory of a scalar field coupled with a chaotic background source field. We show how the instanton associated to the quantum tunneling from a metastable false to the true vacuum will be corrected by an exponential enhancement factor. Possible implications are discussed.
Problem Book in Quantum Field Theory
Radovanovič, Voja
2008-01-01
The Problem Book in Quantum Field Theory contains about 200 problems with solutions or hints that help students to improve their understanding and develop skills necessary for pursuing the subject. It deals with the Klein-Gordon and Dirac equations, classical field theory, canonical quantization of scalar, Dirac and electromagnetic fields, the processes in the lowest order of perturbation theory, renormalization and regularization. The solutions are presented in a systematic and complete manner. The material covered and the level of exposition make the book appropriate for graduate and undergraduate students in physics, as well as for teachers and researchers. The new edition is a corrected paperback edition for students.
On 2-dimensional topological field theories
Dumitrescu, Florin
2010-01-01
In this paper we give a characterization of 2-dimensional topological field theories over a space $X$ as Frobenius bundles with connections over $LX$, the free loop space of $X$. This is a generalization of the folk theorem stating that 2-dimensional topological field theories (over a point) are described by finite-dimensional commutative Frobenius algebras. In another direction, this result extends the description of 1-dimensional topological field theories over a space $X$ as vector bundles with connections over $X$, cf. \\cite{DST}.
Quantum Field Theory on Noncommutative Spaces
Szabó, R J
2003-01-01
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative Yang-Mills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an in-depth study of the gauge group of noncommutative Yang-Mills theory. Some of the more mathematical ideas and techniques of noncommutative geometry are also briefly explained.
Ostrogradsky in theories with multiple fields
Energy Technology Data Exchange (ETDEWEB)
Rham, Claudia de; Matas, Andrew [CERCA, Department of Physics, Case Western Reserve University,10900 Euclid Ave, Cleveland, OH 44106 (United States)
2016-06-23
We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.
Bi-local Fields in Noncommutative Field Theory
Iso, S; Kitazawa, Y; Iso, Satoshi; Kawai, Hikaru; Kitazawa, Yoshihisa
2000-01-01
We propose a bi-local representation in noncommutative field theory. It provides a simple description for high momentum degrees of freedom. It also shows that the low momentum modes can be well approximated by ordinary local fields. Long range interactions are generated in the effective action for the lower momentum modes after integrating out the high momentum bi-local fields. The low momentum modes can be represented by diagonal blocks in the matrix model picture and the high momentum bi-local fields correspond to off-diagonal blocks. This block-block interaction picture simply reproduces the infrared singular behaviors of nonplanar diagrams in noncommutative field theory.
Applying axiomatic design methodology in developing modified libertation products
Directory of Open Access Journals (Sweden)
Bibiana Margarita Vallejo Díaz
2010-04-01
Full Text Available Some conceptual elements regarding the axiomatic design method were applied to a specific case-study regarding developing modified liberation compressed product (CLM-UN, for use in the agricultural sector as pH regulating agent in solil. The study was orientated towards defining functional requeriments, design parameters and process variables for manufacturing the product. Independence and information were evaluated, supporting axiomatic design as an alternative for integral product and process design (as a rational and systemic exercise, facilitating producing products having the quality which future users expect from them.
The Theory of Sets of Ordinals
Koepke, Peter; Koerwien, Martin
2005-01-01
We propose a natural theory SO axiomatizing the class of sets of ordinals in a model of ZFC set theory. Both theories possess equal logical strength. Constructibility theory in SO corresponds to a natural recursion theory on ordinals.
Factorization algebras in quantum field theory
Costello, Kevin
2017-01-01
Factorization algebras are local-to-global objects that play a role in classical and quantum field theory which is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this first volume, the authors develop the theory of factorization algebras in depth, but with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern-Simons theory. Expositions of the relevant background in homological algebra, sheaves and functional analysis are also included, thus making this book ideal for researchers and graduates working at the interface between mathematics and physics.
The conceptual framework of quantum field theory
Duncan, Anthony
2012-01-01
The book attempts to provide an introduction to quantum field theory emphasizing conceptual issues frequently neglected in more "utilitarian" treatments of the subject. The book is divided into four parts, entitled respectively "Origins", "Dynamics", "Symmetries", and "Scales". The emphasis is conceptual - the aim is to build the theory up systematically from some clearly stated foundational concepts - and therefore to a large extent anti-historical, but two historical Chapters ("Origins") are included to situate quantum field theory in the larger context of modern physical theories. The three remaining sections of the book follow a step by step reconstruction of this framework beginning with just a few basic assumptions: relativistic invariance, the basic principles of quantum mechanics, and the prohibition of physical action at a distance embodied in the clustering principle. The "Dynamics" section of the book lays out the basic structure of quantum field theory arising from the sequential insertion of quan...
Magnetic fields, special relativity and potential theory elementary electromagnetic theory
Chirgwin, B H; Kilmister, C W
1972-01-01
Magnetic Fields, Special Relativity and Potential Theory is an introduction to electromagnetism, special relativity, and potential theory, with emphasis on the magnetic field of steady currents (magnetostatics). Topics covered range from the origin of the magnetic field and the magnetostatic scalar potential to magnetization, electromagnetic induction and magnetic energy, and the displacement current and Maxwell's equations. This volume is comprised of five chapters and begins with an overview of magnetostatics, followed by a chapter on the methods of solving potential problems drawn from elec
A New Theory of the Electromagnetic Field
Kriske, Richard
2017-01-01
This author has previously introduced a new theory of the Electromagnetic Field and its interaction with matter. There was from the start a problem with Einstein's formulation of Invariants and its use in describing The EM field. The photon produced by first varying a stationary Electric field in one observer's reference frame is not the same as a photon produced from varying the a stationary Magnetic Field. The Magnetic field photon is thought of as being ``off the mass shell''. The Quantum information seems to carry with it an ordering of these events. You see this ordering in Wick's theory and in Feynman diagrams. This author is proposing that other fields can vary first in another Observers reference frame, not just the ``Scalar Field'' or the ``Fermion Field'', but many other forms of Energy. If the ``Nuclear Field'' varies first, it results in Quantum information that produces a photon that has the Nuclear Field in it and also the Magnetic Field, this is the strange effect seen in Nuclear Magnetic Resonance. This author proposed that there is a large number of photons with different properties, because of this ordering of events that occurs in Quantum Information. One of these photons is the Neutrino which appears to be a three field photon. This is Kriske's Field Theory.
Austerity and Geometric Structure of Field Theories
Kheyfets, Arkady
The relation between the austerity idea and the geometric structure of the three basic field theories- -electrodynamics, Yang-Mills theory, and general relativity --is studied. The idea of austerity was originally suggested by J. A. Wheeler in an attempt to formulate the laws of physics in such a way that they would come into being only within "the gates of time" extending from big bang to big crunch, rather than exist from everlasting to everlasting. One of the most significant manifestations of the austerity idea in field theories is thought to be expressed by the boundary of a boundary principle (BBP). The BBP says that almost all content of the field theories can be deduced from the topological identity (PAR-DIFF)(CCIRC)(PAR -DIFF) = 0 used twice, at the 1-2-3-dimensional level (providing the homgeneous field equations), and at the 2-3-4-dimensional level (providing the conservation laws for the source currents). There are some difficulties in this line of thought due to the apparent lack of universality in application of the BBP to the three basic modern field theories--electrodynamics, Yang-Mills theory, and general relativity. This dissertation: (a) analyses the difficulties by means of algebraic topology, integration theory and modern differential geometry based on the concepts of principal bundles and Ehresmann connections; (b) extends the BBP to the unified Kaluza-Klein theory; (c) reformulates the inhomogeneous field equations and the BBP in terms of E. Cartan moment of rotation, in the way universal for all the three theories and compatible with the original austerity idea; (d) underlines the important role of the soldering structure on spacetime, and indicates that the future development of the austerity idea would involve the generalized theories, including the soldering form as a dynamical variable rather than as a background structure.
Electromagnetic Field Theory A Collection of Problems
Mrozynski, Gerd
2013-01-01
After a brief introduction into the theory of electromagnetic fields and the definition of the field quantities the book teaches the analytical solution methods of Maxwell’s equations by means of several characteristic examples. The focus is on static and stationary electric and magnetic fields, quasi stationary fields, and electromagnetic waves. For a deeper understanding, the many depicted field patterns are very helpful. The book offers a collection of problems and solutions which enable the reader to understand and to apply Maxwell’s theory for a broad class of problems including classical static problems right up to waveguide eigenvalue problems. Content Maxwell’s Equations - Electrostatic Fields - Stationary Current Distributions – Magnetic Field of Stationary Currents – Quasi Stationary Fields: Eddy Currents - Electromagnetic Waves Target Groups Advanced Graduate Students in Electrical Engineering, Physics, and related Courses Engineers and Physicists Authors Professor Dr.-Ing. Gerd Mrozynski...
Dynamical symmetry breaking in quantum field theories
Miransky, Vladimir A
1993-01-01
The phenomenon of dynamical symmetry breaking (DSB) in quantum field theory is discussed in a detailed and comprehensive way. The deep connection between this phenomenon in condensed matter physics and particle physics is emphasized. The realizations of DSB in such realistic theories as quantum chromodynamics and electroweak theory are considered. Issues intimately connected with DSB such as critical phenomenona and effective lagrangian approach are also discussed.
From exceptional field theory to heterotic double field theory via K3
Malek, Emanuel
2017-03-01
In this paper we show how to obtain heterotic double field theory from exceptional field theory by breaking half of the supersymmetry. We focus on the SL(5) exceptional field theory and show that when the extended space contains a generalised SU(2)-structure manifold one can define a reduction to obtain the heterotic SO(3 , n) double field theory. In this picture, the reduction on the SU(2)-structure breaks half of the supersymmetry of the exceptional field theory and the gauge group of the heterotic double field theory is given by the embedding tensor of the reduction used. Finally, we study the example of a consistent truncation of M-theory on K3 and recover the duality with the heterotic string on T 3. This suggests that the extended space can be made sense of even in the case of non-toroidal compactifications.
Butterfly Tachyons in Vacuum String Field Theory
Matlock, P
2003-01-01
We use geometrical conformal field theory methods to investigate tachyon fluctuations about the butterfly projector state in Vacuum String Field Theory. We find that the on-shell condition for the tachyon field is equivalent to the requirement that the quadratic term in the string-field action vanish on shell. This further motivates the interpretation of the butterfly state as a D-brane. We begin a calculation of the tension of the butterfly, and conjecture that this will match the case of the sliver and further strengthen this interpretation.
Klein Topological Field Theories from Group Representations
Directory of Open Access Journals (Sweden)
Sergey A. Loktev
2011-07-01
Full Text Available We show that any complex (respectively real representation of finite group naturally generates a open-closed (respectively Klein topological field theory over complex numbers. We relate the 1-point correlator for the projective plane in this theory with the Frobenius-Schur indicator on the representation. We relate any complex simple Klein TFT to a real division ring.
Field theory for trapped atomic gases
Stoof, H.T.C.
2001-01-01
In this course we give a selfcontained introduction to the quantum field theory for trapped atomic gases, using functional methods throughout. We consider both equilibrium and nonequilibrium phenomena. In the equilibrium case, we first derive the appropriate Hartree-Fock theory for the properties of
The conceptual basis of Quantum Field Theory
Hooft, G. 't
2007-01-01
Relativistic Quantum Field Theory is a mathematical scheme to describe the sub-atomic particles and forces. The basic starting point is that the axioms of Special Relativity on the one hand and those of Quantum Mechanics on the other, should be combined into one theory. The fundamental ingredients f
Medley in finite temperature field theory
Pisarski, R D
1993-01-01
I discuss three subjects in thermal field theory: why in \\sun gauge theories the \\zn symmetry is broken at high (instead of low) temperature, the possible singularity structure of gauge variant propagators, and the problem of how to compute the viscosity from the Kubo formula.
Computer animations of quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Cohen, E. (Centre d' Etudes de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique)
1992-07-01
A visualization mehtod for quantum field theories based on the transfer matrix formalism is presented. It generates computer animations simulating the time evolution of complex physical systems subject to local Hamiltonians. The method may be used as a means of gaining insight to theories such as QCD, and as an educational tool in explaining high-energy physics. (orig.).
Field theory for trapped atomic gases
Stoof, H.T.C.
2001-01-01
In this course we give a selfcontained introduction to the quantum field theory for trapped atomic gases, using functional methods throughout. We consider both equilibrium and nonequilibrium phenomena. In the equilibrium case, we first derive the appropriate Hartree—Fock theory for the properties of
N = 8 supersingleton quantum field theory
Bergshoeff, Eric; Salam, Abdus; Sezgin, Ergin; Tanii, Yoshiaki
1988-01-01
We quantize the N = 8 supersymmetric singleton field theory which is formulated on the boundary of the four-dimensional anti-de Sitter spacetime (ADS4). The theory has rigid OSp(8, 4) symmetry which acts as a superconformal group on the boundary of AdS4. We show that the generators of this symmetry
Path integral quantization of parametrised field theory
Varadarajan, M
2004-01-01
Free scalar field theory on a flat spacetime can be cast into a generally covariant form known as parametrised field theory in which the action is a functional of the scalar field as well as the embedding variables which describe arbitrary, in general curved, foliations of the flat spacetime. We construct the path integral quantization of parametrised field theory in order to analyse issues at the interface of quantum field theory and general covariance in a path integral context. We show that the measure in the Lorentzian path integral is non-trivial and is the analog of the Fradkin- Vilkovisky measure for quantum gravity. We construct Euclidean functional integrals in the generally covariant setting of parametrised field theory using key ideas of Schleich and show that our constructions imply the existence of non-standard `Wick rotations' of the standard free scalar field 2 point function. We develop a framework to study the problem of time through computations of scalar field 2 point functions. We illustra...
Gravitation Field Dynamics in Jeans Theory
Indian Academy of Sciences (India)
A. A. Stupka
2008-09-01
Closed system of time equations for nonrelativistic gravitation field and hydrodynamic medium was obtained by taking into account binary correlations of the field, which is the generalization of Jeans theory. Distribution function of the systemwas built on the basis of the Bogolyubov reduced description method. Calculations were carried out up to the first order of a perturbation theory in interaction. Adiabatic and enthropic types of perturbations were corrected and two new types of perturbations were found.
Covariant Hamilton equations for field theory
Energy Technology Data Exchange (ETDEWEB)
Giachetta, Giovanni [Department of Mathematics and Physics, University of Camerino, Camerino (Italy); Mangiarotti, Luigi [Department of Mathematics and Physics, University of Camerino, Camerino (Italy)]. E-mail: mangiaro@camserv.unicam.it; Sardanashvily, Gennadi [Department of Theoretical Physics, Physics Faculty, Moscow State University, Moscow (Russian Federation)]. E-mail: sard@grav.phys.msu.su
1999-09-24
We study the relations between the equations of first-order Lagrangian field theory on fibre bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. If a Lagrangian is hyperregular, these equations are equivalent. A degenerate Lagrangian requires a set of associated Hamiltonian forms in order to exhaust all solutions of the Euler-Lagrange equations. The case of quadratic degenerate Lagrangians is studied in detail. (author)
Continuous point symmetries in Group Field Theories
Kegeles, Alexander
2016-01-01
We discuss the notion of symmetries in non-local field theories characterized by integro-differential equation of motion, from a geometric perspective. We then focus on Group Field Theory (GFT) models of quantum gravity. We provide a general analysis of their continuous point symmetry transformations, including the generalized conservation laws following from them, and apply it to several GFT models of interest to current research.
Gravitation Field Dynamics in Jeans Theory
Stupka, A A
2016-01-01
Closed system of time equations for nonrelativistic gravitation field and hydrodynamic medium was obtained by taking into account binary correlations of the field, which is the generalization of Jeans theory. Distribution function of the systemwas built on the basis of the Bogolyubov reduced description method. Calculations were carried out up to the first order of a perturbation theory in interaction. Adiabatic and enthropic types of perturbations were corrected and two new types of perturbations were found.
Classical theory of electric and magnetic fields
Good, Roland H
1971-01-01
Classical Theory of Electric and Magnetic Fields is a textbook on the principles of electricity and magnetism. This book discusses mathematical techniques, calculations, with examples of physical reasoning, that are generally applied in theoretical physics. This text reviews the classical theory of electric and magnetic fields, Maxwell's Equations, Lorentz Force, and Faraday's Law of Induction. The book also focuses on electrostatics and the general methods for solving electrostatic problems concerning images, inversion, complex variable, or separation of variables. The text also explains ma
N=3 four dimensional field theories
García-Etxebarria, Iñaki
2015-01-01
We introduce a class of four dimensional field theories constructed by quotienting ordinary $\\mathcal{N}=4$ $U(N)$ SYM by particular combinations of R-symmetry and $SL(2,\\mathbb{Z})$ automorphisms. These theories appear naturally on the worldvolume of D3 branes probing terminal singularities in F-theory, where they can be thought of as non-perturbative generalizations of the O3 plane. We focus on cases preserving only 12 supercharges, where the quotient gives rise to theories with coupling fixed at a value of order one. These constructions posses an unconventional large $N$ limit described by a non-trivial F-theory fibration with base $AdS_5\\times (S^5/\\mathbb{Z}_k)$. Upon reduction on a circle the $\\mathcal{N}=3$ theories flow to well-known $\\mathcal{N}=6$ ABJM theories.
Effective Field Theories and Lattice QCD
Bernard, C
2015-01-01
I describe some of the many connections between lattice QCD and effective field theories, focusing in particular on chiral effective theory, and, to a lesser extent, Symanzik effective theory. I first discuss the ways in which effective theories have enabled and supported lattice QCD calculations. Particular attention is paid to the inclusion of discretization errors, for a variety of lattice QCD actions, into chiral effective theory. Several other examples of the usefulness of chiral perturbation theory, including the encoding of partial quenching and of twisted boundary conditions, are also described. In the second part of the talk, I turn to results from lattice QCD for the low energy constants of the two- and three-flavor chiral theories. I concentrate here on mesonic quantities, but the dependence of the nucleon mass on the pion mass is also discussed. Finally I describe some recent preliminary lattice QCD calculations by the MILC Collaboration relating to the three-flavor chiral limit.
Quantum field theory in a semiotic perspective
Energy Technology Data Exchange (ETDEWEB)
Dosch, H.G. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; Mueller, V.F. [Technische Univ. Kaiserslautern (Germany). Fachbereich Physik; Sieroka, N. [Zurich Univ. (Switzerland)
2005-07-01
Viewing physical theories as symbolic constructions came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic field from mechanics; most notably this happened through the work of Helmholtz, Hertz, Poincare, and later Weyl. The epistemological problems that nourished this development are today highlighted within quantum field theory. The present essay starts off with a concise and non-technical outline of the firmly based aspects of relativistic quantum field theory, i.e. the very successful description of subnuclear phenomena. The particular methods, by which these different aspects have to be accessed, then get described as distinct facets of quantum field theory. The authors show how these different facets vary with respect to the relation between quantum fields and associated particles. Thus, by emphasising the respective role of various basic concepts involved, the authors claim that only a very general epistemic approach can properly account for this diversity - an account they trace back to the philosophical writings of the aforementioned physicists and mathematicians. Finally, what they call their semiotic perspective on quantum field theory gets related to recent discussions within the philosophy of science and turns out to act as a counterbalance to, for instance, structural realism. (orig.)
Discrete Scalar Quantum Field Theory
Gudder, Stan
2016-01-01
We begin with a description of spacetime by a 4-dimensional cubic lattice $\\sscript$. It follows from this framework that the the speed of light is the only nonzero instantaneous speed for a particle. The dual space $\\sscripthat$ corresponds to a cubic lattice of energy-momentum. This description implies that there is a discrete set of possible particle masses. We then define discrete scalar quantum fields on $\\sscript$. These fields are employed to define interaction Hamiltonians and scattering operators. Although the scattering operator $S$ cannot be computed exactly, approximations are possible. Whether $S$ is unitary is an unsolved problem. Besides the definitions of these operators, our main assumption is conservation of energy-momentum for a scattering process. This article concludes with various examples of perturbation approximations. These include simplified versions of electron-electron and electron-proton scattering as well as simple decay processes. We also define scattering cross-sections, decay ...
Space-Time Noncommutative Field Theories And Unitarity
Gomis, Jaume; Mehen, Thomas
2000-01-01
We study the perturbative unitarity of noncommutative scalar field theories. Field theories with space-time noncommutativity do not have a unitary S-matrix. Field theories with only space noncommutativity are perturbatively unitary. This can be understood from string theory, since space noncommutative field theories describe a low energy limit of string theory in a background magnetic field. On the other hand, there is no regime in which space-time noncommutative field theory is an appropriat...
Nilpotent weights in conformal field theory
Directory of Open Access Journals (Sweden)
S. Rouhani
2001-12-01
Full Text Available Logarithmic conformal field theory can be obtained using nilpotent weights. Using such scale transformations various properties of the theory were derived. The derivation of four point function needs a knowledge of singular vectors which is derived by including nilpotent variables into the Kac determinant. This leads to inhomogeneous hypergeometric functions. Finally we consider the theory near a boundary and also introduce the concept of superfields where a multiplet of conformal fields are dealt with together. This leads to the OPE of superfields and a logarithmic partner for the energy momentum tensor.
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.
On level crossing in conformal field theories
Korchemsky, G P
2015-01-01
We study the properties of operators in a unitary conformal field theory whose scaling dimensions approach each other for some values of the parameters and satisfy von Neumann-Wigner non-crossing rule. We argue that the scaling dimensions of such operators and their OPE coefficients have a universal scaling behavior in the vicinity of the crossing point. We demonstrate that the obtained relations are in a good agreement with the known examples of the level-crossing phenomenon in maximally supersymmetric $\\mathcal N=4$ Yang-Mills theory, three-dimensional conformal field theories and QCD.
Noncommutative Time in Quantum Field Theory
Salminen, Tapio
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-K\\"all\\'{e}n 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 light-like noncommutativity.
Intersection Theory, Integrable Hierarchies and Topological Field Theory
Dijkgraaf, Robbert
1992-01-01
In these lecture notes we review the various relations between intersection theory on the moduli space of Riemann surfaces, integrable hierarchies of KdV type, matrix models, and topological quantum field theories. We explain in particular why matrix integrals of the type considered by Kontsevich naturally appear as tau-functions associated to minimal models. Our starting point is the extremely simple form of the string equation for the topological (p,1) models, where the so-called Baker-Akhi...
"Quantum Field Theory and QCD"
Energy Technology Data Exchange (ETDEWEB)
Jaffe, Arthur M.
2006-02-25
This grant partially funded a meeting, "QFT & QCD: Past, Present and Future" held at Harvard University, Cambridge, MA on March 18-19, 2005. The participants ranged from senior scientists (including at least 9 Nobel Prize winners, and 1 Fields medalist) to graduate students and undergraduates. There were several hundred persons in attendance at each lecture. The lectures ranged from superlative reviews of past progress, lists of important, unsolved questions, to provocative hypotheses for future discovery. The project generated a great deal of interest on the internet, raising awareness and interest in the open questions of theoretical physics.
Quantum field theory in a nutshell
Zee, A
2010-01-01
Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading
Entanglement Entropy in Warped Conformal Field Theories
Castro, Alejandra; Iqbal, Nabil
2015-01-01
We present a detailed discussion of entanglement entropy in (1+1)-dimensional Warped Conformal Field Theories (WCFTs). We implement the Rindler method to evaluate entanglement and Renyi entropies for a single interval and along the way we interpret our results in terms of twist field correlation functions. Holographically a WCFT can be described in terms of Lower Spin Gravity, a SL(2,R)xU(1) Chern-Simons theory in three dimensions. We show how to obtain the universal field theory results for entanglement in a WCFT via holography. For the geometrical description of the theory we introduce the concept of geodesic and massive point particles in the warped geometry associated to Lower Spin Gravity. In the Chern-Simons description we evaluate the appropriate Wilson line that captures the dynamics of a massive particle.
Equilibration properties of classical integrable field theories
De Luca, Andrea; Mussardo, Giuseppe
2016-06-01
We study the equilibration properties of classical integrable field theories at a finite energy density, with a time evolution that starts from initial conditions far from equilibrium. These classical field theories may be regarded as quantum field theories in the regime of high occupation numbers. This observation permits to recover the classical quantities from the quantum ones by taking a proper \\hslash \\to 0 limit. In particular, the time averages of the classical theories can be expressed in terms of a suitable version of the LeClair-Mussardo formula relative to the generalized Gibbs ensemble. For the purposes of handling time averages, our approach provides a solution of the problem of the infinite gap solutions of the inverse scattering method.
Towards the mathematics of quantum field theory
Paugam, Frédéric
2014-01-01
The aim of this book is to introduce mathematicians (and, in particular, graduate students) to the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in play. This should in turn promote interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, even if the mathematical one is the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature. The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second...
Axiomatic foundations of quantum mechanics revisited the case for systems
Romero, G E; Romero, Gustavo E; Vucetich, Hector
1995-01-01
We present an axiomatization of non-relativistic Quantum Mechanics for a system with an arbitrary number of components. The interpretation of our system of axioms is realistic and objective. The EPR paradox and its relation with realism is discussed in this framework. It is shown that there is no contradiction between realism and recent experimental results.
Paired Comparisons Analysis : An Axiomatic Approach to Rankings in Tournaments
Gonzalez-Diaz, J.; Hendrickx, R.L.P.; Lohmann, E.R.M.A.
2011-01-01
In this paper we present an axiomatic analysis of several ranking methods for tournaments. We find that two of them exhibit a very good behaviour with respect to the set of properties under consideration. One of them is the maximum likelihood ranking, the most common method in statistics and psychol
An Axiomatic, Unified Representation of Biosystems and Quantum Dynamics
Baianu, I
2004-01-01
An axiomatic representation of system dynamics is introduced in terms of categories, functors, organismal supercategories, limits and colimits of diagrams. Specific examples are considered in Complex Systems Biology, such as ribosome biogenesis and Hormonal Control in human subjects. "Fuzzy" Relational Structures are also proposed for flexible representations of biological system dynamics and organization.
Paired comparisons analysis: an axiomatic approach to ranking methods
Gonzalez-Diaz, J.; Hendrickx, Ruud; Lohmann, E.R.M.A.
2014-01-01
In this paper we present an axiomatic analysis of several ranking methods for general tournaments. We find that the ranking method obtained by applying maximum likelihood to the (Zermelo-)Bradley-Terry model, the most common method in statistics and psychology, is one of the ranking methods that per
On the Axiomatic Characterization of "Who is a J?"
Dimitrov, D.A.; Sung, S.C.
2003-01-01
Recent work by Kasher and Rubinstein (1997) considers the problem of group identification from a social choice perspective.These authors provide an axiomatic characterization of a liberal aggregator whereby the group consist of those and only those individuals each of which views oneself a member of
Chiral effective field theory and nuclear forces
Machleidt, R
2011-01-01
We review how nuclear forces emerge from low-energy QCD via chiral effective field theory. The presentation is accessible to the non-specialist. At the same time, we also provide considerable detailed information (mostly in appendices) for the benefit of researchers who wish to start working in this field.
Group field theories generating polyhedral complexes
Thürigen, Johannes
2015-01-01
Group field theories are a generalization of matrix models which provide both a second quantized reformulation of loop quantum gravity as well as generating functions for spin foam models. While states in canonical loop quantum gravity, in the traditional continuum setting, are based on graphs with vertices of arbitrary valence, group field theories have been defined so far in a simplicial setting such that states have support only on graphs of fixed valency. This has led to the question whether group field theory can indeed cover the whole state space of loop quantum gravity. In this contribution based on [1] I present two new classes of group field theories which satisfy this objective: i) a straightforward, but rather formal generalization to multiple fields, one for each valency and ii) a simplicial group field theory which effectively covers the larger state space through a dual weighting, a technique common in matrix and tensor models. To this end I will further discuss in some detail the combinatorial ...
From theory to field experiments
de Vos, Bram
2016-04-01
Peter Raats' achievements in Haren (NL) 1986-1997 were based on a solid theoretical insight in hydrology and transport process in soil. However, Peter was also the driving force behind many experimental studies and applied research. This will be illustrated by a broad range of examples ranging from the dynamics of composting processes of organic material; modelling and monitoring nutrient leaching at field-scale; wind erosion; water and nutrient dynamics in horticultural production systems; oxygen diffusion in soils; and processes of water and nutrient uptake by plant roots. Peter's leadership led to may new approaches and the introduction of innovative measurement techniques in Dutch research; ranging from TDR to nutrient concentration measurements in closed fertigation systems. This presentation will give a brief overview how Peter's theoretical and mathematical insights accelerated this applied research.
Mean-field magnetohydrodynamics and dynamo theory
Krause, F
2013-01-01
Mean-Field Magnetohydrodynamics and Dynamo Theory provides a systematic introduction to mean-field magnetohydrodynamics and the dynamo theory, along with the results achieved. Topics covered include turbulence and large-scale structures; general properties of the turbulent electromotive force; homogeneity, isotropy, and mirror symmetry of turbulent fields; and turbulent electromotive force in the case of non-vanishing mean flow. The turbulent electromotive force in the case of rotational mean motion is also considered. This book is comprised of 17 chapters and opens with an overview of the gen
Quantum Stability of Chameleon Field Theories
Upadhye, Amol; Khoury, Justin
2012-01-01
Chameleon scalar fields are dark energy candidates which suppress fifth forces in high density regions of the universe by becoming massive. We consider chameleon models as effective field theories and estimate quantum corrections to their potentials. Requiring that quantum corrections be small, so as to allow reliable predictions of fifth forces, leads to an upper bound $m 0.0042$\\,eV. An improvement of less than a factor of two in the range of fifth force experiments could test all classical chameleon field theories whose quantum corrections are well-controlled and couple to matter with nearly gravitational strength regardless of the specific form of the chameleon potential.
Casimir Effects in Renormalizable Quantum Field Theories
Graham, N; Weigel, H; Graham, Noah; Jaffe, Robert L.; Weigel, Herbert
2002-01-01
We review the framework we and our collaborators have developed for the study of one-loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard Casimir sum over modes into a sum over bound states and an integral over scattering states weighted by the density of states. We express the density of states in terms of phase shifts, allowing us to extract divergences by identifying Born approximations to the phase shifts with low order Feynman diagrams. Once isolated in Feynman diagrams, the divergences are canceled against standard counterterms. Thus regulated, the Casimir sum is highly convergent and amenable to numerical computation. Our methods have numerous applications to the theory of solitons, membranes, and quantum field theories in strong external fields or subject to boundary conditions.
Casimir Effects in Renormalizable Quantum Field Theories
Graham, Noah; Jaffe, Robert L.; Weigel, Herbert
We present a framework for the study of one-loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard Casimir sum over modes into a sum over bound states and an integral over scattering states weighted by the density of states. We express the density of states in terms of phase shifts, allowing us to extract divergences by identifying Born approximations to the phase shifts with low order Feynman diagrams. Once isolated in Feynman diagrams, the divergences are canceled against standard counterterms. Thus regulated, the Casimir sum is highly convergent and amenable to numerical computation. Our methods have numerous applications to the theory of solitons, membranes, and quantum field theories in strong external fields or subject to boundary conditions.
String field theory solution corresponding to constant background magnetic field
Ishibashi, Nobuyuki; Takahashi, Tomohiko
2016-01-01
Following the method recently proposed by Erler and Maccaferri, we construct solutions to the equation of motion of Witten's cubic string field theory, which describe constant magnetic field background. We study the boundary condition changing operators relevant to such background and calculate the operator product expansions of them. We obtain solutions whose classical action coincide with the Born-Infeld action.
Quantum gravity, effective fields and string theory
Bjerrum-Bohr, N E J
2004-01-01
We look at the various aspects of treating general relativity as a quantum theory. It is briefly studied how to consistently quantize general relativity as an effective field theory. A key achievement here is the long-range low-energy leading quantum corrections to both the Schwarzschild and Kerr metrics. The leading quantum corrections to the pure gravitational potential between two sources are also calculated, both in the mixed theory of scalar QED and quantum gravity and in the pure gravitational theory. The (Kawai-Lewellen-Tye) string theory gauge/gravity relations is next dealt with. We investigate if the KLT-operator mapping extends to the case of higher derivative effective operators. The KLT-relations are generalized, taking the effective field theory viewpoint, and remarkable tree-level amplitude relations between the field theory operators are derived. Quantum gravity is finally looked at from the the perspective of taking the limit of infinitely many spatial dimensions. It is verified that only a c...
Cutkosky rules for superstring field theory
Pius, Roji; Sen, Ashoke
2016-10-01
Superstring field theory expresses the perturbative S-matrix of superstring theory as a sum of Feynman diagrams each of which is manifestly free from ultraviolet divergences. The interaction vertices fall off exponentially for large space-like external momenta making the ultraviolet finiteness property manifest, but blow up exponentially for large time-like external momenta making it impossible to take the integration contours for loop energies to lie along the real axis. This forces us to carry out the integrals over the loop energies by choosing appropriate contours in the complex plane whose ends go to infinity along the imaginary axis but which take complicated form in the interior navigating around the various poles of the propagators. We consider the general class of quantum field theories with this property and prove Cutkosky rules for the amplitudes to all orders in perturbation theory. Besides having applications to string field theory, these results also give an alternative derivation of Cutkosky rules in ordinary quantum field theories.
Wilson lines in quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Cherednikov, Igor Olegovich [Antwerpen Univ., Antwerp (Belgium). Fysica Dept.; Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Mertens, Tom; Veken, Frederik F. van der [Antwerpen Univ., Antwerp (Belgium). Fysica Dept.
2014-07-01
Wilson lines (also known as gauge links or eikonal lines) can be introduced in any gauge field theory. Although the concept of the Wilson exponentials finds an enormously wide range of applications in a variety of branches of modern quantum field theory, from condensed matter and lattice simulations to quantum chromodynamics, high-energy effective theories and gravity, there are surprisingly few books or textbooks on the market which contain comprehensive pedagogical introduction and consecutive exposition of the subject. The objective of this book is to get the potential reader acquainted with theoretical and mathematical foundations of the concept of the Wilson loops in the context of modern quantum field theory, to teach him/her to perform independently some elementary calculations with Wilson lines, and to familiarize him/her with the recent development of the subject in different important areas of research. The target audience of the book consists of graduate and postgraduate students working in various areas of quantum field theory, as well as researchers from other fields.
Weak gravity conjecture and effective field theory
Saraswat, Prashant
2017-01-01
The weak gravity conjecture (WGC) is a proposed constraint on theories with gauge fields and gravity, requiring the existence of light charged particles and/or imposing an upper bound on the field theory cutoff Λ . If taken as a consistency requirement for effective field theories (EFTs), it rules out possibilities for model building including some models of inflation. I demonstrate simple models which satisfy all forms of the WGC, but which through Higgsing of the original gauge fields produce low-energy EFTs with gauge forces that badly violate the WGC. These models illustrate specific loopholes in arguments that motivate the WGC from a bottom-up perspective; for example the arguments based on magnetic monopoles are evaded when the magnetic confinement that occurs in a Higgs phase is accounted for. This indicates that the WGC should not be taken as a veto on EFTs, even if it turns out to be a robust property of UV quantum gravity theories. However, if the latter is true, then parametric violation of the WGC at low energy comes at the cost of nonminimal field content in the UV. I propose that only a very weak constraint is applicable to EFTs, Λ ≲(log 1/g )-1 /2Mpl , where g is the gauge coupling, motivated by entropy bounds. Remarkably, EFTs produced by Higgsing a theory that satisfies the WGC can saturate but not violate this bound.
Field Theories Without a Holographic Dual
McInnes, Brett
2016-01-01
In applying the gauge-gravity duality to the quark-gluon plasma, one models the plasma using a particular kind of field theory with specified values of the temperature, magnetic field, and so forth. One then assumes that the bulk, an asymptotically AdS black hole spacetime with properties chosen to match those of the boundary field theory, can be embedded in string theory. But this is not always the case: there are field theories with no bulk dual. The question is whether these theories might include those used to study the actual plasmas produced at such facilities as the RHIC experiment or the relevant experiments at the LHC. We argue that, \\emph{provided} that due care is taken to include the effects of the angular momentum associated with the magnetic fields experienced by the plasmas produced by peripheral collisions, the existence of the dual can be established for the RHIC plasmas. In the case of the LHC plasmas, the situation is much more doubtful.
On space of integrable quantum field theories
Smirnov, F. A.; Zamolodchikov, A. B.
2017-02-01
We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields Xs, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars Xs are built from the components of the associated conserved currents in a universal way. The first of these scalars, X1, coincides with the composite field (T T bar) built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by X1 are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations Xs are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators Xs in sine-Gordon theory. We also make some remarks on the problem of UV completeness of such integrable deformations.
Field theories without a holographic dual
McInnes, Brett
2016-12-01
In applying the gauge-gravity duality to the quark-gluon plasma, one models the plasma using a particular kind of field theory with specified values of the temperature, magnetic field, and so forth. One then assumes that the bulk, an asymptotically AdS black hole spacetime with properties chosen to match those of the boundary field theory, can be embedded in string theory. But this is not always the case: there are field theories with no bulk dual. The question is whether these theories might include those used to study the actual plasmas produced at such facilities as the RHIC experiment or the relevant experiments at the LHC. We argue that, provided that due care is taken to include the effects of the angular momentum associated with the magnetic fields experienced by the plasmas produced by peripheral collisions, the existence of the dual can be established for the RHIC plasmas. In the case of the LHC plasmas, the situation is much more doubtful.
Directory of Open Access Journals (Sweden)
Aleksandar Perović
2008-01-01
Full Text Available During the last two decades, Group for intelligent systems at Mathematicalfaculty in Belgrade has developed several theorem provers for different kind of formalsystems. Lately, we have turned our attention to fuzzy logic and development of thecorresponding theorem prover. The first step is to find the suitable axiomatization, i.e., theformalization of fuzzy logic that is sound, complete and decidable. It is well known thatthere are fuzzy logics (such as Product logic that require infinitary axiomatization in orderto tame the non-compactness phenomena. Though such logics are strongly complete (everyconsistent set of formulas is satisfiable, the only possible decidability result is thesatisfiability of a formula. Therefore, we have adapted the method of Fagin, Halpern andMegiddo for polynomial weight formulas in order to interpret the Lukasiewicz and theProduct logic into the first order theory of the reals.
Simple Recursion Relations for General Field Theories
Cheung, Clifford; Trnka, Jaroslav
2015-01-01
On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a covering space of recursion relations which naturally generalizes all existing constructions, including those of BCFW and Risager. The validity of each recursion relation hinges on the large momentum behavior of an n-point scattering amplitude under an m-line momentum shift, which we determine solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are 3-line constructible if an external particle carries spin or if the scalars in the theory carry equal charge under a global or gauge symmetry. Remarkably, this implies the 3-...
Statistical mechanics of vortices from field theory
Kajantie, Keijo; Neuhaus, T; Rajantie, A; Rummukainen, K
1999-01-01
We study with lattice Monte Carlo simulations the interactions and macroscopic behaviour of a large number of vortices in the 3-dimensional U(1) gauge+Higgs field theory, in an external magnetic field. We determine non-perturbatively the (attractive or repelling) interaction energy between two or more vortices, as well as the critical field strength H_c, the thermodynamical discontinuities, and the surface tension related to the boundary between the Meissner phase and the Coulomb phase in the type I region. We also investigate the emergence of vortex lattice and vortex liquid phases in the type II region. For the type I region the results obtained are in qualitative agreement with mean field theory, except for small values of H_c, while in the type II region there are significant discrepancies. These findings are relevant for superconductors and some models of cosmic strings, as well as for the electroweak phase transition in a magnetic field.
The Supersymmetric Effective Field Theory of Inflation
Delacretaz, Luca V; Senatore, Leonardo
2016-01-01
We construct the Supersymmetric Effective Field Theory of Inflation, that is the most general theory of inflationary fluctuations when time-translations and supersymmetry are spontaneously broken. The non-linear realization of these invariances allows us to define a complete SUGRA multiplet containing the graviton, the gravitino, the Goldstone of time translations and the Goldstino, with no auxiliary fields. Going to a unitary gauge where only the graviton and the gravitino are present, we write the most general Lagrangian built out of the fluctuations of these fields, invariant under time-dependent spatial diffeomorphisms, but softly-breaking time diffeomorphisms and gauged SUSY. With a suitable St\\"uckelberg transformation, we introduce the Goldstone boson of time translation and the Goldstino of SUSY. No additional dynamical light field is needed. In the high energy limit, larger than the inflationary Hubble scale for the Goldstino, these fields decouple from the graviton and the gravitino, greatly simplif...
Double Field Theory on Group Manifolds (Thesis)
Hassler, Falk
2015-01-01
This thesis deals with Double Field Theory (DFT), an effective field theory capturing the low energy dynamics of closed strings on a torus. It renders T-duality on a torus manifest by adding $D$ winding coordinates in addition to the $D$ space time coordinates. An essential consistency constraint of the theory, the strong constraint, only allows for field configurations which depend on half of the coordinates of the arising doubled space. I derive DFT${}_\\mathrm{WZW}$, a generalization of the current formalism. It captures the low energy dynamics of a closed bosonic string propagating on a compact group manifold. Its classical action and the corresponding gauge transformations arise from Closed String Field Theory up to cubic order in the massless fields. These results are rewritten in terms of a generalized metric and extended to all orders in the fields. There is an explicit distinction between background and fluctuations. For the gauge algebra to close, the latter have to fulfill a modified strong constrai...
An Introduction to Quantum Field Theory
Peskin, Michael E
1995-01-01
An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the sta
Folding defect affine Toda field theories
Robertson, C
2013-01-01
A folding process is applied to fused a^(1)_r defects to construct defects for the non-simply laced affi?ne Toda ?field theories of c^(1)_n, d^(2)_n and a^(2)_n at the classical level. Support for the hypothesis that these defects are integrable in the folded theories is provided by the observation that transmitted solitons retain their form. Further support is given by the demonstration that energy and momentum are conserved.
On the derivation of effective field theories
Uzunov, D I
2004-01-01
A general self-consistency approach allows a thorough treatment of the corrections to the standard mean-field approximation (MFA). The natural extension of standard MFA with the help of a cumulant expansion leads to a new point of view on the effective field theories. The proposed approach can be used for a systematic treatment of fluctuation effects of various length scales and, perhaps, for the development of a new coarse graining procedure. We outline and justify our method by some preliminary calculations. Concrete results are given for the critical temperature and the Landau parameters of the $\\phi^4_d$-theory - the field counterpart of the Ising model. An important unresolved problem of the modern theory of phase transitions - the problem for the calculation of the true critical temperature, is considered within the framework of the present approach. A comprehensive description of the ground state properties of many-body systems is also demonstrated.
Multisymplectic effective General Boundary Field Theory
Arjang, Mona
2013-01-01
The transfer matrix in lattice field theory connects the covariant and the initial data frameworks; in spin foam models, it can be written as a composition of elementary cellular amplitudes/propagators. We present a framework for discrete spacetime classical field theory in which solutions to the field equations over elementary spacetime cells may be amalgamated if they satisfy simple gluing conditions matching the composition rules of cellular amplitudes in spin foam models. Furthermore, the formalism is endowed with a multisymplectic structure responsible for local conservation laws. Some models within our framework are effective theories modeling a system at a given scale. Our framework allows us to study coarse graining and the continuum limit.
Quantum Finite Elements for Lattice Field Theory
Brower, Richard C; Gasbarro, Andrew; Raben, Timothy; Tan, Chung-I; Weinberg, Evan
2016-01-01
Viable non-perturbative methods for lattice quantum field theories on curved manifolds are difficult. By adapting features from the traditional finite element methods (FEM) and Regge Calculus, a new simplicial lattice Quantum Finite Element (QFE) Lagrangian is constructed for fields on a smooth Riemann manifold. To reach the continuum limit additional counter terms must be constructed to cancel the ultraviolet distortions. This is tested by the comparison of phi 4-th theory at the Wilson-Fisher fixed point with the exact Ising (c =1/2) CFT on a 2D Riemann sphere. The Dirac equation is also constructed on a simplicial lattice approximation to a Riemann manifold by introducing a lattice vierbein and spin connection on each link. Convergence of the QFE Dirac equation is tested against the exact solution for the 2D Riemann sphere. Future directions and applications to Conformal Field Theories are suggested.
Confinement in Einstein's unified field theory
Antoci, S; Mihich, L
2006-01-01
After recalling the mathematical structure of Einstein's Hermitian extension of the gravitational theory of 1915, the problem, whether its field equations should admit of phenomenological sources at their right-hand sides, and how this addition should be done, is expounded by relying on a thread of essential insights and achievements by Schr\\"odinger, Kursunoglu, Lichnerowicz, H\\'ely and Borchsenius. When sources are appended to all the field equations, from the latter and from the contracted Bianchi identities a sort of gravoelectrodynamics appears, that totally departs from the so called Einstein-Maxwell theory, since its constitutive equation, that rules the link between inductions and fields, is a very complicated differential relation that allows for a much wider, still practically unexplored range of possible occurrences. In this sort of theory one can allow for both an electric and a magnetic four-current, which are not a physically wrong replica of each other, like it would occur if both these current...
Magnetic Catalysis in Graphene Effective Field Theory
DeTar, Carleton; Zafeiropoulos, Savvas
2016-01-01
We report on the first observation of magnetic catalysis at zero temperature in a fully nonperturbative simulation of the graphene effective field theory. Using lattice gauge theory, a nonperturbative analysis of the theory of strongly-interacting, massless, (2+1)-dimensional Dirac fermions in the presence of an external magnetic field is performed. We show that in the zero-temperature limit, a nonzero value for the chiral condensate is obtained which signals the spontaneous breaking of chiral symmetry. This result implies a nonzero value for the dynamical mass of the Dirac quasiparticle. This in turn has been posited to account for the quantum-Hall plateaus that are observed at large magnetic fields.
Effective field theory for magnetic compactifications
Buchmuller, Wilfried; Dudas, Emilian; Schweizer, Julian
2016-01-01
Magnetic flux plays an important role in compactifications of field and string theories in two ways, it generates a multiplicity of chiral fermion zero modes and it can break supersymmetry. We derive the complete four-dimensional effective action for N=1 supersymmetric Abelian and non-Abelian gauge theories in six dimensions compactified on a torus with flux. The effective action contains the tower of charged states and it accounts for the mass spectrum of bosonic and fermionic fields as well as their level-dependent interactions. This allows us to compute quantum corrections to the mass and couplings of Wilson lines. We find that the one-loop corrections vanish, contrary to the case without flux. This can be traced back to the spontaneous breaking of a symmetry of the six-dimensional theory by the background gauge field, with the Wilson line as Goldstone boson.
Energy Technology Data Exchange (ETDEWEB)
Liu Baoding [Tsinghua Univ., Beijing (China). Uncertainty Theory Lab.
2007-07-01
Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, and countable subadditivity axioms. The goal of uncertainty theory is to study the behavior of uncertain phenomena such as fuzziness and randomness. The main topics include probability theory, credibility theory, and chance theory. For this new edition the entire text has been totally rewritten. More importantly, the chapters on chance theory and uncertainty theory are completely new. This book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory. The purpose is to equip the readers with an axiomatic approach to deal with uncertainty. Mathematicians, researchers, engineers, designers, and students in the field of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, and management science will find this work a stimulating and useful reference. (orig.)
Field theory a path integral approach
Das, Ashok
2006-01-01
This unique book describes quantum field theory completely within the context of path integrals. With its utility in a variety of fields in physics, the subject matter is primarily developed within the context of quantum mechanics before going into specialized areas.Adding new material keenly requested by readers, this second edition is an important expansion of the popular first edition. Two extra chapters cover path integral quantization of gauge theories and anomalies, and a new section extends the supersymmetry chapter, where singular potentials in supersymmetric systems are described.
Effective field theory for deformed atomic nuclei
Papenbrock, T
2015-01-01
We present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband $E2$ transitions. For rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
Global Anomalies and Effective Field Theory
Golkar, Siavash
2015-01-01
We show that matching anomalies under large gauge transformations and large diffeomorphisms can explain the appearance and non-renormalization of couplings in effective field theory. We focus on %thermal partition functions and thermal effective field theory where we argue that the appearance of certain unusual Chern-Simons couplings is a consequence of global anomalies. As an example, we show that a mixed global anomaly in four dimensions fixes the chiral vortical effect coefficient. This is an experimentally measurable prediction from a global anomaly. For certain situations, we propose a simpler method for calculating global anomalies which uses correlation functions rather than eta invariants.
A geometric formulation of exceptional field theory
Bosque, Pascal du; Lust, Dieter; Malek, Emanuel
2016-01-01
We formulate the full bosonic SL(5) exceptional field theory in a coordinate-invariant manner. Thereby we interpret the 10-dimensional extended space as a manifold with $\\mathrm{SL}(5)\\times\\mathbb{R}^+$-structure. We show that the algebra of generalised diffeomorphisms closes subject to a set of closure constraints which are reminiscent of the quadratic and linear constraints of maximal seven-dimensional gauged supergravities, as well as the section condition. We construct an action for the full bosonic SL(5) exceptional field theory, even when the $\\mathrm{SL}(5)\\times\\mathbb{R}^+$-structure is not locally flat.
Effective field theory for deformed atomic nuclei
Papenbrock, T.; Weidenmüller, H. A.
2016-05-01
We present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. For rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
Thermo-Field Extension of Open String Field Theory
Cantcheff, M Botta
2015-01-01
We study the implementation of Thermo Field Dynamics (TFD) to the covariant formulation of Open String Field Theory (OSFT). In this paper, we extend the state space and fields according to the duplication rules of TFD and construct the corresponding classical action. The result is a theory whose fields would encode the statistical information of open strings and, noticeably, present degrees of freedom that could be identified as those of closed strings. The physical spectrum of the free theory is studied through the cohomology of the extended BRST charge, and, as a result, we get new fields in the spectrum. We also show, however, that their appearing in the action is directly related to the choice of the inner product in the extended algebra, so that many fields could be eliminated from the theory by choosing that product conveniently. Finally, we study the extension of the three-vertex interaction and provide a simple prescription for it whose results at tree-level amplitudes agree with those of the conventi...
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 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.
On space of integrable quantum field theories
Smirnov, F A
2016-01-01
We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields $X_s$, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars $X_s$ are built from the components of the associated conserved currents in a universal way. The first of these scalars, $X_1$, coincides with the composite field $(T{\\bar T})$ built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by $X_1$ are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations $X_s$ are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit...
On space of integrable quantum field theories
Directory of Open Access Journals (Sweden)
F.A. Smirnov
2017-02-01
Full Text Available We study deformations of 2D Integrable Quantum Field Theories (IQFT which preserve integrability (the existence of infinitely many local integrals of motion. The IQFT are understood as “effective field theories”, with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields Xs, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars Xs are built from the components of the associated conserved currents in a universal way. The first of these scalars, X1, coincides with the composite field (TT¯ built from the components of the energy–momentum tensor. The deformations of quantum field theories generated by X1 are “solvable” in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations Xs are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators Xs in sine-Gordon theory. We also make some remarks on the problem of UV completeness of such integrable deformations.
The classical theory of fields electromagnetism
Helrich, Carl S
2012-01-01
The study of classical electromagnetic fields is an adventure. The theory is complete mathematically and we are able to present it as an example of classical Newtonian experimental and mathematical philosophy. There is a set of foundational experiments, on which most of the theory is constructed. And then there is the bold theoretical proposal of a field-field interaction from James Clerk Maxwell. This textbook presents the theory of classical fields as a mathematical structure based solidly on laboratory experiments. Here the student is introduced to the beauty of classical field theory as a gem of theoretical physics. To keep the discussion fluid, the history is placed in a beginning chapter and some of the mathematical proofs in the appendices. Chapters on Green’s Functions and Laplace’s Equation and a discussion of Faraday’s Experiment further deepen the understanding. The chapter on Einstein’s relativity is an integral necessity to the text. Finally, chapters on particle motion and waves in a dis...
Near-field optical thin microcavity theory
Wu, Jiu Hui; Hou, Jiejie
2016-01-01
The thin microcavity theory for near-field optics is proposed in this study. By applying the power flow theorem and the variable theorem,the bi-harmonic differential governing equation for electromagnetic field of a three-dimensional thin microcavity is derived for the first time. Then by using the Hankel transform, this governing equation is solved exactly and all the electromagnetic components inside and outside the microcavity can be obtained accurately. According to the above theory, the near-field optical diffraction from a subwavelength aperture embedded in a thin conducting film is investigated, and numerical computations are performed to illustrate the edge effect by an enhancement factor of 1.8 and the depolarization phenomenon of the near-field transmission in terms of the distance from the film surface. This thin microcavity theory is verified by the good agreement between our results and those in the previous literatures. The thin microcavity theory presented in the study should be useful in the possible applications of the thin microcavities in near-field optics and thin-film optics.
Intersection Theory, Integrable Hierarchies and Topological Field Theory
Dijkgraaf, R
1992-01-01
In these lecture notes we review the various relations between intersection theory on the moduli space of Riemann surfaces, integrable hierarchies of KdV type, matrix models, and topological quantum field theories. We explain in particular why matrix integrals of the type considered by Kontsevich naturally appear as tau-functions associated to minimal models. Our starting point is the extremely simple form of the string equation for the topological (p,1) models, where the so-called Baker-Akhiezer function is given by a (generalized) Airy function.
Nonrelativistic Effective Field Theory for Axions
Braaten, Eric; Zhang, Hong
2016-01-01
Axions can be described by a relativistic field theory with a real scalar field $\\phi$ whose self-interaction potential is a periodic function of $\\phi$. Low-energy axions, such as those produced in the early universe by the vacuum misalignment mechanism, can be described more simply by a nonrelativistic effective field theory with a complex scalar field $\\psi$ whose effective potential is a function of $\\psi^*\\psi$. We determine the coefficients in the expansion of the effective potential to fifth order in $\\psi^*\\psi$ by matching low-energy axion scattering amplitudes. In order to describe a Bose-Einstein condensate of axions that is too dense to expand the effective potential in powers of $\\psi^*\\psi$, we develop a sequence of systematically improvable approximations to the effective potential that include terms of all orders in $\\psi^*\\psi$.
Natural discretization in noncommutative field theory
Energy Technology Data Exchange (ETDEWEB)
Acatrinei, Ciprian Sorin, E-mail: acatrine@theory.nipne.ro [Department of Theoretical Physics, Horia Hulubei National Institute for Nuclear Physics, Bucharest (Romania)
2015-12-07
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Natural discretization in noncommutative field theory
Acatrinei, Ciprian Sorin
2015-12-01
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
On the History of Unified Field Theories
Directory of Open Access Journals (Sweden)
Goenner Hubert F.M.
2004-01-01
Full Text Available This article is intended to give a review of the history of the classical aspects of unified field theories in the 20th century. It includes brief technical descriptions of the theories suggested, short biographical notes concerning the scientists involved, and an extensive bibliography. The present first installment covers the time span between 1914 and 1933, i.e., when Einstein was living and working in Berlin - with occasional digressions into other periods. Thus, the main theme is the unification of the electromagnetic and gravitational fields augmented by short-lived attempts to include the matter field described by Schrödinger's or Dirac's equations. While my focus lies on the conceptual development of the field, by also paying attention to the interaction of various schools of mathematicians with the research done by physicists, some prosopocraphical remarks are included.
Astrophysical data analysis with information field theory
Energy Technology Data Exchange (ETDEWEB)
Enßlin, Torsten, E-mail: ensslin@mpa-garching.mpg.de [Max Planck Institut für Astrophysik, Karl-Schwarzschild-Straße 1, D-85748 Garching, Germany and Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, D-80539 München (Germany)
2014-12-05
Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.
Astrophysical data analysis with information field theory
Enßlin, Torsten
2014-01-01
Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.
Nonrelativistic effective field theory for axions
Braaten, Eric; Mohapatra, Abhishek; Zhang, Hong
2016-10-01
Axions can be described by a relativistic field theory with a real scalar field ϕ whose self-interaction potential is a periodic function of ϕ . Low-energy axions, such as those produced in the early Universe by the vacuum misalignment mechanism, can be described more simply by a nonrelativistic effective field theory with a complex scalar field ψ whose effective potential is a function of ψ*ψ . We determine the coefficients in the expansion of the effective potential to fifth order in ψ*ψ by matching low-energy axion scattering amplitudes. In order to describe a Bose-Einstein condensate of axions that is too dense to truncate the expansion of the effective potential in powers of ψ*ψ , we develop a sequence of systematically improvable approximations to the effective potential that resum terms of all orders in ψ*ψ .
Scalar Quantum Field Theory on Fractals
Kar, Arnab
2011-01-01
We construct a family of measures for random fields based on the iterated subdivision of simple geometric shapes (triangles, squares, tetrahedrons) into a finite number of similar shapes. The intent is to construct continuum limits of scale invariant scalar field theories, by imitating Wiener's construction of the measure on the space of functions of one variable. These are Gaussian measures, except for one example of a non-Gaussian fixed point for the Ising model on a fractal. In the continuum limits what we construct have correlation functions that vary as a power of distance. In most cases this is a positive power (as for the Wiener measure) but we also find a few examples with negative exponent. In all cases the exponent is an irrational number, which depends on the particular subdivision scheme used. This suggests that the continuum limits corresponds to quantum field theories (random fields) on spaces of fractional dimension.
Chiral deformations of conformal field theories
Dijkgraaf, Robbert
1997-02-01
We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product expansion. These models have applications to vertex operator algebras, two-dimensional QCD, topological strings, holomorphic anomaly equations and modular properties of generalized characters of chiral algebras such as the W1+∞ algebra, that is treated in detail.
Chiral Deformations of Conformal Field Theories
Dijkgraaf, R
1996-01-01
We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product expansion. These models have applications to vertex operator algebras, two-dimensional QCD, topological strings, holomorphic anomaly equations and modular properties of generalized characters of chiral algebras such as the $W_{1+\\infty}$ algebra, that is treated in detail.
Chiral deformations of conformal field theories
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, R. [Amsterdam Univ. (Netherlands). Dept. of Math.
1997-06-02
We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product expansion. These models have applications to vertex operator algebras, two-dimensional QCD, topological strings, holomorphic anomaly equations and modular properties of generalized characters of chiral algebras such as the W{sub 1+{infinity}} algebra, that is treated in detail. (orig.).
Chiral Deformations of Conformal Field Theories
Dijkgraaf, R.
1996-01-01
We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product expansion. These models have applications to vertex operator algebras, two-dimensional QCD, topological strings, holomorphic anomaly equations and modular properties of generalized characters of chiral algebras such as the $W_{1+\\infty}$ algebra, that is treat...
Symmetry analysis for anisotropic field theories
Energy Technology Data Exchange (ETDEWEB)
Parra, Lorena; Vergara, J. David [Instituto de Ciencias Nucleares, UNAM, Circuito Exterior s/n, Ciudad Universitaria. Delg. Coyoacan. C.P. 04510 Mexico DF (Mexico)
2012-08-24
The purpose of this paper is to study with the help of Noether's theorem the symmetries of anisotropic actions for arbitrary fields which generally depend on higher order spatial derivatives, and to find the corresponding current densities and the Noether charges. We study in particular scale invariance and consider the cases of higher derivative extensions of the scalar field, electrodynamics and Chern-Simons theory.
Quantum Field Theory from First Principles
Esposito, Giampiero
2000-01-01
When quantum fields are studied on manifolds with boundary, the corresponding one-loop quantum theory for bosonic gauge fields with linear covariant gauges needs the assignment of suitable boundary conditions for elliptic differential operators of Laplace type. There are however deep reasons to modify such a scheme and allow for pseudo-differential boundary-value problems. When the boundary operator is allowed to be pseudo-differential while remaining a projector, the conditions on its kernel...
Quantum statistical correlations in thermal field theories: boundary effective theory
Bessa, A; de Carvalho, C A A; Fraga, E S
2010-01-01
We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field $\\phi_c$, and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schr\\"{o}dinger field-representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle-point for fixed boundary fields, which is the classical field $\\phi_c$, a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally-reduced effective theory for the thermal system. We calculate the two-point correlation as an example.
Upper Bounds on the Degeneracy of the Ground State in Quantum Field Models
Directory of Open Access Journals (Sweden)
Asao Arai
2016-01-01
Full Text Available Axiomatic abstract formulations are presented to derive upper bounds on the degeneracy of the ground state in quantum field models including massless ones. In particular, given is a sufficient condition under which the degeneracy of the ground state of the perturbed Hamiltonian is less than or equal to the degeneracy of the ground state of the unperturbed one. Applications of the abstract theory to models in quantum field theory are outlined.
New covariant Lagrange formulation for field theories
Ootsuka, T
2012-01-01
A novel approach for Lagrange formulation for field theories is proposed in terms of Kawaguchi geometry (areal metric space). On the extended configuration space M for classical field theory composed of spacetime and field configuration space, one can define a geometrical structure called Kawaguchi areal metric K from the field Lagrangian and (M,K) can be regarded as Kawaguchi manifold. The geometrical action functional is given by K and the dynamics of field is determined by covariant Euler-Lagrange equation derived from the variational principle of the action. The solution to the equation becomes a minimal hypersurface on (M,K) which has the same dimension as spacetime. We propose that this hypersurface is what we should regard as our real spacetime manifold, while the usual way to understand spacetime is to consider it as the parameter spacetime (base manifold) of a fibre bundle. In this way, the dynamics of field and spacetime structure is unified by Kawaguchi geometry. The theory has the property of stro...
Euclidean quantum field theory: Curved spacetimes and gauge fields
Ritter, William Gordon
This thesis presents a new formulation of quantum field theory (QFT) on curved spacetimes, with definite advantages over previous formulations, and an introduction to the millennium prize problem on four-dimensional gauge theory. Our constructions are completely rigorous, making QFT on curved spacetimes into a subfield of mathematics, and we achieve the first analytic control over nonperturbative aspects of interacting theories on curved spacetimes. The success of Euclidean path integrals to capture nonperturbative aspects of QFT has been striking. The Euclidean path integral is the most accurate method of calculating strong-coupling effects in gauge theory (such as glueball masses). Euclidean methods are also useful in the study of black holes, as evidenced by the Hartle-Hawking calculation of black-hole radiance. From a mathematical point of view, on flat spacetimes the Euclidean functional integral provides the most elegant method of constructing examples of interacting relativistic field theories. Yet until now, the incredibly-useful Euclidean path integral had never been given a definitive mathematical treatment on curved backgrounds. It is our aim to rectify this situation. Along the way, we discover that the Dirac operator on an arbitrary Clifford bundle has a resolvent kernel which is the Laplace transform of a positive measure. In studying spacetime symmetries, we discover a new way of constructing unitary representations of noncompact Lie groups. We also define and explore an interesting notion of convergence for Laplacians. The same mathematical framework applies to scalar fields, fermions, and gauge fields. The later chapters are devoted to gauge theory. We present a rigorous, self-contained introduction to the subject, aimed at mathematicians and using the language of modern mathematics, with a view towards nonperturbative renormalization in four dimensions. The latter ideas are unfinished. A completion of the final chapter would imply the construction
Field theories of condensed matter physics
Fradkin, Eduardo
2013-01-01
Presenting the physics of the most challenging problems in condensed matter using the conceptual framework of quantum field theory, this book is of great interest to physicists in condensed matter and high energy and string theorists, as well as mathematicians. Revised and updated, this second edition features new chapters on the renormalization group, the Luttinger liquid, gauge theory, topological fluids, topological insulators and quantum entanglement. The book begins with the basic concepts and tools, developing them gradually to bring readers to the issues currently faced at the frontiers of research, such as topological phases of matter, quantum and classical critical phenomena, quantum Hall effects and superconductors. Other topics covered include one-dimensional strongly correlated systems, quantum ordered and disordered phases, topological structures in condensed matter and in field theory and fractional statistics.
Observable currents in lattice field theories
Zapata, José A
2016-01-01
Observable currents are spacetime local objects that induce physical observables when integrated on an auxiliary codimension one surface. Since the resulting observables are independent of local deformations of the integration surface, the currents themselves carry most of the information about the induced physical observables. I study observable currents in a multisymplectic framework for Lagrangian field theory over discrete spacetime. A weak version of observable currents preserves many of their properties, while inducing a family of observables capable of separating points in the space of physically distinct solutions. A Poisson bracket gives the space of observable currents the structure of a Lie algebra. Peierls bracket for bulk observables gives an algebra homomorphism mapping equivalence classes of bulk observables to weak observable currents. The study covers scalar fields, nonlinear sigma models and gauge theories (including gauge theory formulations of general relativity) on the lattice. Even when ...
Effective Field Theory of Cosmological Perturbations
Piazza, Federico
2013-01-01
The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry---that allows to write down the most general Lagrangian---and of the Stueckelberg "trick"---that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed ana...
Nonlocal and quasi-local field theories
Tomboulis, E T
2015-01-01
We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasi-local (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasi-local kernels all acausal effects are confined within the compact support regi...
Causality Constraints in Conformal Field Theory
CERN. Geneva
2015-01-01
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d-dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (∂φ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinni...
Causality Constraints in Conformal Field Theory
Hartman, Thomas; Kundu, Sandipan
2015-01-01
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d-dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the $(\\partial\\phi)^4$ coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning o...
Perturbative quantum gravity in double field theory
Boels, Rutger H.; Horst, Christoph
2016-04-01
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
Perturbative quantum gravity in double field theory
Boels, Rutger H
2015-01-01
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
Scalar Field Theory on Fuzzy S^4
Medina, J; Medina, Julieta; Connor, Denjoe O'
2003-01-01
Scalar fields are studied on fuzzy $S^4$ and a solution is found for the elimination of the unwanted degrees of freedom that occur in the model. The resulting theory can be interpreted as a Kaluza-Klein reduction of CP^3 to S^4 in the fuzzy context.
Wilson lines in quantum field theory
Cherednikov, Igor O; Veken, Frederik F van der
2014-01-01
The objective of this book is to get the reader acquainted with theoretical and mathematical foundations of the concept of Wilson loops in the context of modern quantum field theory. It teaches how to perform independently with some elementary calculations on Wilson lines, and shows the recent development of the subject in different important areas of research.
Dirac-Kahler Theory and Massless Fields
Pletyukhov, V A
2010-01-01
Three massless limits of the Dirac-Kahler theory are considered. It is shown that the Dirac-Kahler equation for massive particles can be represented as a result of the gauge-invariant mixture (topological interaction) of the above massless fields.
Monopole in the dilatonic gauge field theory
Karczewska, D
2000-01-01
A numerical study of coupled to the dilaton field, static, spherically symmetric monopole solutions inspired by the Kaluza-Klein theory with large extra dimensions are presented. The generalized Prasad-Sommerfield solution is obtained. We show that monopole may have also the dilaton cloud configurations.
An Introduction to Effective Field Theory
Burgess, C. P.
2007-11-01
This review summarizes effective field theory techniques, which are the modern theoretical tools for exploiting the existence of hierarchies of scale in a physical problem. The general theoretical framework is described and evaluated explicitly for a simple model. Power-counting results are illustrated for a few cases of practical interest, and several applications to quantum electrodynamics are described.
Modular bootstrap in Liouville field theory
Energy Technology Data Exchange (ETDEWEB)
Hadasz, Leszek, E-mail: hadasz@th.if.uj.edu.p [M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Krakow (Poland); Jaskolski, Zbigniew, E-mail: jask@ift.uni.wroc.p [Institute of Theoretical Physics, University of Wroclaw, pl. M. Borna, 50-204 Wroclaw (Poland); Suchanek, Paulina, E-mail: paulina@ift.uni.wroc.p [Institute of Theoretical Physics, University of Wroclaw, pl. M. Borna, 50-204 Wroclaw (Poland)
2010-02-22
The modular matrix for the generic 1-point conformal blocks on the torus is expressed in terms of the fusion matrix for the 4-point blocks on the sphere. The modular invariance of the toric 1-point functions in the Liouville field theory with DOZZ structure constants is proved.
Modular bootstrap in Liouville field theory
Hadasz, Leszek; Suchanek, Paulina
2009-01-01
The modular matrix for the generic 1-point conformal blocks on the torus is expressed in terms of the fusion matrix for the 4-point blocks on the sphere. The modular invariance of the toric 1-point functions in the Liouville field theory with DOZZ structure constants is proved.
Geometry, topology and quantum field theory (fundamental theories of physics)
Bandyopadhyay, P.
2013-01-01
This monograph deals with the geometrical and topological aspects related to quantum field theory with special reference to the electroweak theory and skyrmions. This book is unique in its emphasis on the topological aspects of a fermion manifested through chiral anomaly which is responsible for the generation of mass. This has its relevance in electroweak theory where it is observed that weak interaction gauge bosons attain mass topologically. These geometrical and topological features help us to consider a massive fermion as a skyrmion and for a composite state we can realise the internal symmetry of hadrons from reflection group. Also, an overview of noncommutative geometry has been presented and it is observed that the manifold M 4 x Z2 has its relevance in the description of a massive fermion as skyrmion when the discrete space is considered as the internal space and the symmetry breaking gives rise to chiral anomaly leading to topological features.
Relating field theories via stochastic quantization
Dijkgraaf, Robbert; Orlando, Domenico; Reffert, Susanne
2010-01-01
This note aims to subsume several apparently unrelated models under a common framework. Several examples of well-known quantum field theories are listed which are connected via stochastic quantization. We highlight the fact that the quantization method used to obtain the quantum crystal is a discrete analog of stochastic quantization. This model is of interest for string theory, since the (classical) melting crystal corner is related to the topological A-model. We outline several ideas for interpreting the quantum crystal on the string theory side of the correspondence, exploring interpretations in the Wheeler-De Witt framework and in terms of a non-Lorentz invariant limit of topological M-theory.
Relating field theories via stochastic quantization
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, Robbert [KdV Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam (Netherlands); Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Orlando, Domenico [Institute for the Mathematics and Physics of the Universe, University of Tokyo, Kashiwa-no-Ha 5-1-5, Kashiwa-shi, 277-8568 Chiba (Japan); Reffert, Susanne, E-mail: susanne.reffert@impu.j [Institute for the Mathematics and Physics of the Universe, University of Tokyo, Kashiwa-no-Ha 5-1-5, Kashiwa-shi, 277-8568 Chiba (Japan)
2010-01-11
This note aims to subsume several apparently unrelated models under a common framework. Several examples of well-known quantum field theories are listed which are connected via stochastic quantization. We highlight the fact that the quantization method used to obtain the quantum crystal is a discrete analog of stochastic quantization. This model is of interest for string theory, since the (classical) melting crystal corner is related to the topological A-model. We outline several ideas for interpreting the quantum crystal on the string theory side of the correspondence, exploring interpretations in the Wheeler-De Witt framework and in terms of a non-Lorentz invariant limit of topological M-theory.
Relating Field Theories via Stochastic Quantization
Dijkgraaf, Robbert; Reffert, Susanne
2009-01-01
This note aims to subsume several apparently unrelated models under a common framework. Several examples of well-known quantum field theories are listed which are connected via stochastic quantization. We highlight the fact that the quantization method used to obtain the quantum crystal is a discrete analog of stochastic quantization. This model is of interest for string theory, since the (classical) melting crystal corner is related to the topological A-model. We outline several ideas for interpreting the quantum crystal on the string theory side of the correspondence, exploring interpretations in the Wheeler-De Witt framework and in terms of a non-Lorentz invariant limit of topological M-theory.
Gravitational Goldstone fields from affine gauge theory
Tresguerres, R
2000-01-01
In order to facilitate the application of standard renormalization techniques, gravitation should be decribed, if possible, in pure connection formalism, as a Yang-Mills theory of a certain spacetime group, say the Poincare or the affine group. This embodies the translational as well as the linear connection. However, the coframe is not the standard Yang-Mills type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring the "hidden" piece responsible for this behavior within the framework of nonlinear realizations, the usual geometrical interpretation of the dynamical theory becomes possible, and in addition one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. We claim that nonlinear realizations provide a general mathematical scheme clarifying the foundations of gauge theories of spacetime symmetries. When applied to construct the Yang-Mills theory of the aff...
Superconformal quantum field theories in string. Gauge theory dualities
Energy Technology Data Exchange (ETDEWEB)
Wiegandt, Konstantin
2012-08-14
In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.
A periodic table of effective field theories
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Shen, Chia-Hsien; Trnka, Jaroslav
2017-02-01
We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix. To do so we define an EFT classification based on four parameters characterizing 1) the number of derivatives per interaction, 2) the soft properties of amplitudes, 3) the leading valency of the interactions, and 4) the spacetime dimension. Carving out the allowed space of EFTs, we prove that exceptional EFTs like the non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using on-shell momentum shifts and recursion relations, we prove that EFTs with arbitrarily soft behavior are forbidden and EFTs with leading valency much greater than the spacetime dimension cannot have enhanced soft behavior. We then enumerate all single scalar EFTs in d < 6 and verify that they correspond to known theories in the literature. Our results suggest that the exceptional theories are the natural EFT analogs of gauge theory and gravity because they are one-parameter theories whose interactions are strictly dictated by properties of the S-matrix.
Gaussian Markov random fields theory and applications
Rue, Havard
2005-01-01
Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studies and, online, a c-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important.
Effective field theory approach to quasi-single field inflation
Noumi, Toshifumi; Yokoyama, Daisuke
2012-01-01
We apply the effective field theory approach to quasi-single field inflation, which contains an additional scalar field with Hubble scale mass other than inflaton. Based on the time-dependent spatial diffeomorphism, which is not broken by the time-dependent background evolution, the most generic action of quasi-single field inflation is constructed up to third order fluctuations. Using the obtained action, the effects of the additional massive scalar field on the primordial curvature perturbations are discussed. In particular, we calculate the power spectrum and discuss the momentum-dependence of three point functions in the squeezed limit for general settings of quasi-single field inflation. Our framework can be also applied to inflation models with heavy particles. We make a qualitative discussion on the effects of heavy particles during inflation and that of sharp turning trajectory in our framework.
Group field cosmology: a cosmological field theory of quantum geometry
Calcagni, Gianluca; Oriti, Daniele
2012-01-01
Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted to a field, the coordinates are minisuperspace variables, the kinetic operator is the Hamiltonian constraint operator, and the action features a nonlinear and possibly nonlocal interaction term. We discuss free-field classical solutions, the quantum propagator, and a mean-field approximation linearizing the equation of motion and augmenting the Hamiltonian constraint by an effective term mixing gravitational and matter variables. Depending on the choice of interaction, this can reproduce, for example, a cosmological constant, a scalar-field potential, or a curvature contribution.
A computational theory of visual receptive fields.
Lindeberg, Tony
2013-12-01
A receptive field constitutes a region in the visual field where a visual cell or a visual operator responds to visual stimuli. This paper presents a theory for what types of receptive field profiles can be regarded as natural for an idealized vision system, given a set of structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world. These symmetry properties include (i) covariance properties under scale changes, affine image deformations, and Galilean transformations of space-time as occur for real-world image data as well as specific requirements of (ii) temporal causality implying that the future cannot be accessed and (iii) a time-recursive updating mechanism of a limited temporal buffer of the past as is necessary for a genuine real-time system. Fundamental structural requirements are also imposed to ensure (iv) mutual consistency and a proper handling of internal representations at different spatial and temporal scales. It is shown how a set of families of idealized receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic, and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives, or closely related operators. Such image filters have been successfully used as a basis for expressing a large number of visual operations in computer vision, regarding feature detection, feature classification, motion estimation, object recognition, spatio-temporal recognition, and shape estimation. Hence, the associated so-called scale-space theory constitutes a both theoretically well-founded and general framework for expressing visual operations. There are very close similarities between receptive field profiles predicted from this scale-space theory and receptive field profiles found by cell recordings in biological vision. Among the family of receptive field profiles derived by necessity from the assumptions, idealized models with very good qualitative
Gauge Field Theories, 2nd Edition
Frampton, Paul H.
2000-08-01
The first edition of Gauge Field Theories, published in 1985, quickly became widely used in universities and other institutions of higher learning around the world. Written by well-known physicist Paul Frampton, the new edition continues to offer a first-rate mathematical treatment of gauge field theories, while thoroughly updating all chapters to keep pace with developments in the field. Frampton emphasizes formalism rather than experiments and provides sufficient detail for readers wishing to do their own calculations or pursue theoretical physics research. Special features of the Second Edition include: * Improved, logical organization of the material on gauge invariance, quantization, and renormalization * Major revision of the chapter on electroweak interactions, incorporating the latest precision data and discovery of the top quark * Discussions of renormalization group and quantum chromodynamics * A completely new chapter on model building
Effective Field Theory for Jet Processes.
Becher, Thomas; Neubert, Matthias; Rothen, Lorena; Shao, Ding Yu
2016-05-13
Processes involving narrow jets receive perturbative corrections enhanced by logarithms of the jet opening angle and the ratio of the energies inside and outside the jets. Analyzing cone-jet processes in effective field theory, we find that in addition to soft and collinear fields their description requires degrees of freedom that are simultaneously soft and collinear to the jets. These collinear-soft particles can resolve individual collinear partons, leading to a complicated multi-Wilson-line structure of the associated operators at higher orders. Our effective field theory provides, for the first time, a factorization formula for a cone-jet process, which fully separates the physics at different energy scales. Its renormalization-group equations control all logarithmically enhanced higher-order terms, in particular also the nonglobal logarithms.
General principles of quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Bogolubov, N.N.; Logunov, A.A. (AN SSSR, Moscow (USSR) Moskovskij Gosudarstvennyj Univ., Moscow (USSR)); Oksak, A.I. (Institute for High Energy Physics, Moscow (USSR)); Todorov, I.T. (Bylgarska Akademiya na Naukite, Sofia (Bulgaria) Bulgarian Institute for Nuclear Research and Nuclear Energy, Sofia (Bulgaria))
1990-01-01
This major volume provides a account of general quantum field theory, with an emphasis on model-independent methods. The important aspects of the development of the subject are described in detail and are shown to have promising links with many branches of modern mathematics and theoretical physics, such as random fields (probability), statistical physics, and elemantary particles. The material is presented in a thorough, systematic way and the mathematical methods of quantum field theory are also given. The text is self-contained and contains numerous exercises. Topics of independent interest are given in appendices. The book also contains a large bibliography. (author). 1181 refs. Includes index of notation and subject index; includes 1181 refs.
Phase-space quantization of field theory.
Energy Technology Data Exchange (ETDEWEB)
Curtright, T.; Zachos, C.
1999-04-20
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999.
An Axiomatic Basis for Quantum Mechanics
Cassinelli, Gianni; Lahti, Pekka
2016-10-01
In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in this derivation are the co-ordinatization of generalized geometries and a theorem of Solér which characterizes Hilbert spaces among the orthomodular spaces. A generalized Wigner theorem is applied to reduce some of the assumptions of Solér's theorem to the theory of symmetry in quantum mechanics. Since this reduction is only partial we also point out the remaining open questions.
Field theory description of neutrino oscillations
Dvornikov, Maxim
2010-01-01
We review various field theory approaches to the description of neutrino oscillations in vacuum and external fields. First we discuss a relativistic quantum mechanics based approach which involves the temporal evolution of massive neutrinos. To describe the dynamics of the neutrinos system we use exact solutions of wave equations in presence of an external field. It allows one to exactly take into account both the characteristics of neutrinos and the properties of an external field. In particular, we examine flavor oscillations an vacuum and in background matter as well as spin flavor oscillations in matter under the influence of an external electromagnetic field. Moreover we consider the situation of hypothetical nonstandard neutrino interactions with background fermions. In the case of ultrarelativistic particles we reproduce an effective Hamiltonian which is used in the standard quantum mechanical approach for the description of neutrino oscillations. The corrections to the quantum mechanical Hamiltonian a...
Unified Gauge Field Theory and Topological Transitions
Patwardhan, A
2004-01-01
The search for a Unified description of all interactions has created many developments of mathematics and physics. The role of geometric effects in the Quantum Theory of particles and fields and spacetime has been an active topic of research. This paper attempts to obtain the conditions for a Unified Gauge Field Theory, including gravity. In the Yang Mills type of theories with compactifications from a 10 or 11 dimensional space to a spacetime of 4 dimensions, the Kaluza Klein and the Holonomy approach has been used. In the compactifications of Calabi Yau spaces and sub manifolds, the Euler number Topological Index is used to label the allowed states and the transitions. With a SU(2) or SL(2,C) connection for gravity and the U(1)*SU(2)*SU(3) or SU(5) gauge connection for the other interactions, a Unified gauge field theory is expressed in the 10 or 11 dimension space. Partition functions for the sum over all possible configurations of sub spaces labeled by the Euler number index and the Action for gauge and m...
Nonrelativistic Fermions in Magnetic Fields a Quantum Field Theory Approach
Espinosa, Olivier R; Lepe, S; Méndez, F
2001-01-01
The statistical mechanics of nonrelativistic fermions in a constant magnetic field is considered from the quantum field theory point of view. The fermionic determinant is computed using a general procedure that contains all possible regularizations. The nonrelativistic grand-potential can be expressed in terms polylogarithm functions, whereas the partition function in 2+1 dimensions and vanishing chemical potential can be compactly written in terms of the Dedekind eta function. The strong and weak magnetic fields limits are easily studied in the latter case by using the duality properties of the Dedekind function.
Matrix field theory: Applications to superconductivity
Zhou, Lubo
In this thesis a systematic, functional matrix field theory is developed to describe both clean and disordered s-wave and d-wave superconductors and the quantum phase transitions associated with them. The thesis can be divided into three parts. The first part includes chapters 1 to 3. In chapter one a general physical introduction is given. In chapters two and three the theory is developed and used to compute the equation of state as well as the number-density susceptibility, spin-density susceptibility, the sound attenuation coefficient, and the electrical conductivity in both clean and disordered s-wave superconductors. The second part includes chapter four. In this chapter we use the theory to describe the disorder-induced metal - superconductor quantum phase transition. The key physical idea here is that in addition to the superconducting order-parameter fluctuations, there are also additional soft fermionic fluctuations that are important at the transition. We develop a local field theory for the coupled fields describing superconducting and soft fermionic fluctuations. Using simple renormalization group and scaling ideas, we exactly determine the critical behavior at this quantum phase transition. Our theory justifies previous approaches. The third part includes chapter five. In this chapter we study the analogous quantum phase transition in disordered d-wave superconductors. This theory should be related to high Tc superconductors. Surprisingly, we show that in both the underdoped and overdoped regions, the coupling of superconducting fluctuations to the soft disordered fermionic fluctuations is much weaker than that in the s-wave case. The net result is that the disordered quantum phase transition in this case is a strong coupling, or described by an infinite disordered fixed point, transition and cannot be described by the perturbative RG description that works so well in the s-wave case. The transition appears to be related to the one that occurs in
A Simple Axiomatization of Nonadditive Expected Utility
R.K. Sarin (Rakesh); P.P. Wakker (Peter)
1992-01-01
textabstractThis paper provides an extension of Savage's subjective expected utility theory for decisions under uncertainty. It includes in the set of events both unambiguous events for which probabilities are additive and ambiguous events for which probabilities are permitted to be nonadditive. The
Melonic phase transition in group field theory
Baratin, Aristide; Oriti, Daniele; Ryan, James P; Smerlak, Matteo
2013-01-01
Group field theories have recently been shown to admit a 1/N expansion dominated by so-called `melonic graphs', dual to triangulated spheres. In this note, we deepen the analysis of this melonic sector. We obtain a combinatorial formula for the melonic amplitudes in terms of a graph polynomial related to a higher dimensional generalization of the Kirchhoff tree-matrix theorem. Simple bounds on these amplitudes show the existence of a phase transition driven by melonic interaction processes. We restrict our study to the Boulatov-Ooguri models, which describe topological BF theories and are the basis for the construction of four dimensional models of quantum gravity.
Knot Invariants from Classical Field Theories
Leal, L C
1999-01-01
We consider the Non-Abelian Chern-Simons term coupled to external particles, in a gauge and diffeomorphism invariant form. The classical equations of motion are perturbativelly studied, and the on-shell action is shown to produce knot-invariants associated with the sources. The first contributions are explicitly calculated, and the corresponding knot-invariants are recognized. We conclude that the interplay between Knot Theory and Topological Field Theories is manifested not only at the quantum level, but in a classical context as well.
Recursion equations in gauge field theories
Migdal, A. A.
An approximate recursion equation is formulated, describing the scale transformation of the effective action of a gauge field. In two-dimensional space-time the equation becomes exact. In four-dimensional theories it reproduces asymptotic freedom to an accuracy of 30% in the coefficients of the β-function. In the strong-coupling region the β-function remains negative and this results in an asymptotic prison in the infrared region. Possible generalizations and applications to the quark-gluon gauge theory are discussed.
On field theory quantization around instantons
Anselmi, D
2009-01-01
With the perspective of looking for experimentally detectable physical applications of the so-called topological embedding, a procedure recently proposed by the author for quantizing a field theory around a non-discrete space of classical minima (instantons, for example), the physical implications are discussed in a ``theoretical'' framework, the ideas are collected in a simple logical scheme and the topological version of the Ginzburg-Landau theory of superconductivity is solved in the intermediate situation between type I and type II superconductors.
Tachyon Vacuum in Cubic Superstring Field Theory
Erler, Theodore
2008-01-01
In this paper we give an exact analytic solution for tachyon condensation in the modified (picture 0) cubic superstring field theory. We prove the absence of cohomology and, crucially, reproduce the correct value for the D-brane tension. The solution is surprising for two reasons: First, the existence of a tachyon vacuum in this theory has not been definitively established in the level expansion. Second, the solution {\\it vanishes} in the GSO$(-)$ sector, implying a ``tachyon vacuum'' solution exists even for a {\\it BPS} D-brane.
Inclusive fitness maximization: An axiomatic approach.
Okasha, Samir; Weymark, John A; Bossert, Walter
2014-06-01
Kin selection theorists argue that evolution in social contexts will lead organisms to behave as if maximizing their inclusive, as opposed to personal, fitness. The inclusive fitness concept allows biologists to treat organisms as akin to rational agents seeking to maximize a utility function. Here we develop this idea and place it on a firm footing by employing a standard decision-theoretic methodology. We show how the principle of inclusive fitness maximization and a related principle of quasi-inclusive fitness maximization can be derived from axioms on an individual׳s 'as if preferences' (binary choices) for the case in which phenotypic effects are additive. Our results help integrate evolutionary theory and rational choice theory, help draw out the behavioural implications of inclusive fitness maximization, and point to a possible way in which evolution could lead organisms to implement it.
The Axiomatic Foundation of Space in GFO
Baumann, Ringo
2011-01-01
Space and time are basic categories of any top-level ontology. They are fundamental assumptions for the mode of existence of those individuals which are said to be in space and time. In the present paper the ontology of space in the General Formal Ontology (GFO) is expounded. This ontology is represented as a theory BT (Brentano Theory), which is specified by a set of axioms formalized in first-order logic. This theory uses four primitive relations: SReg(x) (x is space region), spart(x, y) (x is spatial part of y), sb(x, y) (x is spatial boundary of y), and scoinc(x, y) (x and y spatially coincide). This ontology is inspired by ideas of Franz Brentano. The investigation and exploration of Franz Brentano's ideas on space and time began about twenty years ago by work of R.M. Chisholm, B. Smith and A. Varzi. The present paper takes up this line of research and makes a further step in establishing an ontology of space which is based on rigorous logical methods and on principles of the new philosophical approach o...
Nuclear effective field theory on the lattice
Krebs, H; Epelbaum, E; Lee, D; ner, Ulf-G Mei\\ss
2008-01-01
In the low-energy region far below the chiral symmetry breaking scale (which is of the order of 1 GeV) chiral perturbation theory provides a model-independent approach for quantitative description of nuclear processes. In the two- and more-nucleon sector perturbation theory is applicable only at the level of an effective potential which serves as input in the corresponding dynamical equation. To deal with the resulting many-body problem we put chiral effective field theory (EFT) on the lattice. Here we present the results of our lattice EFT study up to next-to-next-to-leading order in the chiral expansion. Accurate description of two-nucleon phase-shifts and ground state energy ratio of dilute neutron matter up to corrections of higher orders shows that lattice EFT is a promising tool for a quantitative description of low-energy few- and many-body systems.
The Effective Field Theory of Multifield Inflation
Senatore, Leonardo
2010-01-01
We generalize the Effective Field Theory of Inflation to include additional light scalar degrees of freedom that are in their vacuum at the time the modes of interest are crossing the horizon. In order to make the scalars light in a natural way we consider the case where they are the Goldstone bosons of a global symmetry group or are partially protected by an approximate supersymmetry. We write the most general Lagrangian that couples the scalar mode associated to the breaking of time translation during inflation to the additional light scalar fields. This Lagrangian is constrained by diffeomorphism invariance and the additional symmetries that keep the new scalars light. This Lagrangian describes the fluctuations around the time of horizon crossing and it is supplemented with a general parameterization describing how the additional fluctuating fields can affect cosmological perturbations. We find that multifield inflation can reproduce the non-Gaussianities that can be generated in single field inflation but...
Quantum field theory on projective modules
Gayral, V; Krajewski, T; Wulkenhaar, R
2006-01-01
We propose a general formulation of perturbative quantum field theory on (finitely generated) projective modules over noncommutative algebras. This is the analogue of scalar field theories with non-trivial topology in the noncommutative realm. We treat in detail the case of Heisenberg modules over noncommutative tori and show how these models can be understood as large rectangular pxq matrix models, in the limit p/q->theta, where theta is a possibly irrational number. We find out that the modele is highly sensitive to the number-theoretical aspect of theta and suffers from an UV/IR-mixing. We give a way to cure the entanglement and prove one-loop renormalizability.
Probabilities and Signalling in Quantum Field Theory
Dickinson, Robert; Millington, Peter
2016-01-01
We present an approach to computing probabilities in quantum field theory for a wide class of source-detector models. The approach works directly with probabilities and not with squared matrix elements, and the resulting probabilities can be written in terms of expectation values of nested commutators and anti-commutators. We present results that help in the evaluation of these, including an expression for the vacuum expectation values of general nestings of commutators and anti-commutators in scalar field theory. This approach allows one to see clearly how faster-than-light signalling is prevented, because it leads to a diagrammatic expansion in which the retarded propagator plays a prominent role. We illustrate the formalism using the simple case of the much-studied Fermi two-atom problem.
The Effective Field Theory of Dark Energy
Gubitosi, Giulia; Vernizzi, Filippo
2012-01-01
We propose a universal description of dark energy and modified gravity that includes all single-field models. By extending a formalism previously applied to inflation, we consider the metric universally coupled to matter fields and we write in terms of it the most general unitary gauge action consistent with the residual unbroken symmetries of spatial diffeomorphisms. Our action is particularly suited for cosmological perturbation theory: the background evolution depends on only three operators. All other operators start at least at quadratic order in the perturbations and their effects can be studied independently and systematically. In particular, we focus on the properties of a few operators which appear in non-minimally coupled scalar-tensor gravity and galileon theories. In this context, we study the mixing between gravity and the scalar degree of freedom. We assess the quantum and classical stability, derive the speed of sound of fluctuations and the renormalization of the Newton constant. The scalar ca...
The Topology of Double Field Theory
Hassler, Falk
2016-01-01
We describe the doubled space of Double Field Theory as a group manifold $G$ with an arbitrary generalized metric. Local information from the latter is not relevant to our discussion and so $G$ only captures the topology of the doubled space. Strong Constraint solutions are maximal isotropic submanifold $M$ in $G$. We construct them and their Generalized Geometry in Double Field Theory on Group Manifolds. In general, $G$ admits different physical subspace $M$ which are T-dual to each other. By studying two examples, we reproduce the topology changes induced by T-duality with non-trivial $H$-flux which were discussed by Bouwknegt, Evslin and Mathai [hep-th/0306062].
Effective Field Theory for Rydberg Polaritons
Gullans, M. J.; Thompson, J. D.; Wang, Y.; Liang, Q.-Y.; Vuletić, V.; Lukin, M. D.; Gorshkov, A. V.
2016-01-01
We develop an effective field theory (EFT) to describe the few- and many-body propagation of one dimensional Rydberg polaritons. We show that the photonic transmission through the Rydberg medium can be found by mapping the propagation problem to a non-equilibrium quench, where the role of time and space are reversed. We include effective range corrections in the EFT and show that they dominate the dynamics near scattering resonances in the presence of deep bound states. Finally, we show how the long-range nature of the Rydberg-Rydberg interactions induces strong effective N-body interactions between Rydberg polaritons. These results pave the way towards studying non-perturbative effects in quantum field theories using Rydberg polaritons. PMID:27661685
Gravity duals for nonrelativistic conformal field theories.
Balasubramanian, Koushik; McGreevy, John
2008-08-08
We attempt to generalize the anti-de Sitter/conformal field theory correspondence to nonrelativistic conformal field theories which are invariant under Galilean transformations. Such systems govern ultracold atoms at unitarity, nucleon scattering in some channels, and, more generally, a family of universality classes of quantum critical behavior. We construct a family of metrics which realize these symmetries as isometries. They are solutions of gravity with a negative cosmological constant coupled to pressureless dust. We discuss realizations of the dust, which include a bulk superconductor. We develop the holographic dictionary and find two-point correlators of the correct form. A strange aspect of the correspondence is that the bulk geometry has two extra noncompact dimensions.
Magnetic fields and density functional theory
Energy Technology Data Exchange (ETDEWEB)
Salsbury Jr., Freddie [Univ. of California, Berkeley, CA (United States)
1999-02-01
A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.
Kouranbaeva, Shinar; Shkoller, Steve
1999-01-01
This paper presents a geometric-variational approach to continuous and discrete {\\it second-order} field theories following the methodology of \\cite{MPS}. Staying entirely in the Lagrangian framework and letting $Y$ denote the configuration fiber bundle, we show that both the multisymplectic structure on $J^3Y$ as well as the Noether theorem arise from the first variation of the action function. We generalize the multisymplectic form formula derived for first order field theories in \\cite{MPS...
A 1+1 field theory spectrum from M theory
Rodríguez, M J; Rodriguez, Maria Jose; Talavera, Pere
2005-01-01
The spectrum of a 1+1 dimensional field theory with dynamical quarks is constructed. We focus in testing the possible brane embeddings that can support fundamental matter. The requirement on the wave function normalisation and the dependence on the quark mass of the quark condensate allow to discard most of the embeddings. We pay attention to some more general considerations comparing the behaviour of the non-compact theory at different dimensions. In particular we explored the possibility that the AdS/CFT duality ``formalism'' introduce a scale breaking parameter at (1+1)d allowing the existence of classical glueballs and its possible relation with point-like string configurations. The screening effects and the appearance of a possible phase transition is also discussed.
Conformal invariance in quantum field theory
Todorov, Ivan T; Petkova, Valentina B
1978-01-01
The present volume is an extended and up-to-date version of two sets of lectures by the first author and it reviews more recent work. The notes aim to present a self-contained exposition of a constructive approach to conformal invariant quantum field theory. Other parts in application of the conformal group to quantum physics are only briefly mentioned. The relevant mathematical material (harmonic analysis on Euclidean conformal groups) is briefly summarized. A new exposition of physical applications is given, which includes an explicit construction of the vacuum operator product expansion for the free zero mass fields.
Scalar Field Theories with Polynomial Shift Symmetries
Griffin, Tom; Horava, Petr; Yan, Ziqi
2014-01-01
We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG) modes associated with spontaneous symmetry breaking. Such systems allow for an extension of the constant shift symmetry to a shift by a polynomial of degree $P$ in spatial coordinates. These "polynomial shift symmetries" in turn protect the technical naturalness of modes with a higher-order dispersion relation, and lead to a refinement of the proposed classification of infrared Gaussian fixed points available to describe NG modes in nonrelativistic theories. Generic interactions in such theories break the polynomial shift symmetry explicitly to the constant shift. It is thus natural to ask: Given a Gaussian fixed point with polynomial shift symmetry of degree $P$, what are the lowest-dimension operators that preserve this symmetry, and deform the theory into a self-interacting scalar field theory with the shift symmetry of degree $P$? To answer this (essen...
Cosmological phase transitions from lattice field theory
Energy Technology Data Exchange (ETDEWEB)
Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2011-11-22
In this proceedings contribution we discuss the fate of the electroweak and the quantum chromodynamics phase transitions relevant for the early stage of the universe at non-zero temperature. These phase transitions are related to the Higgs mechanism and the breaking of chiral symmetry, respectively. We will review that non-perturbative lattice field theory simulations show that these phase transitions actually do not occur in nature and that physical observables show a completely smooth behaviour as a function of the temperature.
Bosonic Dynamical Mean-Field Theory
Snoek, Michiel; Hofstetter, Walter
2013-02-01
We derive the bosonic dynamical mean-field equations for bosonic atoms in optical lattices with arbitrary lattice geometry. The equations are presented as a systematic expansion in 1/z, z being the number of lattice neighbours. Hence the theory is applicable in sufficiently high-dimensional lattices. We apply the method to a two-component mixture, for which a rich phase diagram with spin order is revealed.
A product formula and combinatorial field theory
Horzela, A; Duchamp, G H E; Penson, K A; Solomon, A I
2004-01-01
We treat the problem of normally ordering expressions involving the standard boson operators a, a* where [a,a*]=1. We show that a simple product formula for formal power series - essentially an extension of the Taylor expansion - leads to a double exponential formula which enables a powerful graphical description of the generating functions of the combinatorial sequences associated with such functions - in essence, a combinatorial field theory. We apply these techniques to some examples related to specific physical Hamiltonians.
On level crossing in conformal field theories
Korchemsky, G.
2016-01-01
We study the properties of operators in a unitary conformal field theory whose scaling dimensions approach each other for some values of the parameters and satisfy von Neumann-Wigner non-crossing rule. We argue that the scaling dimensions of such operators and their OPE coefficients have a universal scaling behavior in the vicinity of the crossing point. We demonstrate that the obtained relations are in a good agreement with the known examples of the level-crossing phenomenon in maximally sup...
Kisil, Vladimir V.
2004-01-01
The orbit method of Kirillov is used to derive the p-mechanical brackets [math-ph/0007030, quant-ph/0212101]. They generate the quantum (Moyal) and classic (Poisson) brackets on respective orbits corresponding to representations of the Heisenberg group. The extension of p-mechanics to field theory is made through the De Donder--Weyl Hamiltonian formulation. The principal step is the substitution of the Heisenberg group with Galilean. Keywords: Classic and quantum mechanics, Moyal brackets, Po...
Conformal Field Theories and Deep Inelastic Scattering
Komargodski, Zohar; Parnachev, Andrei; Zhiboedov, Alexander
2016-01-01
We consider Deep Inelastic Scattering (DIS) thought experiments in unitary Conformal Field Theories (CFTs). We explore the implications of the standard dispersion relations for the OPE data. We derive positivity constraints on the OPE coefficients of minimal-twist operators of even spin s \\geq 2. In the case of s=2, when the leading-twist operator is the stress tensor, we reproduce the Hofman-Maldacena bounds. For s>2 the bounds are new.
Fermionic ghosts in Moyal string field theory
Bars, Itzhak; Kishimoto, Isao; Matsuo, Yutaka
2003-07-01
We complete the construction of the Moyal star formulation of bosonic open string field theory (MSFT) by providing a detailed study of the fermionic ghost sector. In particular, as in the case of the matter sector, (1) we construct a map from Witten's star product to the Moyal product, (2) we propose a regularization scheme which is consistent with the matter sector and (3) as a check of the formalism, we derive the ghost Neumann coefficients algebraically directly from the Moyal product. The latter satisfy the Gross-Jevicki nonlinear relations even in the presence of the regulator, and when the regulator is removed they coincide numerically with the expression derived from conformal field theory. After this basic construction, we derive a regularized action of string field theory in the Siegel gauge and define the Feynman rules. We give explicitly the analytic expression of the off-shell four point function for tachyons, including the ghost contribution. Some of the results in this paper have already been used in our previous publications. This paper provides the technical details of the computations which were omitted there.
Fermionic Ghosts in Moyal String Field Theory
Bars, Itzhak; Matsuo, Y
2003-01-01
We complete the construction of the Moyal star formulation of bosonic open string field theory (MSFT) by providing a detailed study of the fermionic ghost sector. In particular, as in the case of the matter sector, (1) we construct a map from Witten's star product to the Moyal product, (2) we propose a regularization scheme which is consistent with the matter sector and (3) as a check of the formalism, we derive the ghost Neumann coefficients algebraically directly from the Moyal product. The latter satisfy the Gross-Jevicki nonlinear relations even in the presence of the regulator, and when the regulator is removed they coincide numerically with the expression derived from conformal field theory. After this basic construction, we derive a regularized action of string field theory in the Siegel gauge and define the Feynman rules. We give explicitly the analytic expression of the off-shell four point function for tachyons, including the ghost contribution. Some of the results in this paper have already been us...
Dual Field Theories of Quantum Computation
Vanchurin, Vitaly
2016-01-01
Given two quantum states of $N$ q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large $N$ limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an $N+1$ dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an $N$ dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli $Z$ matrices. Since such situation is not generic we call it the $Z$-problem. On the dual field the...
Superconformal partial waves in Grassmannian field theories
Doobary, Reza
2015-01-01
We derive superconformal partial waves for all scalar four-point functions on a super Grassmannian space Gr(m|n,2m|2n) for all m,n. This family of four-point functions includes those of all (arbitrary weight) half BPS operators in both N=4 SYM (m=n=2) and in N=2 superconformal field theories in four dimensions (m=2,n=1) on analytic superspace. It also includes four-point functions of all (arbitrary dimension) scalar fields in non-supersymmetric conformal field theories (m=2,n=0) on Minkowski space, as well as those of a certain class of representations of the compact SU(2n) coset spaces. As an application we then specialise to N=4 SYM and use these results to perform a detailed superconformal partial wave analysis of the four- point functions of arbitrary weight half BPS operators. We discuss the non-trivial separation of protected and unprotected sectors for the , and cases in an SU(N) gauge theory at finite N. The correlator predicts a non-trivial protected twist four sector for which we can completely ...
A Periodic Table of Effective Field Theories
Cheung, Clifford; Novotny, Jiri; Shen, Chia-Hsien; Trnka, Jaroslav
2016-01-01
We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix. To do so we define an EFT classification based on four parameters characterizing 1) the number of derivatives per interaction, 2) the soft properties of amplitudes, 3) the leading valency of the interactions, and 4) the spacetime dimension. Carving out the allowed space of EFTs, we prove that exceptional EFTs like the non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using on-shell momentum shifts and recursion relations, we prove that EFTs with arbitrarily soft behavior are forbidden and EFTs with leading valency much greater than the spacetime dimension cannot have enhanced soft behavior. We then enumerate all single scalar EFTs in d<6 and verify that they correspond to known theories in the literature. Our results suggest that the exceptional theories are the natural EFT analogs of gauge theor...
Undergraduate Lecture Notes in Topological Quantum Field Theory
2008-01-01
These third-year lecture notes are designed for a 1-semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second-year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagnetism. Keywords: quantum mechanics/field theory, path integral, Hodge decomposition, Chern-Simons and Yang-Mills gauge theories, conformal field theory
Quantum field theories of extended objects
Friedan, Daniel
2016-01-01
First steps are taken in a project to construct a general class of conformal and perhaps, eventually, non-conformal quantum field theories of (n-1)-dimensional extended objects in a d=2n dimensional conformal space-time manifold M. The fields live on the spaces E of relative integral (n-1)-cycles in M -- the integral (n-1)-currents of given boundary. Each E is a complete metric space geometrically analogous to a Riemann surface $\\Sigma$. For example, if $M=S^d$, $\\Sigma = S^2$. The quantum fields on E are to be mapped to observables in a 2d CFT on $\\Sigma$. The correlation functions on E are to be given by the 2d correlation functions on $\\Sigma$. The goal is to construct a CFT of extended objects in d=2n dimensions for every 2d CFT, and eventually a non-conformal QFT of extended objects for every non-conformal 2d QFT, so that all the technology of 2d QFT can be applied to the construction and analysis of quantum field theories of extended objects. The project depends crucially on settling some mathematical q...
Quantum field theory from classical statistics
Wetterich, C
2011-01-01
An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external electromagnetic fields, corresponding to a mean field approximation to quantum electrodynamics. All quantum features for the motion of an arbitrary number of electrons and positrons, including the characteristic interference effects for two-fermion states, are described by the classical statistical model. For one-particle states in the non-relativistic approximation we derive the Schr\\"odinger equation for a particle in a potential from the time evolution law for the probability distribution of the Ising-spins. Thus all characteristic quantum features, as interference in a double slit experiment, tunneling or discrete energy levels for stationary states, are derived from a classical statistical ensemble. Concerning the particle-wave-duality of quantum mechanics, the discret...
Quasiparticle excitations in relativistic quantum field theory
Arteaga, Daniel
2008-01-01
We analyze the particle-like excitations arising in relativistic field theories in states different than the vacuum. The basic properties characterizing the quasiparticle propagation are studied using two different complementary methods. First we introduce a frequency-based approach, wherein the quasiparticle properties are deduced from the spectral analysis of the two-point propagators. Second, we put forward a real-time approach, wherein the quantum state corresponding to the quasiparticle excitation is explicitly constructed, and the time-evolution is followed. Both methods lead to the same result: the energy and decay rate of the quasiparticles are determined by the real and imaginary parts of the retarded self-energy respectively. Both approaches are compared, on the one hand, with the standard field-theoretic analysis of particles in the vacuum and, on the other hand, with the mean-field-based techniques in general backgrounds.
Institute of Scientific and Technical Information of China (English)
赵福垚; 宋二祥
2015-01-01
The axiomatic solution process for a one dimensional finite space elastic dynamic boundary value problem can be given by using Laplace transform under the premise of uniform convergence of series,and this process can be a supplement of the work of famous scholars such as Lavrentieff and Hilbert.This solution can be used for the free field analysis in geotechmical engineering,and it can also avoid truncation error in principle.The method in this paper has significantly higher efficiency than that of the finite element method in the calculation for a specific problem,and it can make up for the disadvantage of the existing free field dedicated calculation software which cannot calculate pure elastic bodies to a certain extent.Also,as an analytical algorithm,the method has some significance for the precision analysis of numerical algorithm.%在保证级数的一致收敛的前提下,可以利用Laplace变换对有限一维空间弹性动力学边值问题给出公理化的严格求解过程,此过程能够作为Lavrentieff与Hilbert等著名学者的工作的补充.这一解答能够应用于岩土工程中的自由场计算问题,并且能够从原则上避免截断误差.在针对特定问题的计算中,该方法的效率明显高于有限元,并且在一定程度上弥补了现有的自由场专用计算软件不能计算纯弹性体的缺点.同时,作为解析解算法,该方法对于数值算法的精度分析有一定意义.
Haag's Theorem and Parameterized Quantum Field Theory
Seidewitz, Edwin
2017-01-01
``Haag's theorem is very inconvenient; it means that the interaction picture exists only if there is no interaction''. In traditional quantum field theory (QFT), Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. But the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field, but which must still account for interactions. So, the usual derivation of the scattering matrix in QFT is mathematically ill defined. Nevertheless, perturbative QFT is currently the only practical approach for addressing realistic scattering, and it has been very successful in making empirical predictions. This success can be understood through an alternative derivation of the Dyson series in a covariant formulation of QFT using an invariant, fifth path parameter in addition to the usual four position parameters. The parameterization provides an additional degree of freedom that allows Haag's Theorem to be avoided, permitting the consistent use of a form of interaction picture in deriving the Dyson expansion. The extra symmetry so introduced is then broken by the choice of an interacting vacuum.
On field theory from gravity duals
Hockings, J R
2002-01-01
We review strings and branes in general, and then introduce the AdS/CFT Correspondence. The original work begins with an examination of the geometry for N = 4 on moduli space. We find a neat prescription for the encoding of the gravity solution in terms of the dual gauge theory. We next try to extend this to the N = 2* scenario, but encounter problems due to the gravity solution giving unexpected renormalization. Then we consider the correspondence applied to two field theories off their moduli spaces. We encounter unexpected problems with N = 2* again, but are successful in interpreting the Leigh-Strassler case. Finally, we apply the AdS/CFT correspondence to examine N = 4 super Yang-Mills at finite U(1) sub R charge density, using the supergravity backgrounds around spinning D3 branes. We complete the interpretation of the field theory duals of these backgrounds by interpreting the non-supersymmetric naked singularity class of the solutions. We find that these naked spinning D-brane distributions describe t...
Inhomogeneous field theory inside the arctic circle
Allegra, Nicolas; Dubail, Jérôme; Stéphan, Jean-Marie; Viti, Jacopo
2016-05-01
Motivated by quantum quenches in spin chains, a one-dimensional toy-model of fermionic particles evolving in imaginary-time from a domain-wall initial state is solved. The main interest of this toy-model is that it exhibits the arctic circle phenomenon, namely a spatial phase separation between a critically fluctuating region and a frozen region. Large-scale correlations inside the critical region are expressed in terms of correlators in a (euclidean) two-dimensional massless Dirac field theory. It is observed that this theory is inhomogenous: the metric is position-dependent, so it is in fact a Dirac theory in curved space. The technique used to solve the toy-model is then extended to deal with the transfer matrices of other models: dimers on the honeycomb and square lattice, and the six-vertex model at the free fermion point (Δ =0 ). In all cases, explicit expressions are given for the long-range correlations in the critical region, as well as for the underlying Dirac action. Although the setup developed here is heavily based on fermionic observables, the results can be translated into the language of height configurations and of the gaussian free field, via bosonization. Correlations close to the phase boundary and the generic appearance of Airy processes in all these models are also briefly revisited in the appendix.
Effective Field Theories for the LHC
Moult, Ian
2016-01-01
In this thesis I study applications of effective field theories to understand aspects of QCD jets and their substructure at the Large Hadron Collider. In particular, I introduce an observable, $D_2$, which can be used for distinguishing boosted $W/Z/H$ bosons from the QCD background using information about the radiation pattern within the jet, and perform a precision calculation of this observable. To simplify calculations in the soft collinear effective theory, I also develop a helicity operator basis, which facilitates matching calculations to fixed order computations performed using spinor-helicity techniques, and demonstrate its utility by computing an observable relevant for studying the properties of the newly discovered Higgs boson.
Effective field theory of dissipative fluids
Crossley, Michael; Liu, Hong
2015-01-01
We develop an effective field theory for dissipative fluids which governs the dynamics of gapless modes associated to conserved quantities. The system is put in a curved spacetime and coupled to external sources for charged currents. The invariance of the hydrodynamical action under gauge symmetries and diffeomorphisms suggests a natural set of dynamical variables which provide a mapping between an emergent "fluid spacetime" and the physical spacetime. An essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. Our theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional Z_2 symmetry, to which we refer as the local KMS condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, with a higher derivative version required for the full quantum regim...
Bayesian parameter estimation for effective field theories
Wesolowski, S.; Klco, N.; Furnstahl, R. J.; Phillips, D. R.; Thapaliya, A.
2016-07-01
We present procedures based on Bayesian statistics for estimating, from data, the parameters of effective field theories (EFTs). The extraction of low-energy constants (LECs) is guided by theoretical expectations in a quantifiable way through the specification of Bayesian priors. A prior for natural-sized LECs reduces the possibility of overfitting, and leads to a consistent accounting of different sources of uncertainty. A set of diagnostic tools is developed that analyzes the fit and ensures that the priors do not bias the EFT parameter estimation. The procedures are illustrated using representative model problems, including the extraction of LECs for the nucleon-mass expansion in SU(2) chiral perturbation theory from synthetic lattice data.
Working Group Report: Lattice Field Theory
Energy Technology Data Exchange (ETDEWEB)
Blum, T.; et al.,
2013-10-22
This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.
Bayesian parameter estimation for effective field theories
Wesolowski, S; Furnstahl, R J; Phillips, D R; Thapaliya, A
2015-01-01
We present procedures based on Bayesian statistics for effective field theory (EFT) parameter estimation from data. The extraction of low-energy constants (LECs) is guided by theoretical expectations that supplement such information in a quantifiable way through the specification of Bayesian priors. A prior for natural-sized LECs reduces the possibility of overfitting, and leads to a consistent accounting of different sources of uncertainty. A set of diagnostic tools are developed that analyze the fit and ensure that the priors do not bias the EFT parameter estimation. The procedures are illustrated using representative model problems and the extraction of LECs for the nucleon mass expansion in SU(2) chiral perturbation theory from synthetic lattice data.
Tachyon Condensation in Superstring Field Theory
Berkovits, N; Zwiebach, B; Berkovits, Nathan; Sen, Ashoke; Zwiebach, Barton
2000-01-01
It has been conjectured that at the stationary point of the tachyon potentialfor the D-brane-anti-D-brane pair or for the non-BPS D-brane of superstringtheories, the negative energy density cancels the brane tensions. We study thisconjecture using a Wess-Zumino-Witten-like open superstring field theory freeof contact term divergences and recently shown to give 600f the vacuum energyby condensation of the tachyon field alone. While the action is non-polynomial,the multiscalar tachyon potential to any fixed level involves only a finitenumber of interactions. We compute this potential to level three, obtaining 85of the expected vacuum energy, a result consistent with convergence that canalso be viewed as a successful test of the string field theory. The resultingeffective tachyon potential is bounded below and has two degenerate globalminima. We calculate the energy density of the kink solution interpolatingbetween these minima finding good agreement with the tension of the D-brane ofone lower dimension.
Field theory approaches to new media practices
DEFF Research Database (Denmark)
Willig, Ida; Waltorp, Karen; Hartley, Jannie Møller
2015-01-01
This special issue of MedieKultur specifically addresses new media practices and asks how field theory approaches can help us understand how culture is (prod)used via various digital platforms. In this article introducing the theme of the special issue, we argue that studies of new media practice...... of a reflexive sociology are capable of prompting important questions without necessarily claiming to offer a complete and self-sufficient sociology of media, including new media.......This special issue of MedieKultur specifically addresses new media practices and asks how field theory approaches can help us understand how culture is (prod)used via various digital platforms. In this article introducing the theme of the special issue, we argue that studies of new media practices...... could benefit particularly from Pierre Bourdieu’s research on cultural production. We introduce some of the literature that concerns digital media use and has been significant for field theory’s development in this context. We then present the four thematic articles in this issue and the articles...
String Field Theory from Quantum Gravity
Crane, Louis
2012-01-01
Recent work on neutrino oscillations suggests that the three generations of fermions in the standard model are related by representations of the finite group A(4), the group of symmetries of the tetrahedron. Motivated by this, we explore models which extend the EPRL model for quantum gravity by coupling it to a bosonic quantum field of representations of A(4). This coupling is possible because the representation category of A(4) is a module category over the representation categories used to construct the EPRL model. The vertex operators which interchange vacua in the resulting quantum field theory reproduce the bosons and fermions of the standard model, up to issues of symmetry breaking which we do not resolve. We are led to the hypothesis that physical particles in nature represent vacuum changing operators on a sea of invisible excitations which are only observable in the A(4) representation labels which govern the horizontal symmetry revealed in neutrino oscillations. The quantum field theory of the A(4) ...
Statistical mechanics approach to lattice field theory
Amador, Arturo; Olaussen, Kåre
2016-01-01
The mean spherical approximation (MSA) is a closure relation for pair correlation functions (two-point functions) in statistical physics. It can be applied to a wide range of systems, is computationally fairly inexpensive, and when properly applied and interpreted lead to rather good results. In this paper we promote its applicability to euclidean quantum field theories formulated on a lattice, by demonstrating how it can be used to locate the critical lines of a class of multi-component bosonic models. The MSA has the potential to handle models lacking a positive definite integration measure, which therefore are difficult to investigate by Monte-Carlo simulations.
A matrix model from string field theory
Directory of Open Access Journals (Sweden)
Syoji Zeze
2016-09-01
Full Text Available We demonstrate that a Hermitian matrix model can be derived from level truncated open string field theory with Chan-Paton factors. The Hermitian matrix is coupled with a scalar and U(N vectors which are responsible for the D-brane at the tachyon vacuum. Effective potential for the scalar is evaluated both for finite and large N. Increase of potential height is observed in both cases. The large $N$ matrix integral is identified with a system of N ZZ branes and a ghost FZZT brane.
Eigenstate Thermalization Hypothesis in Conformal Field Theory
Lashkari, Nima; Liu, Hong
2016-01-01
We investigate the eigenstate thermalization hypothesis (ETH) in d+1 dimensional conformal field theories by studying reduced density matrices in energy eigenstates. We show that if local probes of high energy primary eigenstates satisfy ETH, then any finite energy observable with support on a subsystem of finite size satisfies ETH. In two dimensions, we discover that if ETH holds locally, the finite size reduced density matrix of states created by heavy primary operators is well-approximated by a projection to the Virasoro identity block.
A matrix model from string field theory
Zeze, Syoji
2016-09-01
We demonstrate that a Hermitian matrix model can be derived from level truncated open string field theory with Chan-Paton factors. The Hermitian matrix is coupled with a scalar and U(N) vectors which are responsible for the D-brane at the tachyon vacuum. Effective potential for the scalar is evaluated both for finite and large N. Increase of potential height is observed in both cases. The large N matrix integral is identified with a system of N ZZ branes and a ghost FZZT brane.
The Effective Field Theory of nonsingular cosmology
Cai, Yong; Li, Hai-Guang; Qiu, Taotao; Piao, Yun-Song
2016-01-01
In this paper, we explore the nonsingular cosmology within the framework of the Effective Field Theory(EFT) of cosmological perturbations. Due to the recently proved no-go theorem, any nonsingular cosmological models based on the cubic Galileon suffer from pathologies. We show how the EFT could help us clarify the origin of the no-go theorem, and offer us solutions to break the no-go. Particularly, we point out that the gradient instability can be removed by using some spatial derivative operators in EFT. Based on the EFT description, we obtain a realistic healthy nonsingular cosmological model, and show the perturbation spectrum can be consistent with the observations.
Higher Spin Double Field Theory : A Proposal
Bekaert, Xavier
2016-01-01
We construct a double field theory of higher spin gravity. Employing "semi-covariant" differential geometry, we spell a functional in which each term is completely covariant with respect to $\\mathbf{O}(4,4)$ T-duality, doubled diffeomorphisms, $\\mathbf{Spin}(1,3)$ local Lorentz symmetry and, separately, $\\mathbf{HS}(4)$ higher spin gauge symmetry. We also propose a set of BPS-like conditions whose solutions automatically satisfy the full Euler-Lagrange equations. As such a solution, we derive a linear dilaton vacuum. With extra algebraic constraints further imposed, our BPS proposal reduces to the bosonic Vasiliev equations.
QCD unitarity constraints on Reggeon Field Theory
Kovner, Alex; Lublinsky, Michael
2016-01-01
We point out that the unitarity of QCD imposes meaningful constraints on a possible form of the QCD Reggeon Field Theory. We show that neither the BFKL nor JIMWLK nor Braun's Hamiltonian satisfy the said constraints. In a toy, zero transverse dimensional case we construct a model that satisfies the analogous constraint and show that at infinite energy it indeed tends to a "black disk limit" as opposed to the model with triple Pomeron vertex only, routinely used as a toy model in the literature
Supersymmetry in Open Superstring Field Theory
Erler, Theodore
2016-01-01
We realize the 16 unbroken supersymmetries on a BPS D-brane as invariances of the action of the corresponding open superstring field theory. We work in the small Hilbert space approach, where a symmetry of the action translates into a symmetry of the associated cyclic $A_\\infty$ structure. We compute the supersymmetry algebra, being careful to disentangle the components which produce a translation, a gauge transformation, and a symmetry transformation which vanishes on-shell. Via the minimal model theorem, we illustrate how supersymmetry of the action implies supersymmetry of the tree level open string scattering amplitudes.
Scalar-field theory of dark matter
Huang, Kerson; Zhao, Xiaofei
2013-01-01
We develop a theory of dark matter based on a previously proposed picture, in which a complex vacuum scalar field makes the universe a superfluid, with the energy density of the superfluid giving rise to dark energy, and variations from vacuum density giving rise to dark matter. We formulate a nonlinear Klein-Gordon equation to describe the superfluid, treating galaxies as external sources. We study the response of the superfluid to the galaxies, in particular, the emergence of the dark-matter galactic halo, contortions during galaxy collisions, and the creation of vortices due to galactic rotation.
Purely cubic action for string field theory
Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.
1986-01-01
It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.
Ramond Equations of Motion in Superstring Field Theory
Erler, Theodore; Sachs, Ivo
2015-01-01
We extend the recently constructed NS superstring field theories in the small Hilbert space to give classical field equations for all superstring theories, including Ramond sectors. We also comment on the realization of supersymmetry in this framework.
Quantum field theory lectures of Sidney Coleman
Derbes, David; Griffiths, David; Hill, Brian; Sohn, Richard; Ting, Yuan-Sen
2017-01-01
Sidney Coleman was a physicist's physicist. He is largely unknown outside of the theoretical physics community, and known only by reputation to the younger generation. He was an unusually effective teacher, famed for his wit, his insight and his encyclopedic knowledge of the field to which he made many important contributions. There are many first-rate quantum field theory books (the ancient Bjorken and Drell, the more modern Itzykson and Zuber, the now-standard Peskin and Schroder, and the recent Zee), but the immediacy of Prof. Coleman's approach and his ability to present an argument simply without sacrificing rigor makes his book easy to read and ideal for the student. Part of the motivation in producing this book is to pass on the work of this outstanding physicist to later generations, a record of his teaching that he was too busy to leave himself.
Propagation in Polymer Parameterised Field Theory
Varadarajan, Madhavan
2016-01-01
The Hamiltonian constraint operator in Loop Quantum Gravity acts ultralocally. Smolin has argued that this ultralocality seems incompatible with the existence of a quantum dynamics which propagates perturbations between macroscopically seperated regions of quantum geometry. We present evidence to the contrary within an LQG type `polymer' quantization of two dimensional Parameterised Field Theory (PFT). PFT is a generally covariant reformulation of free field propagation on flat spacetime. We show explicitly that while, as in LQG, the Hamiltonian constraint operator in PFT acts ultralocally, states in the joint kernel of the Hamiltonian and diffeomorphism constraints of PFT necessarily describe propagation effects. The particular structure of the finite triangulation Hamiltonian constraint operator plays a crucial role, as does the necessity of imposing (the continuum limit of) its kinematic adjoint as a constraint. Propagation is seen as a property encoded by physical states in the kernel of the constraints r...
Advanced concepts in particle and field theory
Hübsch, Tristan
2015-01-01
Uniting the usually distinct areas of particle physics and quantum field theory, gravity and general relativity, this expansive and comprehensive textbook of fundamental and theoretical physics describes the quest to consolidate the basic building blocks of nature, by journeying through contemporary discoveries in the field, and analysing elementary particles and their interactions. Designed for advanced undergraduates and graduate students and abounding in worked examples and detailed derivations, as well as including historical anecdotes and philosophical and methodological perspectives, this textbook provides students with a unified understanding of all matter at the fundamental level. Topics range from gauge principles, particle decay and scattering cross-sections, the Higgs mechanism and mass generation, to spacetime geometries and supersymmetry. By combining historically separate areas of study and presenting them in a logically consistent manner, students will appreciate the underlying similarities and...
Superluminality, Black Holes and Effective Field Theory
Goon, Garrett
2016-01-01
Under the assumption that a UV theory does not display superluminal behavior, we ask what constraints on superluminality are satisfied in the effective field theory (EFT). We study two examples of effective theories: quantum electrodynamics (QED) coupled to gravity after the electron is integrated out, and the flat-space galileon. The first is realized in nature, the second is more speculative, but they both exhibit apparent superluminality around non-trivial backgrounds. In the QED case, we attempt, and fail, to find backgrounds for which the superluminal signal advance can be made larger than the putative resolving power of the EFT. In contrast, in the galileon case it is easy to find such backgrounds, indicating that if the UV completion of the galileon is (sub)luminal, quantum corrections must become important at distance scales of order the Vainshtein radius of the background configuration, much larger than the naive EFT strong coupling distance scale. Such corrections would be reminiscent of the non-per...
Thermal field theories and shifted boundary conditions
Giusti, Leonardo
2013-01-01
The analytic continuation to an imaginary velocity of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted boundary conditions. The Poincare' invariance underlying a relativistic theory implies a dependence of the free-energy on the compact length L_0 and the shift xi only through the combination beta=L_0(1+xi^2)^(1/2). This in turn implies that the energy and the momentum distributions of the thermal theory are related, a fact which is encoded in a set of Ward identities among the correlators of the energy-momentum tensor. The latter have interesting applications in lattice field theory: they offer novel ways to compute thermodynamic potentials, and a set of identities to renormalize non-perturbatively the energy-momentum tensor. At fixed bare parameters the shifted boundary conditions also provide a simple method to vary the temperature in much smaller steps than with the standard procedur...
Entanglement negativity in quantum field theory.
Calabrese, Pasquale; Cardy, John; Tonni, Erik
2012-09-28
We develop a systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory, using a path integral formalism to construct the partial transpose ρ(A)(T(2) of the reduced density matrix of a subsystem [formula: see text], and introducing a replica approach to obtain its trace norm which gives the logarithmic negativity E=ln//ρ(A)(T(2))//. This is shown to reproduce standard results for a pure state. We then apply this method to conformal field theories, deriving the result E~(c/4)ln[ℓ(1)ℓ(2)/(ℓ(1)+ℓ(2))] for the case of two adjacent intervals of lengths ℓ(1), ℓ(2) in an infinite system, where c is the central charge. For two disjoint intervals it depends only on the harmonic ratio of the four end points and so is manifestly scale invariant. We check our findings against exact numerical results in the harmonic chain.
Theory of sound field in a room
Institute of Scientific and Technical Information of China (English)
MAADah-You
2003-01-01
In the normal-mode theory of Morse, it gives a series of normal modes as the solution of forced vibration in a room. But actually there is always the direct radiation besides the normal modes which represent the reverbrant sound field only. The reason is that the normal modes were assumed only in the source, and naturally normal modes only are obtained in the solution. A theory of double source is proposed, that the sound source is both the source of the direct radiation as if in free space before the boundary surfaces were reached by the direct radiation, and after the first reflection from the boundary surfaces, the source of the reflected wavelets, randomly distributed both in space an in time on the boundary surfaces that build up the normal modes after further reflections. The wave equation is formed accordingly, and the solution of the wave equation, the sound field in a room, contains explicitly both the direct radiation and the reverberant sound formed of normal modes. The approximate mean square sound pressure is found to be the dircet sound determined by the sound power of the source,and reverberant sound determined by the sound power reduced by a factor of π/2, different slightly from the result obtained from energy consideration, if the source is pure tone. There is essentially no difference for a source of band noise.
The Superspinorial Field Theory in Riemannian Coordinates
Derbenev, Yaroslav
2016-01-01
The Superspinorial Dual-covariant Field Theory (SSFT) developed in papers [1, 2] is treated in terms of Riemannian coordinates (RC) [7, 8] in space of the N dimensions unified manifold (UM). Metric tensor of UM (grand metric, GM) is built on the split metric matrices (SM) [1] which are a proportion of the Cartan's affinors (an extended analog of Dirac's matrices) of his Theory of Spinors [3] as explicated in [2]. Transition to RC based on consideration of geodesics is described. A principal property of an orthogonal RC frame (ORC) utilized in the present paper is constancy of the rotation matrix A of the Riemannian space of UM, while transformation matrix B of the dual superspinorial state vector field (DSV) varies together with Cartan's affinors according to the dynamical law of SSFT derived in [2]. The spinorial genesis of notion of the orthogonality as aspect of irreducible SSFT is pointed out in the present paper. The main outcome of resorting to an orthogonal RC frame (ORC) is explication of the conforma...
Mean field theory, topological field theory, and multi-matrix models
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, R. (Princeton Univ., NJ (USA). Joseph Henry Labs.); Witten, E. (Institute for Advanced Study, Princeton, NJ (USA). School of Natural Sciences)
1990-10-08
We show that the genus zero correlation functions of an arbitrary topological field theory coupled to two-dimensional topological gravity are determined by an appropriate Landau-Ginzburg potential. We determine the potentials that arise for topological sigma models with CP{sup 1} or a Calabi-Yau manifold for target space. We present substantial evidence that the multi-matrix models that have been studied recently are equivalent to certain topological field theories coupled to topological gravity. We also describe a topological version of the general 'string equation'. (orig.).
Mean field theory, topological field theory, and multi-matrix models
Dijkgraaf, Robbert; Witten, Edward
1990-10-01
We show that the genus zero correlation functions of an arbitrary topological field theory coupled to two-dimensional topological gravity are determined by an appropriate Landau-Ginzburg potential. We determine the potentials that arise for topological sigma models with CP 1 or a Calabi-Yau manifold for target space. We present substantial evidence that the multi-matrix models that have been studied recently are equivalent to certain topological field theories coupled to topological gravity. We also describe a topological version of the general "string equation".
The 2D effective field theory of interfaces derived from 3D field theory
Provero, P; Provero, Paolo; Vinti, Stefano
1995-01-01
The one--loop determinant computed around the kink solution in the 3D \\phi^4 theory, in cylindrical geometry, allows one to obtain the partition function of the interface separating coexisting phases. The quantum fluctuations of the interface around its equilibrium position are described by a c=1 two--dimensional conformal field theory, namely a 2D free massless scalar field living on the interface. In this way the capillary wave model conjecture for the interface free energy in its gaussian approximation is proved.
Multivector field formulation of Hamiltonian field theories: equations and symmetries
Energy Technology Data Exchange (ETDEWEB)
Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N. [Departamento de Matematica Aplicada y Telematica, Edificio C-3, Campus Norte UPC, Barcelona (Spain)
1999-12-03
We state the intrinsic form of the Hamiltonian equations of first-order classical field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analysed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between Cartan-Noether symmetries and general symmetries of the system is discussed. Noether's theorem is also stated in this context, both the 'classical' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed. (author)
Towards a quantum field theory of primitive string fields
Ruehl, Werner
2010-01-01
We denote generating functions of massless even higher spin fields "primitive string fields" (PSF's). In an introduction we present the necessary definitions and derive propagators and currents of these PDF's on flat space. Their off-shell cubic interaction can be derived after all off-shell cubic interactions of triplets of higher spin fields have become known [2],[3]. Then we discuss four-point functions of any quartet of PSF's. In subsequent sections we exploit the fact that higher spin field theories in $AdS_{d+1}$ are determined by AdS/CFT correspondence from universality classes of critical systems in $d$ dimensional flat spaces. The O(N) invariant sectors of the O(N) vector models for $1\\leq N \\leq \\infty$ play for us the role of "standard models", for varying $N$, they contain e.g. the Ising model for N=1 and the spherical model for $N=\\infty$. A formula for the masses squared that break gauge symmetry for these O(N) classes is presented for d = 3. For the PSF on $AdS$ space it is shown that it can be...
The universality question for noncommutative quantum field theory
Schlesinger, K G
2006-01-01
Present day physics rests on two main pillars: General relativity and quantum field theory. We discuss the deep and at the same time problematic interplay between these two theories. Based on an argument by Doplicher, Fredenhagen, and Roberts, we propose a possible universality property for noncommutative quantum field theory in the sense that any theory of quantum gravity should involve quantum field theories on noncommutative space-times as a special limit. We propose a mathematical framework to investigate such a universality property and start the discussion of its mathematical properties. The question of its connection to string theory could be a starting point for a new perspective on string theory.
Effective field theory analysis of Higgs naturalness
Energy Technology Data Exchange (ETDEWEB)
Bar-Shalom, Shaouly [Technion-Israel Inst. of Tech., Haifa (Israel); Soni, Amarjit [Brookhaven National Lab. (BNL), Upton, NY (United States); Wudka, Jose [Univ. of California, Riverside, CA (United States)
2015-07-20
Assuming the presence of physics beyond the Standard Model ( SM) with a characteristic scale M ~ O (10) TeV, we investigate the naturalness of the Higgs sector at scales below M using an effective field theory (EFT) approach. We obtain the leading 1 -loop EFT contributions to the Higgs mass with a Wilsonian-like hard cutoff, and determine t he constraints on the corresponding operator coefficients for these effects to alleviate the little hierarchy problem up to the scale of the effective action Λ < M , a condition we denote by “EFT-naturalness”. We also determine the types of physics that can lead to EFT-naturalness and show that these types of new physics are best probed in vector-boson and multiple-Higgs production. The current experimental constraints on these coefficients are also discussed.
Theory of electrolyte crystallization in magnetic field
DEFF Research Database (Denmark)
Madsen, Hans Erik Lundager
2007-01-01
Crystallization from aqueous solution of a sparingly soluble electrolyte is accelerated by magnetic field if the crystalizing phase is a diamagnetic salt of a weak acid, and crystallization is from neutral or acid solution in ordinary (not heavy) water. Since the effect of Lorentz force...... is negligible, if not absent, the key property is likely to be the spin of protons which, by virtue of their half-integral spin, are fermions. An effect on crystal growth kinetics has been demonstrated, and the apparent effect on nucleation concerns the growth rate of nuclei. We are thus dealing with surface...... phenomena. The basis of the theory is a crystal model of a sparingly soluble salt with NaCl structure, where the ions are divalent, and the anion is a base. It is assumed that almost all the anions in the surface layer are protonized, and that an approaching metal ion pushes the proton away...
Quantifying truncation errors in effective field theory
Furnstahl, R J; Phillips, D R; Wesolowski, S
2015-01-01
Bayesian procedures designed to quantify truncation errors in perturbative calculations of quantum chromodynamics observables are adapted to expansions in effective field theory (EFT). In the Bayesian approach, such truncation errors are derived from degree-of-belief (DOB) intervals for EFT predictions. Computation of these intervals requires specification of prior probability distributions ("priors") for the expansion coefficients. By encoding expectations about the naturalness of these coefficients, this framework provides a statistical interpretation of the standard EFT procedure where truncation errors are estimated using the order-by-order convergence of the expansion. It also permits exploration of the ways in which such error bars are, and are not, sensitive to assumptions about EFT-coefficient naturalness. We first demonstrate the calculation of Bayesian probability distributions for the EFT truncation error in some representative examples, and then focus on the application of chiral EFT to neutron-pr...
Effective Field Theory for Rydberg Polaritons
Gullans, M J; Thompson, J D; Liang, Q -Y; Vuletic, V; Lukin, M D; Gorshkov, A V
2016-01-01
We study non-perturbative effects in N-body scattering of Rydberg polaritons using effective field theory (EFT). We develop an EFT in one dimension and show how a suitably long medium can be used to prepare shallow N-body bound states. We then derive the effective N-body interaction potential for Rydberg polaritons and the associated N-body contact force that arises in the EFT. We use the contact force to find the leading order corrections to the binding energy of the N-body bound states and determine the photon number at which the EFT description breaks down. We find good agreement throughout between the predictions of EFT and numerical simulations of the exact two and three photon wavefunction transmission.
Superconformal field theory and Jack superpolynomials
Desrosiers, Patrick; Mathieu, Pierre
2012-01-01
We uncover a deep connection between the N=1 superconformal field theory in 2D and eigenfunctions of the supersymmetric Sutherland model known as Jack superpolynomials (sJacks). Specifically, the singular vector at level rs/2 of the Kac module labeled by the two integers r and s can be obtained explicitly as a sum of sJacks whose indexing diagrams are contained in a rectangle with r columns and s rows. As a second compelling evidence for the distinguished status of the sJack-basis in SCFT, we find that the degenerate Whittaker vectors (Gaiotto states), in both the Neveu-Schwarz and Ramond sectors, can be expressed rather simply in terms of sJacks. As a consequence, we are able to reformulate the supersymmetric version of the (degenerate) AGT conjecture in terms of the combinatorics of sJacks.
Topological Field Theory and Matrix Product States
Kapustin, Anton; You, Minyoung
2016-01-01
It is believed that most (perhaps all) gapped phases of matter can be described at long distances by Topological Quantum Field Theory (TQFT). On the other hand, it has been rigorously established that in 1+1d ground states of gapped Hamiltonians can be approximated by Matrix Product States (MPS). We show that the state-sum construction of 2d TQFT naturally leads to MPS in their standard form. In the case of systems with a global symmetry G, this leads to a classification of gapped phases in 1+1d in terms of Morita-equivalence classes of G-equivariant algebras. Non-uniqueness of the MPS representation is traced to the freedom of choosing an algebra in a particular Morita class. In the case of Short-Range Entangled phases, we recover the group cohomology classification of SPT phases.
Matrix product states for gauge field theories.
Buyens, Boye; Haegeman, Jutho; Van Acoleyen, Karel; Verschelde, Henri; Verstraete, Frank
2014-08-29
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study (1+1)-dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground-state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum nonequilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field.
Hadronic Transport Coefficients from Effective Field Theories
Torres-Rincon, Juan M
2012-01-01
This dissertation focuses on the calculation of transport coefficients in the matter created in a relativistic heavy-ion collision after the chemical freeze-out. This matter can be well approximated by a pion gas out of equilibrium. We describe the theoretical framework to obtain the shear and bulk viscosities, the thermal and electrical conductivities and the flavor diffusion coefficients of a meson gas at low temperatures. To describe the interactions of the degrees of freedom, we use effective field theories with chiral and heavy quark symmetries. We introduce the unitarization methods in order to obtain a scattering amplitude that satisfies the unitarity condition exactly. We perform the calculation of the transport properties of the low temperature phase of quantum chromodynamics -the hadronic medium- that can be used in the hydrodynamic simulations of a relativistic heavy-ion collision and its subsequent evolution. We show that the shear viscosity over entropy density exhibits a minimum in a phase trans...
Nonequilibrium fermion production in quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Pruschke, Jens
2010-06-16
The creation of matter in the early universe or in relativistic heavy-ion collisions is inevitable connected to nonequilibrium physics. One of the key challenges is the explanation of the corresponding thermalization process following nonequilibrium instabilities. The role of fermionic quantum fields in such scenarios is discussed in the literature by using approximations of field theories which neglect important quantum corrections. This thesis goes beyond such approximations. A quantum field theory where scalar bosons interact with Dirac fermions via a Yukawa coupling is analyzed in the 2PI effective action formalism. The chosen approximation allows for a correct description of the dynamics including nonequilibrium instabilities. In particular, fermion-boson loop corrections allow to study the interaction of fermions with large boson fluctuations. The applied initial conditions generate nonequilibrium instabilities like parametric resonance or spinodal instabilities. The equations of motion for correlation functions are solved numerically and major characteristics of the fermion dynamics are described by analytical solutions. New mechanisms for the production of fermions are found. Simulations in the case of spinodal instability show that unstable boson fluctuations induce exponentially growing fermion modes with approximately the same growth rate. If the unstable regime lasts long enough a thermalization of the infrared part of the fermion occupation number occurs on time scales much shorter than the time scale on which bosonic quantum fields thermalize. Fermions acquire an excess of occupation in the ultraviolet regime compared to a Fermi-Dirac statistic characterized by a power-law with exponent two. The fermion production mechanism via parametric resonance is found to be most efficient after the instability ends. Quantum corrections then provide a very efficient particle creation mechanism which is interpreted as an amplification of decay processes. The ratio
Multidimensional wave field signal theory: Mathematical foundations
Directory of Open Access Journals (Sweden)
Natalie Baddour
2011-06-01
Full Text Available Many important physical phenomena are described by wave or diffusion-wave type equations. Since these equations are linear, it would be useful to be able to use tools from the theory of linear signals and systems in solving related forward or inverse problems. In particular, the transform domain signal description from linear system theory has shown concrete promise for the solution of problems that are governed by a multidimensional wave field. The aim is to develop a unified framework for the description of wavefields via multidimensional signals. However, certain preliminary mathematical results are crucial for the development of this framework. This first paper on this topic thus introduces the mathematical foundations and proves some important mathematical results. The foundation of the framework starts with the inhomogeneous Helmholtz or pseudo-Helmholtz equation, which is the mathematical basis of a large class of wavefields. Application of the appropriate multi-dimensional Fourier transform leads to a transfer function description. To return to the physical spatial domain, certain mathematical results are necessary and these are presented and proved here as six fundamental theorems. These theorems are crucial for the evaluation of a certain class of improper integrals which arise in the evaluation of inverse multi-dimensional Fourier and Hankel transforms, upon which the framework is based. Subsequently, applications of these theorems are demonstrated, in particular for the derivation of Green's functions in different coordinate systems.
A Renormalizable 4-Dimensional Tensor Field Theory
Geloun, Joseph Ben
2011-01-01
We prove that an integrated version of the Gurau colored tensor model supplemented with the usual Bosonic propagator on $U(1)^4$ is renormalizable to all orders in perturbation theory. The model is of the type expected for quantization of space-time in 4D Euclidean gravity and is the first example of a renormalizable model of this kind. Its vertex and propagator are four-stranded like in 4D group field theories, but without gauge averaging on the strands. Surprisingly perhaps, the model is of the $\\phi^6$ rather than of the $\\phi^4$ type, since two different $\\phi^6$-type interactions are log-divergent, i.e. marginal in the renormalization group sense. The renormalization proof relies on a multiscale analysis. It identifies all divergent graphs through a power counting theorem. These divergent graphs have internal and external structure of a particular kind called melonic. Melonic graphs dominate the 1/N expansion of colored tensor models and generalize the planar ribbon graphs of matrix models. A new localit...
Reflections on Topological Quantum Field Theory
Picken, R F
1997-01-01
(Talk presented at the XVth Workshop on Geometric Methods in Physics, Quantizations, Deformations and Coherent States, in Bialowieza, Poland, July 1-7, 1996.) The aim of this article is to introduce some basic notions of Topological Quantum Field Theory (TQFT) and to consider a modification of TQFT, applicable to embedded manifolds. After an introduction based around a simple example (Section 1) the notion of a d-dimensional TQFT is defined in category-theoretical terms, as a certain type of functor from a category of d-dimensional cobordisms to the category of vector spaces (Section 2). A construction due to Turaev, an operator-valued invariant of tangles, is discussed in Section 3. It bears a strong resemblance to 1-dimensional TQFTs, but carries much richer structure due to the fact that the 1-dimensional manifolds involved are embedded in a 3-dimensional space. This leads us, in Section 4, to propose a class of TQFT-like theories, appropriate to embedded, rather than pure, manifolds.
Lee, Dai Gil; Suh, Nam Pyo
2005-11-01
The idea that materials can be designed to satisfy specific performance requirements is relatively new. With high-performance composites, however, the entire process of designing and fabricating a part can be worked out before manufacturing. The purpose of this book is to present an integrated approach to the design and manufacturing of products from advanced composites. It shows how the basic behavior of composites and their constitutive relationships can be used during the design stage, which minimizes the complexity of manufacturing composite parts and reduces the repetitive "design-build-test" cycle. Designing it right the first time is going to determine the competitiveness of a company, the reliability of the part, the robustness of fabrication processes, and ultimately, the cost and development time of composite parts. Most of all, it should expand the use of advanced composite parts in fields that use composites only to a limited extent at this time. To achieve these goals, this book presents the design and fabrication of novel composite parts made for machine tools and other applications like robots and automobiles. This book is suitable as a textbook for graduate courses in the design and fabrication of composites. It will also be of interest to practicing engineers learning about composites and axiomatic design. A CD-ROM is included in every copy of the book, containing Axiomatic CLPT software. This program, developed by the authors, will assist readers in calculating material properties from the microstructure of the composite. This book is part of the Oxford Series on Advanced Manufacturing.
Propagation in polymer parameterised field theory
Varadarajan, Madhavan
2017-01-01
The Hamiltonian constraint operator in loop quantum gravity acts ultralocally. Smolin has argued that this ultralocality seems incompatible with the existence of a quantum dynamics which propagates perturbations between macroscopically seperated regions of quantum geometry. We present evidence to the contrary within an LQG type ‘polymer’ quantization of two dimensional parameterised field theory (PFT). PFT is a generally covariant reformulation of free field propagation on flat spacetime. We show explicitly that while, as in LQG, the Hamiltonian constraint operator in PFT acts ultralocally, states in the joint kernel of the Hamiltonian and diffeomorphism constraints of PFT necessarily describe propagation effects. The particular structure of the finite triangulation Hamiltonian constraint operator plays a crucial role, as does the necessity of imposing (the continuum limit of) its kinematic adjoint as a constraint. Propagation is seen as a property encoded by physical states in the kernel of the constraints rather than that of repeated actions of the finite triangulation Hamiltonian constraint on kinematic states. The analysis yields robust structural lessons for putative constructions of the Hamiltonian constraint in LQG for which ultralocal action co-exists with a description of propagation effects by physical states.
Topological field theory of dynamical systems.
Ovchinnikov, Igor V
2012-09-01
Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the "edge of chaos." Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.
Topological and differential geometrical gauge field theory
Saaty, Joseph
Recent Quantum Field Theory books have defined the topological charge (Q) in terms of the winding number (N). Contrary to this definition, my proof defines Q in terms of the quantum number (n). Defining Q in terms of n, instead of in terms of N, enables me to determine a precise value for Q. The solutions of all kinds of homotopy classification are referred to as instanton solutions, hence the terms homotopy classification and instanton solution will be used interchangeably. My proof replaces the use of these techniques with the use of the Dirac quantization condition, the covariant Dirac's equation, and the covariant Maxwell's equation. Unlike the earlier approaches, my proof accounts for the concept of the spin quantum number and the concept of time. Using the three methods noted above, my proof yields results not obtained by earlier methods. I have dealt similarly with the Pontryagin Index. I have used the Covariant Electrodynamics, in place of homotopy classification techniques, to create for the Pontryagin Index a proof that is alternative to the one cited in recent literature. The homotopy classification techniques gives an expression that excludes the fact that particles have spin quantum number. Therefore, the homotopy classification techniques does not really describe what the topological charge is in reality. I did derive an expression which does include the spin quantum numbers for particles and this has not been done before. Therefore, this will give a better idea for theoretical physicists about the nature of the topological charge. Contribution to knowledge includes creativity. I created an alternative method to the instanton solution for deriving an expression for the topological charge and this method led to new discoveries as a contribution to knowledge in which I found that topological charge for fermions cannot be quantized (to be quantized means to take discrete values only in integer steps), whereas the instanton solution cannot distinguish
Symmetries and defects in three-dimensional topological field theory
Fuchs, Jurgen
2015-01-01
Boundary conditions and defects of any codimension are natural parts of any quantum field theory. Surface defects in three-dimensional topological field theories of Turaev-Reshetikhin type have applications to two-dimensional conformal field theories, in solid state physics and in quantum computing. We explain an obstruction to the existence of surface defects that takes values in a Witt group. We then turn to surface defects in Dijkgraaf-Witten theories and their construction in terms of relative bundles; this allows one to exhibit Brauer-Picard groups as symmetry groups of three-dimensional topological field theories.
An axiomatic approach to intrinsic dimension of a dataset
Pestov, Vladimir
2007-01-01
We perform a deeper analysis of an axiomatic approach to the concept of intrinsic dimension of a dataset proposed by us in the IJCNN'07 paper (arXiv:cs/0703125). The main features of our approach are that a high intrinsic dimension of a dataset reflects the presence of the curse of dimensionality (in a certain mathematically precise sense), and that dimension of a discrete i.i.d. sample of a low-dimensional manifold is, with high probability, close to that of the manifold. At the same time, the intrinsic dimension of a sample is easily corrupted by moderate high-dimensional noise (of the same amplitude as the size of the manifold) and suffers from prohibitevely high computational complexity (computing it is an $NP$-complete problem). We outline a possible way to overcome these difficulties.
Applying causality principles to the axiomatization of probabilistic cellular automata
Arrighi, Pablo; Nesme, Vincent; Thierry, Eric
2011-01-01
Cellular automata (CA) consist of an array of identical cells, each of which may take one of a finite number of possible states. The entire array evolves in discrete time steps by iterating a global evolution G. Further, this global evolution G is required to be shift-invariant (it acts the same everywhere) and causal (information cannot be transmitted faster than some fixed number of cells per time step). At least in the classical, reversible and quantum cases, these two top-down axiomatic conditions are sufficient to entail more bottom-up, operational descriptions of G. We investigate whether the same is true in the probabilistic case. Keywords: Characterization, noise, Markov process, stochastic Einstein locality, screening-off, common cause principle, non-signalling, Multi-party non-local box.
Fractional Quantum Field Theory: From Lattice to Continuum
Directory of Open Access Journals (Sweden)
Vasily E. Tarasov
2014-01-01
Full Text Available An approach to formulate fractional field theories on unbounded lattice space-time is suggested. A fractional-order analog of the lattice quantum field theories is considered. Lattice analogs of the fractional-order 4-dimensional differential operators are proposed. We prove that continuum limit of the suggested lattice field theory gives a fractional field theory for the continuum 4-dimensional space-time. The fractional field equations, which are derived from equations for lattice space-time with long-range properties of power-law type, contain the Riesz type derivatives on noninteger orders with respect to space-time coordinates.
Generalized BRST symmetry for arbitrary spin conformal field theory
Energy Technology Data Exchange (ETDEWEB)
Upadhyay, Sudhaker, E-mail: sudhakerupadhyay@gmail.com [Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016 (India); Mandal, Bhabani Prasad, E-mail: bhabani.mandal@gmail.com [Department of Physics, Banaras Hindu University, Varanasi 221005 (India)
2015-05-11
We develop the finite field-dependent BRST (FFBRST) transformation for arbitrary spin-s conformal field theories. We discuss the novel features of the FFBRST transformation in these systems. To illustrate the results we consider the spin-1 and spin-2 conformal field theories in two examples. Within the formalism we found that FFBRST transformation connects the generating functionals of spin-1 and spin-2 conformal field theories in linear and non-linear gauges. Further, the conformal field theories in the framework of FFBRST transformation are also analyzed in Batalin–Vilkovisky (BV) formulation to establish the results.
Applying axiomatic design to a medication distribution system
Raguini, Pepito B.
As the need to minimize medication errors drives many medical facilities to come up with robust solutions to the most common error that affects patient's safety, these hospitals would be wise to put a concerted effort into finding methodologies that can facilitate an optimized medical distribution system. If the hospitals' upper management is looking for an optimization method that is an ideal fit, it is just as important that the right tool be selected for the application at hand. In the present work, we propose the application of Axiomatic Design (AD), which is a process that focuses on the generation and selection of functional requirements to meet the customer needs for product and/or process design. The appeal of the axiomatic approach is to provide both a formal design process and a set of technical coefficients for meeting the customer's needs. Thus, AD offers a strategy for the effective integration of people, design methods, design tools and design data. Therefore, we propose the AD methodology to medical applications with the main objective of allowing nurses the opportunity to provide cost effective delivery of medications to inpatients, thereby improving quality patient care. The AD methodology will be implemented through the use of focused stores, where medications can be readily stored and can be conveniently located near patients, as well as a mobile apparatus that can also store medications and is commonly used by hospitals, the medication cart. Moreover, a robust methodology called the focused store methodology will be introduced and developed for both the uncapacitated and capacitated case studies, which will set up an appropriate AD framework and design problem for a medication distribution case study.
Quantum field theories on categories fibered in groupoids
Benini, Marco
2016-01-01
We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geometric structures such as bundles, connections and spin structures. Using right Kan extensions, we can assign to any such theory an ordinary quantum field theory defined on the category of spacetimes and we shall clarify under which conditions it satisfies the axioms of locally covariant quantum field theory. The same constructions can be performed in a homotopy theoretic framework by using homotopy right Kan extensions, which allows us to obtain first examples of homotopical quantum field theories resembling some aspects of gauge theories.
Analytic solutions for marginal deformations in open superstring field theory
Energy Technology Data Exchange (ETDEWEB)
Okawa, Y.
2007-04-15
We extend the calculable analytic approach to marginal deformations recently developed in open bosonic string field theory to open superstring field theory formulated by Berkovits. We construct analytic solutions to all orders in the deformation parameter when operator products made of the marginal operator and the associated superconformal primary field are regular. (orig.)
Nonequilibrium dynamical mean-field theory
Energy Technology Data Exchange (ETDEWEB)
Eckstein, Martin
2009-12-21
The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)
Path Integral Techniques in Conformal Field Theory
Van Tonder, A J
2004-01-01
We present the theory of a two-dimensional conformal scalar field using path integral techniques. We derive the conformal anomaly using an adaptation of the method of Fujikawa, and compare the result with a derivation based on a Pauli-Villars measure, where the anomaly is shifted from the path integral measure to the energy-momentum trace. In the path integral approach the energy-momentum is a true coordinate-invariant tensor quantity, and we explain how it is related to the corresponding non-tensor object arising in the operator approach, obtaining an intuitive explanation within the context of the path integral approach for the anomalous transformation law and anomalous Ward identities of the latter. After carefully calculating nontrivial contact terms arising in certain energy-momentum products, we use these to provide a simple consistency check confirming the change of variables formula for the path integral and to review the relationship between the conformal anomaly and the energy-momentum two-point fun...
Higgs Effective Field Theories - Systematics and Applications
Krause, Claudius
2016-01-01
We discuss effective field theories (EFTs) for the Higgs particle, which is not necessarily the Higgs of the Standard Model. We distinguish two different consistent expansions: EFTs that describe decoupling new-physics effects and EFTs that describe non-decoupling new-physics effects. We briefly discuss the first case, the SM-EFT. The focus of this thesis is on the non-decoupling EFTs. We argue that the loop expansion is the consistent expansion in the second case. We introduce the concept of chiral dimensions, equivalent to the loop expansion. Using the chiral dimensions, we expand the electroweak chiral Lagrangian up to next-to-leading order, $\\mathcal{O}(f^{2}/\\Lambda^{2})=\\mathcal{O}(1/16\\pi^{2})$. We then compare the decoupling and the non-decoupling EFT. We also consider scenarios in which the new-physics sector is non-decoupling at a scale $f$, far above the electroweak-scale $v$. We discuss the relevance of the resulting double expansion in $\\xi=v^{2}/f^{2}$ and $f^{2}/\\Lambda^{2}$ for the data analys...
Protected gates for topological quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Beverland, Michael E.; Pastawski, Fernando; Preskill, John [Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125 (United States); Buerschaper, Oliver [Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin (Germany); Koenig, Robert [Institute for Advanced Study and Zentrum Mathematik, Technische Universität München, 85748 Garching (Germany); Sijher, Sumit [Institute for Quantum Computing and Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)
2016-02-15
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.
Twist Field as Three String Interaction Vertex in Light Cone String Field Theory
Kishimoto, Isao; Moriyama, Sanefumi; Teraguchi, Shunsuke
2006-01-01
It has been suggested that matrix string theory and light-cone string field theory are closely related. In this paper, we investigate the relation between the twist field, which represents string interactions in matrix string theory, and the three-string interaction vertex in light-cone string field theory carefully. We find that the three-string interaction vertex can reproduce some of the most important OPEs satisfied by the twist field.
Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models
2015-01-01
We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory captures not only dynamical transitions but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bos...
Twisted Backgrounds, PP-Waves and Nonlocal Field Theories
Alishahiha, M; Alishahiha, Mohsen; Ganor, Ori J.
2003-01-01
We study partially supersymmetric plane-wave like deformations of string theories and M-theory on brane backgrounds. These deformations are dual to nonlocal field theories. We calculate various expectation values of configurations of closed as well as open Wilson loops and Wilson surfaces in those theories. We also discuss the manifestation of the nonlocality structure in the supergravity backgrounds. A plane-wave like deformation of little string theory has also been studied.
Effective field theory for halo nuclei
Energy Technology Data Exchange (ETDEWEB)
Hagen, Philipp Robert
2014-02-19
We investigate properties of two- and three-body halo systems using effective field theory. If the two-particle scattering length a in such a system is large compared to the typical range of the interaction R, low-energy observables in the strong and the electromagnetic sector can be calculated in halo EFT in a controlled expansion in R/ vertical stroke a vertical stroke. Here we focus on universal properties and stay at leading order in the expansion. Motivated by the existence of the P-wave halo nucleus {sup 6}He, we first set up an EFT framework for a general three-body system with resonant two-particle P-wave interactions. Based on a Lagrangian description, we identify the area in the effective range parameter space where the two-particle sector of our model is renormalizable. However, we argue that for such parameters, there are two two-body bound states: a physical one and an additional deeper-bound and non-normalizable state that limits the range of applicability of our theory. With regard to the three-body sector, we then classify all angular-momentum and parity channels that display asymptotic discrete scale invariance and thus require renormalization via a cut-off dependent three-body force. In the unitary limit an Efimov effect occurs. However, this effect is purely mathematical, since, due to causality bounds, the unitary limit for P-wave interactions can not be realized in nature. Away from the unitary limit, the three-body binding energy spectrum displays an approximate Efimov effect but lies below the unphysical, deep two-body bound state and is thus unphysical. Finally, we discuss possible modifications in our halo EFT approach with P-wave interactions that might provide a suitable way to describe physical three-body bound states. We then set up a halo EFT formalism for two-neutron halo nuclei with resonant two-particle S-wave interactions. Introducing external currents via minimal coupling, we calculate observables and universal correlations for
Reggeon field theory for large Pomeron loops
Energy Technology Data Exchange (ETDEWEB)
Altinoluk, Tolga [Departamento de Física de Partículas and IGFAE, Universidade de Santiago de Compostela,E-15782 Santiago de Compostela, Galicia (Spain); Kovner, Alex [Physics Department, University of Connecticut,2152 Hillside road, Storrs, CT 06269 (United States); Levin, Eugene [Departamento de Física, Universidad Técnica Federico Santa María, and Centro Científico-Tecnolgico de Valparaíso,Avda. España 1680, Casilla 110-V, Valparaíso (Chile); Department of Particle Physics, Tel Aviv University,Tel Aviv 69978 (Israel); Lublinsky, Michael [Physics Department, Ben-Gurion University of the Negev,Beer Sheva 84105 (Israel)
2014-04-10
We analyze the range of applicability of the high energy Reggeon Field Theory H{sub RFT} derived in http://dx.doi.org/10.1088/1126-6708/2009/03/109. We show that this theory is valid as long as at any intermediate value of rapidity η throughout the evolution at least one of the colliding objects is dilute. Importantly, at some values of η the dilute object could be the projectile, while at others it could be the target, so that H{sub RFT} does not reduce to either H{sub JIMWLK} or H{sub KLWMIJ}. When both objects are dense, corrections to the evolution not accounted for in http://dx.doi.org/10.1088/1126-6708/2009/03/109 become important. The same limitation applies to other approaches to high energy evolution available today, such as for example (http://dx.doi.org/10.1103/PhysRevD.78.054019; http://dx.doi.org/10.1103/PhysRevD.78.054020 and http://dx.doi.org/10.1016/S0370-2693(00)00571-2; http://dx.doi.org/10.1140/epjc/s2003-01565-9; http://dx.doi.org/10.1016/j.physletb.2005.10.054). We also show that, in its regime of applicability H{sub RFT} can be simplified. We derive the simpler version of H{sub RFT} and in the large N{sub c} limit rewrite it in terms of the Reggeon creation and annihilation operators. The resulting H{sub RFT} is explicitly self dual and provides the generalization of the Pomeron calculus developed in (http://dx.doi.org/10.1016/S0370-2693(00)00571-2; http://dx.doi.org/10.1140/epjc/s2003-01565-9; http://dx.doi.org/10.1016/j.physletb.2005.10.054) by including higher Reggeons in the evolution. It is applicable for description of ‘large’ Pomeron loops, namely Reggeon graphs where all the splittings occur close in rapidity to one dilute object (projectile), while all the merging close to the other one (target). Additionally we derive, in the same regime expressions for single and double inclusive gluon production (where the gluons are not separated by a large rapidity interval) in terms of the Reggeon degrees of freedom.
Accretion Disks and Dynamos: Toward a Unified Mean Field Theory
Blackman, Eric G
2012-01-01
Conversion of gravitational energy into radiation near stars and compact objects in accretion disks the origin of large scale magnetic fields in astrophysical rotators have long been distinct topics of active research in astrophysics. In semi-analytic work on both problems it has been useful to presume large scale symmetries, which necessarily results in mean field theories; magnetohydrodynamic turbulence makes the underlying systems locally asymmetric and highly nonlinear. Synergy between theory and simulations should aim for the development of practical, semi-analytic mean field models that capture the essential physics and can be used for observational modeling. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory have exemplified such distinct pursuits. Both are presently incomplete, but 21st century MFD theory has nonlinear predictive power compared to 20th century MFD. in contrast, alpha-viscosity accretion theory is still in a 20th century state. In fact, insights from MFD theory ar...
N=2 Quantum Field Theories and Their BPS Quivers
Alim, Murad; Cordova, Clay; Espahbodi, Sam; Rastogi, Ashwin; Vafa, Cumrun
2011-01-01
We explore the relationship between four-dimensional N=2 quantum field theories and their associated BPS quivers. For a wide class of theories including super-Yang-Mills theories, Argyres-Douglas models, and theories defined by M5-branes on punctured Riemann surfaces, there exists a quiver which implicitly characterizes the field theory. We study various aspects of this correspondence including the quiver interpretation of flavor symmetries, gauging, decoupling limits, and field theory dualities. In general a given quiver describes only a patch of the moduli space of the field theory, and a key role is played by quantum mechanical dualities, encoded by quiver mutations, which relate distinct quivers valid in different patches. Analyzing the consistency conditions imposed on the spectrum by these dualities results in a powerful and novel mutation method for determining the BPS states. We apply our method to determine the BPS spectrum in a wide class of examples, including the strong coupling spectrum of super-...
A novel string field theory solving string theory by liberating left and right movers
Energy Technology Data Exchange (ETDEWEB)
Nielsen, Holger B. [Niels Bohr Institute, University of Copenhagen,17 Belgdamsvej, DK 2100 (Denmark); Ninomiya, Masao [Okayama Institute for Quantum Physics,Kyoyama 1-9-1 Kita-ku, Okayama-city 700-0015 (Japan)
2014-05-08
We put forward ideas to a novel string field theory based on making some “objects” that essentially describe “liberated” left- and right- mover fields X{sub L}{sup μ}(τ+σ) and X{sub R}{sup μ}(τ−σ) on the string. Our novel string field theory is completely definitely different from any other string theory in as far as a “null set” of information in the string field theory Fock space has been removed relatively, to the usual string field theories. So our theory is definitely new. The main progress is that we manage to make our novel string field theory provide the correct mass square spectrum for the string. We finally suggest how to obtain the Veneziano amplitude in our model.
Multivector Fields and Jet Fields Setting Evolution Equations in Field Theories
Echeverría-Enríquez, A; Román-Roy, N
1997-01-01
The integrability of multivector fields in a differentiable manifold is studied. Then, given a jet bundle $J^1E\\to E\\to M$, it is shown that integrable multivector fields in $E$ are equivalent to integrable jet fields in $J^1E$ (connections in $E$). This result is applied to the particular case of multivector fields in the manifold $J^1E$ and jet fields in the repeated jet bundle $J^1J^1E$, in order to characterize integrable multivector fields and jet fields whose integral manifolds are canonical liftings of sections. These results allow us to set the lagrangian evolution equations for first-order classical field theories in three equivalent geometrical ways (in a form similar to that in which the lagrangian dynamical equations of non-autonomous mechanical systems are usually given).
Entanglement and mutual information in 2d nonrelativistic field theories
Hosseini, Seyed Morteza
2015-01-01
We carry out a systematic study of entanglement entropy in nonrelativistic conformal field theories via holographic techniques. After a discussion of recent results concerning Galilean conformal field theories, we deduce a novel expression for the entanglement entropy of (1+1)-dimensional Lifshitz field theories --- this is done both at zero and finite temperature. Based on these results, we pose a conjecture for the anomaly coefficient of a Lifshitz field theory dual to new massive gravity. It is found that the Lifshitz entanglement entropy at finite temperature displays a striking similarity with that corresponding to a flat space cosmology in three dimensions. We claim that this structure is an inherent feature of the entanglement entropy for nonrelativistic conformal field theories. We finish by exploring the behavior of the mutual information for such theories.
Variational principles for multisymplectic second-order classical field theories
Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso
2015-06-01
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework.
Variational principles for multisymplectic second-order classical field theories
Román Roy, Narciso; Prieto Martínez, Pedro Daniel
2015-01-01
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework. Peer Reviewed
Linear Transformation Theory of Quantum Field Operators and Its Applications
Institute of Scientific and Technical Information of China (English)
MA Lei
2003-01-01
We extend the linear quantum transformation theory to the case of quantum field operators. The corresponding general transformation expressions of CPT transformations and gauge field transformations are considered as its applications.
CPT/Lorentz Invariance Violation and Quantum Field Theory
Arias, P; Gamboa-Rios, J; López-Sarrion, J; Méndez, F; Arias, Paola; Das, Ashok; Gamboa, Jorge; Lopez-Sarrion, Justo; Mendez, Fernando
2006-01-01
Analogies between the noncommutative harmonic oscillator and noncommutative fields are analyzed. Following this analogy we construct examples of quantum fields theories with explicit CPT and Lorentz symmetry breaking. Some applications to baryogenesis and neutrino oscillation are also discussed
Magnetism and rotation in relativistic field theory
Mameda, Kazuya; Yamamoto, Arata
2016-09-01
We investigate the analogy between magnetism and rotation in relativistic theory. In nonrelativistic theory, the exact correspondence between magnetism and rotation is established in the presence of an external trapping potential. Based on this, we analyze relativistic rotation under external trapping potentials. A Landau-like quantization is obtained by considering an energy-dependent potential.
Quantum Field Theory in de Sitter spacetime
So, Ashaq Hussain; Sibuea, Marlina Rosalinda; Akhoon, Shabir Ahmad; Khanday, Bilal Nisar; Majeed, Sajad Ul; Rather, Asloob Ahmad; Nahvi, Ishaq
2013-01-01
In this paper we will analyse quantum ?eld theory on de Sitter space- time. We will ?rst analyse a general scalar and vector ?eld theory on de Sitter spacetime. This is done by ?rst calculating these propagators on four-Sphere and then analytically continuing it to de Sitter spacetime.
Bershtein, Mikhail; Ronzani, Massimiliano; Tanzini, Alessandro
2016-01-01
We show that equivariant Donaldson polynomials of compact toric surfaces can be calculated as residues of suitable combinations of Virasoro conformal blocks, by building on AGT correspondence between N = 2 supersymmetric gauge theories and two-dimensional conformal field theory.
Effective field theory of slowly-moving "extreme black holes"
Degura, Yoshitaka; Shiraishi, Kiyoshi
2000-01-01
We consider the non-relativistic effective field theory of ``extreme black holes'' in the Einstein-Maxwell-dilaton theory with an arbitrary dilaton coupling. We investigate finite-temperature behavior of gas of ``extreme black holes'' using the effective theory. The total energy of the classical many-body system is also derived.
Non perturbative methods in two dimensional quantum field theory
Abdalla, Elcio; Rothe, Klaus D
1991-01-01
This book is a survey of methods used in the study of two-dimensional models in quantum field theory as well as applications of these theories in physics. It covers the subject since the first model, studied in the fifties, up to modern developments in string theories, and includes exact solutions, non-perturbative methods of study, and nonlinear sigma models.
Modern Quantum Field Theory II - Proceeeings of the International Colloquium
Das, S. R.; Mandal, G.; Mukhi, S.; Wadia, S. R.
1995-08-01
The Table of Contents for the book is as follows: * Foreword * 1. Black Holes and Quantum Gravity * Quantum Black Holes and the Problem of Time * Black Hole Entropy and the Semiclassical Approximation * Entropy and Information Loss in Two Dimensions * Strings on a Cone and Black Hole Entropy (Abstract) * Boundary Dynamics, Black Holes and Spacetime Fluctuations in Dilation Gravity (Abstract) * Pair Creation of Black Holes (Abstract) * A Brief View of 2-Dim. String Theory and Black Holes (Abstract) * 2. String Theory * Non-Abelian Duality in WZW Models * Operators and Correlation Functions in c ≤ 1 String Theory * New Symmetries in String Theory * A Look at the Discretized Superstring Using Random Matrices * The Nested BRST Structure of Wn-Symmetries * Landau-Ginzburg Model for a Critical Topological String (Abstract) * On the Geometry of Wn Gravity (Abstract) * O(d, d) Tranformations, Marginal Deformations and the Coset Construction in WZNW Models (Abstract) * Nonperturbative Effects and Multicritical Behaviour of c = 1 Matrix Model (Abstract) * Singular Limits and String Solutions (Abstract) * BV Algebra on the Moduli Spaces of Riemann Surfaces and String Field Theory (Abstract) * 3. Condensed Matter and Statistical Mechanics * Stochastic Dynamics in a Deposition-Evaporation Model on a Line * Models with Inverse-Square Interactions: Conjectured Dynamical Correlation Functions of the Calogero-Sutherland Model at Rational Couplings * Turbulence and Generic Scale Invariance * Singular Perturbation Approach to Phase Ordering Dynamics * Kinetics of Diffusion-Controlled and Ballistically-Controlled Reactions * Field Theory of a Frustrated Heisenberg Spin Chain * FQHE Physics in Relativistic Field Theories * Importance of Initial Conditions in Determining the Dynamical Class of Cellular Automata (Abstract) * Do Hard-Core Bosons Exhibit Quantum Hall Effect? (Abstract) * Hysteresis in Ferromagnets * 4. Fundamental Aspects of Quantum Mechanics and Quantum Field Theory
Boson-Fermion Duality in A2 Toda Field Theory
Institute of Scientific and Technical Information of China (English)
YANG Zhan-Ying; ZHAO Liu; SHI Kang-Jie
2002-01-01
In this paper, we consider a two-dimensional integrable and conformal invariant field theory with two Diracspinors and two scalar fields. This model has chiral symmetry and CP-like symmetry. Moreover, this model also has aNeother current depending only on the matter field. At last, we bosonize the spinor fields.
A geometrical approach to two-dimensional Conformal Field Theory
Dijkgraaf, Robertus Henricus
1989-01-01
This thesis is organized in the following way. In Chapter 2 we will give a brief introduction to conformal field theory along the lines of standard quantum field theory, without any claims to originality. We introduce the important concepts of the stress-energy tensor, the Virasoro algebra, and prim
Noncommuting Electric Fields and Algebraic Consistency in Noncommutative Gauge theories
Banerjee, R
2003-01-01
We show that noncommuting electric fields occur naturally in noncommutative gauge theories. Using this noncommutativity, which is field dependent, and a hamiltonian generalisation of the Seiberg-Witten Map, the algebraic consistency in the lagrangian and hamiltonian formulations of these theories, is established. The stability of the Poisson algebra, under this generalised map, is studied.
Euclidean Quantum Field Theory on Commutative and Noncommutative Spaces
Wulkenhaar, R.
I give an introduction to Euclidean quantum field theory from the point of view of statistical physics, with emphasis both on Feynman graphs and on the Wilson-Polchinski approach to renormalisation. In the second part I discuss attempts to renormalise quantum field theories on noncommutative spaces.
The quantum field theory interpretation of quantum mechanics
de la Torre, Alberto C.
2015-01-01
It is shown that adopting the \\emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.
NS-NS Sector of Closed Superstring Field Theory
Erler, Theodore; Sachs, Ivo
2014-01-01
We give a construction for a general class of vertices in superstring field theory which include integration over bosonic moduli as well as the required picture changing insertions. We apply this procedure to find a covariant action for the NS-NS sector of Type II closed superstring field theory.
Theory of field induced incommensurability: CsFeCl3
DEFF Research Database (Denmark)
Lindgård, Per-Anker
1986-01-01
Using correlation theory for the singlet-doublet magnet CsFeCl3 in a magnetic field, a field induced incommensurate ordering along K-M is predicted without invoking dipolar effects. A fully self-consistent RPA theory gives Hc=44 kG in agreement with experiments at T=1.3K. Correlation and dipolar ...
An introduction to supersymmetric field theories in curved space
Dumitrescu, Thomas T
2016-01-01
In this review, we give a pedagogical introduction to a systematic framework for constructing and analyzing supersymmetric field theories on curved spacetime manifolds. The framework is based on the use of off-shell supergravity background fields. We present the general principles, which broadly apply to theories with different amounts of supersymmetry in diverse dimensions, as well as specific applications to N=1 theories in four dimensions and their three-dimensional cousins with N=2 supersymmetry.
Finite Deformations of Conformal Field Theories Using Analytically Regularized Connections
von Gussich, Alexander; Sundell, Per
1996-01-01
We study some natural connections on spaces of conformal field theories using an analytical regularization method. The connections are based on marginal conformal field theory deformations. We show that the analytical regularization preserves conformal invariance and leads to integrability of the marginal deformations. The connections are shown to be flat and to generate well-defined finite parallel transport. These finite parallel transports yield formulations of the deformed theories in the...
Minimal lectures on two-dimensional conformal field theory
Ribault, Sylvain
2016-01-01
We provide a brief but self-contained review of conformal field theory on the Riemann sphere. We first introduce general axioms such as local conformal invariance, and derive Ward identities and BPZ equations. We then define Liouville theory and minimal models by specific axioms on their spectrums and degenerate fields. We solve these theories by computing three- and four-point functions, and discuss their existence and uniqueness.
Quantum Field Theory on Pseudo-Complex Spacetime
Schuller, F P; Grimm, T W; Schuller, Frederic P.; Wohlfarth, Mattias N.R.; Grimm, Thomas W.
2003-01-01
The pseudo-complex Poincare group encodes both a universal speed and a maximal acceleration, which can be viewed as the kinematics of Born-Infeld electrodynamics. The irreducible representations of this group are constructed, providing the particle spectrum of a relativistic quantum theory that also respects a maximal acceleration. One finds that each standard relativistic particle is associated with a 'pseudo'-partner of equal spin but generically different mass. These pseudo-partners act as Pauli-Villars regulators for the other member of the doublet, as is found from the explicit construction of quantum field theory on pseudo-complex spacetime. Conversely, a Pauli-Villars regularised quantum field theory on real spacetime possesses a field phase space with integrable pseudo-complex structure, which gives rise to a quantum field theory on pseudo-complex spacetime. This equivalence between (i) maximal acceleration kinematics, (ii) pseudo-complex quantum field theory, and (iii) Pauli-Villars regularisation ri...
Noether's theorems applications in mechanics and field theory
Sardanashvily, Gennadi
2016-01-01
The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory.
Correlation functions in a c=1 boundary conformal field theory
Kristjansson, K R; Kristjansson, Kristjan R.; Thorlacius, Larus
2005-01-01
We obtain exact results for correlation functions of primary operators in the two-dimensional conformal field theory of a scalar field interacting with a critical periodic boundary potential. Amplitudes involving arbitrary bulk discrete primary fields are given in terms of SU(2) rotation coefficients while boundary amplitudes involving discrete boundary fields are independent of the boundary interaction. Mixed amplitudes involving both bulk and boundary discrete fields can also be obtained explicitly. Two- and three-point boundary amplitudes involving fields at generic momentum are determined, up to multiplicative constants, by the band spectrum in the open-string sector of the theory.
Quantum correlations in nuclear mean field theory through source terms
Lee, S J
1996-01-01
Starting from full quantum field theory, various mean field approaches are derived systematically. With a full consideration of external source dependence, the stationary phase approximation of an action gives a nuclear mean field theory which includes quantum correlation effects (such as particle-hole or ladder diagram) in a simpler way than the Brueckner-Hartree-Fock approach. Implementing further approximation, the result can be reduced to Hartree-Fock or Hartree approximation. The role of the source dependence in a mean field theory is examined.
Scattering matrix theory for stochastic scalar fields.
Korotkova, Olga; Wolf, Emil
2007-05-01
We consider scattering of stochastic scalar fields on deterministic as well as on random media, occupying a finite domain. The scattering is characterized by a generalized scattering matrix which transforms the angular correlation function of the incident field into the angular correlation function of the scattered field. Within the accuracy of the first Born approximation this matrix can be expressed in a simple manner in terms of the scattering potential of the scatterer. Apart from determining the angular distribution of the spectral intensity of the scattered field, the scattering matrix makes it possible also to determine the changes in the state of coherence of the field produced on scattering.
An axiomatic approach to soft learning vector quantization and clustering.
Karayiannis, N B
1999-01-01
This paper presents an axiomatic approach to soft learning vector quantization (LVQ) and clustering based on reformulation. The reformulation of the fuzzy c-means (FCM) algorithm provides the basis for reformulating entropy-constrained fuzzy clustering (ECFC) algorithms. This analysis indicates that minimization of admissible reformulation functions using gradient descent leads to a broad variety of soft learning vector quantization and clustering algorithms. According to the proposed approach, the development of specific algorithms reduces to the selection of a generator function. Linear generator functions lead to the FCM and fuzzy learning vector quantization (FLVQ) algorithms while exponential generator functions lead to ECFC and entropy-constrained learning vector quantization (ECLVQ) algorithms. The reformulation of LVQ and clustering algorithms also provides the basis for developing uncertainty measures that can identify feature vectors equidistant from all prototypes. These measures are employed by a procedure developed to make soft LVQ and clustering algorithms capable of identifying outliers in the data set. This procedure is evaluated by testing the algorithms generated by linear and exponential generator functions on speech data.
Structural aspects of quantum field theory and noncommutative geometry
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...
Wave model and self-organization theory of C-space: application in the ergonomics and design
Kovalev, Y. N.; National Aviation University, Ukraine
2012-01-01
Axiomatic wave model and self-organization theory of s– spaceand their application for modeling and optimization of human–machine systems and person–dwelling–environment systems are considered. Axiomatic wave model and self-organization theory of s– spaceand their application for modeling and optimization of human–machine systems and person–dwelling–environment systems are considered.
Noether's theorem in non-local field theories
Krivoruchenko, M I
2016-01-01
Explicit expressions are constructed for a locally conserved vector current associated with a continuous internal symmetry and for energy-momentum and angular-momentum density tensors associated with the Poincar\\'e group in field theories with higher-order derivatives and in non-local field theories. An example of non-local charged scalar field equations with broken C and CPT symmetries is considered. For this case, we find simple analytical expressions for the conserved currents.
Heavy Quarks, QCD, and Effective Field Theory
Energy Technology Data Exchange (ETDEWEB)
Thomas Mehen
2012-10-09
The research supported by this OJI award is in the area of heavy quark and quarkonium production, especially the application Soft-Collinear E ective Theory (SCET) to the hadronic production of quarkonia. SCET is an e ffective theory which allows one to derive factorization theorems and perform all order resummations for QCD processes. Factorization theorems allow one to separate the various scales entering a QCD process, and in particular, separate perturbative scales from nonperturbative scales. The perturbative physics can then be calculated using QCD perturbation theory. Universal functions with precise fi eld theoretic de nitions describe the nonperturbative physics. In addition, higher order perturbative QCD corrections that are enhanced by large logarithms can be resummed using the renormalization group equations of SCET. The applies SCET to the physics of heavy quarks, heavy quarkonium, and similar particles.
String organization of field theories duality and gauge invariance
Feng, Y J; Feng, Y J; Lam, C S
1994-01-01
String theories should reduce to ordinary four-dimensional field theories at low energies. Yet the formulation of the two are so different that such a connection, if it exists, is not immediately obvious. With the Schwinger proper-time representation, and the spinor helicity technique, it has been shown that field theories can indeed be written in a string-like manner, thus resulting in simplifications in practical calculations, and providing novel insights into gauge and gravitational theories. This paper continues the study of string organization of field theories by focusing on the question of local duality. It is shown that a single expression for the sum of many diagrams can indeed be written for QED, thereby simulating the duality property in strings. The relation between a single diagram and the dual sum is somewhat analogous to the relation between a old- fashioned perturbation diagram and a Feynman diagram. Dual expressions are particularly significant for gauge theories because they are gauge invari...
Lorentz symmetry breaking as a quantum field theory regulator
Visser, Matt
2009-01-01
Perturbative expansions of relativistic quantum field theories typically contain ultraviolet divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. We shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory, and discuss its implications. We shall quantify just "how much" Lorentz symmetry breaking is required to fully regulate the theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Horava's recent article [arXiv:0901.3775 [hep-th
Chiral Orbifold Construction Of Field Theories With Extra Dimensions
Hailu, G
2003-01-01
We build higher dimensional field theories which have chiral fermion zero-modes on orbifolds. We show that orbifold boundary conditions and scalar vacuum expectation values interplay to produce chiral fermions localized on fat three branes. We develop a scheme for computing field propagators in higher dimensional theories obeying chiral orbifold boundary conditions. Using this scheme we compute the loop corrections to an effective field theory in five dimensions. We find that the renormalization group running of the higher dimensional bulk theory leads to a running of the four dimensional brane couplings. We generalize an argument to verify that the chiral anomaly that arises in these chiral orbifold theories is entirely confined on and uniformly distributed over the fixed points of the orbifold, independent of the shape of the chiral zero-modes. We construct a setup in which a scalar field with appropriate profile in the extra dimension is used to address the hierarchy problem and also localize both chiral f...
Fractal tracer distributions in turbulent field theories
DEFF Research Database (Denmark)
Hansen, J. Lundbek; Bohr, Tomas
1998-01-01
We study the motion of passive tracers in a two-dimensional turbulent velocity field generated by the Kuramoto-Sivashinsky equation. By varying the direction of the velocity-vector with respect to the field-gradient we can continuously vary the two Lyapunov exponents for the particle motion and t...
Energy Technology Data Exchange (ETDEWEB)
Bossard, G
2007-10-15
This thesis contains 2 parts based on scientific contributions that have led to 2 series of publications. The first one concerns the introduction of vector symmetry in cohomological theories, through a generalization of the so-called Baulieu-Singer equation. Together with the topological BRST (Becchi-Rouet-Stora-Tyutin) operator, this symmetry gives an off-shell closed sub-sector of supersymmetry that permits to determine the action uniquely. The second part proposes a methodology for re-normalizing supersymmetric Yang-Mills theory without assuming a regularization scheme which is both supersymmetry and gauge invariance preserving. The renormalization prescription is derived thanks to the definition of 2 consistent Slavnov-Taylor operators for supersymmetry and gauge invariance, whose construction requires the introduction of the so-called shadow fields. We demonstrate the renormalizability of supersymmetric Yang-Mills theories. We give a fully consistent, regularization scheme independent, proof of the vanishing of the {beta} function and of the anomalous dimensions of the one half BPS operators in maximally supersymmetric Yang-Mills theory. After a short introduction, in chapter two, we give a review of the cohomological Yang-Mills theory in eight dimensions. We then study its dimensional reductions in seven and six dimensions. The last chapter gives quite independent results, about a geometrical interpretation of the shadow fields, an unpublished work about topological gravity in four dimensions, an extension of the shadow formalism to superconformal invariance, and finally the solution of the constraints in a twisted superspace. (author)
Two problems in thermal field theory
Indian Academy of Sciences (India)
François Gelis
2000-07-01
In this talk, I review recent progress made in two areas of thermal ﬁeld theory. In particular, I discuss various approaches for the calculation of the quark gluon plasma thermodynamical properties, and the problem of its photon production rate.
Flat Holography: Aspects of the dual field theory
Bagchi, Arjun; Kakkar, Ashish; Mehra, Aditya
2016-01-01
Assuming the existence of a field theory in D dimensions dual to (D+1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review briefly some successes of the 3d bulk - 2d boundary case and then focus on the 4d bulk - 3d boundary example, where the symmetry in question is the infinite dimensional BMS4 algebra. We look at the constraints imposed by this symmetry on a 3d field theory by constructing highest weight representations of this algebra. We construct two and three point functions of BMS primary fields and surprisingly find that symmetries constrain these correlators to be identical to those of a 2d relativistic conformal field theory. We then go one dimension higher and construct prototypical examples of 4d field theories which are putative duals of 5d Minkowski spacetimes. These field theories are ultra-relativistic limits of electrodynamics and Yang-Mills theories which exhibit invariance under th...
Flowing in group field theory space: a review
Carrozza, Sylvain
2016-01-01
We provide a non--technical overview of recent extensions of renormalization methods and techniques to Group Field Theories (GFTs), a class of combinatorially non--local quantum field theories which generalize matrix models to dimension $d \\geq 3$. More precisely, we focus on GFTs with so--called closure constraint, which are closely related to lattice gauge theories and quantum gravity spin foam models. With the help of modern tensor model tools, a rich landscape of renormalizable theories has been unravelled. We review our current understanding of their renormalization group flows, at both perturbative and non--perturbative levels.
Fundamental Field Theory in Ten Dimensions and The Early Universe
Patwardhan, A
2006-01-01
A unified field theory in ten dimensions, of all interactions, can describe high energy processes occuring in the early universe. In such a theory transitions that give properties of the universe can occur due to the presence of algebraic and geometric structures. A correspondence between theory and observations of the universe is made, to obtain a new interpretation and properties. This paper consists of a field theory and cosmological model of dark and normal energy and matter, cosmological constant, acceleration and inflation in the early universe.
Decoherence in Field Theory General Couplings and Slow Quenches
Lombardo, F C; Rivers, R J
2003-01-01
We study the onset of a classical order parameter after a second-order phase transition in quantum field theory. We consider a quantum scalar field theory in which the system-field (long-wavelength modes), interacts with its environment, represented both by a set of scalar fields and by its own short-wavelength modes. We compute the decoherence times for the system-field modes and compare them with the other time scales of the model. We analyze different couplings between the system and the environment for both instantaneous and slow quenches. Within our approximations decoherence is in general a short time event.
Steps towards an axiomatic pregeometry of space-time
Bergliaffa, S E P; Vucetich, H; Bergliaffa, Santiago E. Perez; Romero, Gustavo E.; Vucetich, Hector
1998-01-01
We present a deductive theory of space-time which is realistic, objective, and relational. It is realistic because it assumes the existence of physical things endowed with concrete properties. It is objective because it can be formulated without any reference to cognoscent subjects or sensorial fields. Finally, it is relational because it assumes that space-time is not a thing but a complex of relations among things. In this way, the original program of Leibniz is consummated, in the sense that space is ultimately an order of coexistents, and time is an order of succesives. In this context, we show that the metric and topological properties of Minkowskian space-time are reduced to relational properties of concrete things. We also sketch how our theory can be extended to encompass a Riemmanian space-time.
Statistical approach to quantum field theory an introduction
Wipf, Andreas
2013-01-01
Over the past few decades the powerful methods of statistical physics and Euclidean quantum field theory have moved closer together, with common tools based on the use of path integrals. The interpretation of Euclidean field theories as particular systems of statistical physics has opened up new avenues for understanding strongly coupled quantum systems or quantum field theories at zero or finite temperatures. Accordingly, the first chapters of this book contain a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics. The resulting high-dimensional integrals can be estimated with the help of Monte Carlo simulations based on Markov processes. The most commonly used algorithms are presented in detail so as to prepare the reader for the use of high-performance computers as an “experimental” tool for this burgeoning field of theoretical physics. Several chapters are then devoted to an introduction to simple lattice field theories and a variety of spin systems w...
Lectures on classical and quantum theory of fields
Energy Technology Data Exchange (ETDEWEB)
Arodz, Henryk; Hadasz, Leszek [Jagiellonian Univ., Krakow (Poland). Inst. Physics
2010-07-01
This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course. (orig.)
Lectures on Classical and Quantum Theory of Fields
Arodź, Henryk
2010-01-01
This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course.
The tensor hierarchy of 8-dimensional field theories
Andino, Óscar Lasso; Ortín, Tomás
2016-10-01
We construct the tensor hierarchy of generic, bosonic, 8-dimensional field theories. We first study the form of the most general 8-dimensional bosonic theory with Abelian gauge symmetries only and no massive deformations. This study determines the tensors that occur in the Chern-Simons terms of the (electric and magnetic) field strengths and the action for the electric fields, which we determine. Having constructed the most general Abelian theory we study the most general gaugings of its global symmetries and the possible massive deformations using the embedding tensor formalism, constructing the complete tensor hierarchy using the Bianchi identities. We find the explicit form of all the field strengths of the gauged theory up to the 6-forms. Finally, we find the equations of motion comparing the Noether identities with the identities satisfied by the Bianchi identities themselves. We find that some equations of motion are not simply the Bianchi identities of the dual fields, but combinations of them.
The tensor hierarchy of 8-dimensional field theories
Andino, Oscar Lasso
2016-01-01
We construct the tensor hierarchy of generic, bosonic, 8-dimensional field theories. We first study the form of the most general 8-dimensional bosonic theory with Abelian gauge symmetries only and no massive deformations. This study determines the tensors that occur in the Chern-Simons terms of the (electric and magnetic) field strengths and the action for the electric fields, which we determine. Having constructed the most general Abelian theory we study the most general gaugings of its global symmetries and the possible massive deformations using the embedding tensor formalism, constructing the complete tensor hierarchy using the Bianchi identities. We find the explicit form of all the field strengths of the gauged theory up to the 6-forms. Finally, we find the equations of motion comparing the Noether identities with the identities satisfied by the Bianchi identities themselves. We find that some equations of motion are not simply the Bianchi identities of the dual fields, but combinations of them.
Unambiguous formalism for higher order Lagrangian field theories
Energy Technology Data Exchange (ETDEWEB)
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn [Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM, Serrano 123, 28006 Madrid (Spain); Vankerschaver, Joris [Control and Dynamical Systems, California Institute of Technology, CA (United States)], E-mail: cedricmc@imaff.cfmac.csic.es, E-mail: mdeleon@imaff.cfmac.csic.es, E-mail: d.martin@imaff.cfmac.csic.es, E-mail: jv@caltech.edu
2009-11-27
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
Polchinski's equation for group field theory
Energy Technology Data Exchange (ETDEWEB)
Krajewski, T. [Centre de Physique Theorique, Campus de Luminy, 13 288 Marseille cedex 9 (France); Laboratoire d' Informatique de Paris Nord, 99 avenue Jean Baptiste Clement, 93 430 Villetaneuse (France); Toriumi, R. [Centre de Physique Theorique, Campus de Luminy, 13 288 Marseille cedex 9 (France)
2014-09-11
We derive an exact renormalization group equation in the context of (colored) group field theories. This equation describes the variation of the effective action as some of the modes of the fields are integrated out. From a combinatorial point of view, the effective action can be expressed using a boundary triangulation and the corresponding renormalization group equation identifies some of its simplexes, In group field theory, terms in the effective action are parametrized by spin networks, while the group field theory Feynman graphs correspond to spin foams. This provides a formulation of group field theories that only involves boundary graphs. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Second order higher-derivative corrections in Double Field Theory
Lescano, Eric
2016-01-01
HSZ Double Field Theory is a higher-derivative theory of gravity with exact and manifest T-duality symmetry. The first order corrections in the massless sector were shown to be governed solely by Chern-Simons deformations of the three-form field strength. We compute the full action with up to six derivatives ${\\cal O} (\\alpha'{}^2)$ for the universal sector containing the metric, two-form and dilaton fields. The Green-Schwarz transformation of the two-form field remains uncorrected to second order. In addition to the expected Chern-Simons-squared and Riemann-cubed terms the theory contains a cubic Gauss-Bonnet interaction, plus other six-derivative unambiguous terms involving the three-form field strength whose presence indicates that the theory must contain further higher-derivative corrections.
Avoiding Haag's Theorem with Parameterized Quantum Field Theory
Seidewitz, Ed
2017-03-01
Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that Haag's Theorem can be avoided when quantum field theory is formulated using an invariant, fifth path parameter in addition to the usual four position parameters, such that the Dyson perturbation expansion for the scattering matrix can still be reproduced. As a result, the parameterized formalism provides a consistent foundation for the interpretation of quantum field theory as used in practice and, perhaps, for better dealing with other mathematical issues.
Grützmann, Melchior; Strobl, Thomas
2015-10-01
Starting with minimal requirements from the physical experience with higher gauge theories, i.e. gauge theories for a tower of differential forms of different form degrees, we discover that all the structural identities governing such theories can be concisely recombined into what is called a Q-structure or, equivalently, an L∞-algebroid. This has many technical and conceptual advantages: complicated higher bundles become just bundles in the category of Q-manifolds in this approach (the many structural identities being encoded in the one operator Q squaring to zero), gauge transformations are generated by internal vertical automorphisms in these bundles and even for a relatively intricate field content the gauge algebra can be determined in some lines and is given by what is called the derived bracket construction. This paper aims equally at mathematicians and theoretical physicists; each more physical section is followed by a purely mathematical one. While the considerations are valid for arbitrary highest form degree p, we pay particular attention to p = 2, i.e. 1- and 2-form gauge fields coupled nonlinearly to scalar fields (0-form fields). The structural identities of the coupled system correspond to a Lie 2-algebroid in this case and we provide different axiomatic descriptions of those, inspired by the application, including e.g. one as a particular kind of a vector-bundle twisted Courant algebroid.
Field Theory for Function Fields of Plane Quintic Curves
Institute of Scientific and Technical Information of China (English)
Kei Miura
2002-01-01
We study the structure of function fields of plane curves following our method developed in [3]. Let K be the function field of a smooth plane curve C.Let Km be a g-maximal rational subfield of K. Then the field extension K/Km is obtained by the projection from C to a line with center P ∈ C. By using this fact, we study the field extension K/Km from a geometrical viewpoint. In this paper, we treat quintic curves as a continuation of [3, 4].
Light-front variational approach to scalar field theories
Energy Technology Data Exchange (ETDEWEB)
Bartnik, E.A.; Gl-dash-barazek, S.
1989-02-15
We present a variational method of estimating the ground-state energy for quantum field theories on the light front in an arbitrary number of dimensions. For scalar fields, variational parameters are the constant background field and the boson mass. In this case our method is equivalent to the standard equal-time approach.
Correlation functions in conformal Toda field theory II
Fateev, V A
2009-01-01
This is the second part of the paper 0709.3806v2. Here we show that three-point correlation function with one semi-degenerate field in Toda field theory as well as four-point correlation function with one completely degenerate and one semi-degenerate field can be represented by the finite dimensional integrals.
SUSY sine-Gordon theory as a perturbed conformal field theory and finite size effects
Bajnok, Z; Palla, L; Takács, G; Wagner, F
2004-01-01
We consider SUSY sine-Gordon theory in the framework of perturbed conformal field theory. Using an argument from Zamolodchikov, we obtain the vacuum structure and the kink adjacency diagram of the theory, which is cross-checked against the exact S matrix prediction, first-order perturbed conformal field theory (PCFT), the NLIE method and truncated conformal space approach. We provide evidence for consistency between the usual Lagrangian description and PCFT on the one hand, and between PCFT, NLIE and a massgap formula conjectured by Baseilhac and Fateev, on the other. In addition, we extend the NLIE description to all the vacua of the theory.
Chiral Symmetry in Light-Cone Field Theory
Lenz, F; Thies, M; Yazaki, K
2004-01-01
An analysis of spontaneously broken chiral symmetry in light-cone field theory is presented. The non-locality inherent to light-cone field theory requires revision of the standard procedure in the derivation of Ward-Takahashi identities. We derive the general structure of chiral Ward-Takahashi identities and construct them explicitly for various model field theories. Gell-Mann-Oakes-Renner relations and relations between fermion propagators and the structure functions of Nambu-Goldstone bosons are discussed and the necessary modifications of the Ward-Takahashi identities due to the axial anomaly are indicated.
Dark Solitons, D-branes and Noncommutative Tachyon Field Theory
Giaccari, Stefano
2016-01-01
In this paper we discuss the boson/vortex duality by mapping the Gross-Pitaevskii theory into an effective string theory, both with and without boundaries. Through the effective string theory, we find the Seiberg-Witten map between the commutative and the noncommutative tachyon field theories, and consequently identify their soliton solutions with the D-branes in the effective string theory. We perform various checks of the duality map and the identification of classical solutions. This new insight of the duality between the Gross-Pitaevskii theory and the effective string theory allows us to test many results of string theory in Bose-Einstein condensates, and at the same time help us understand the quantum behavior of superfluids and cold atom systems.
Hitchin equation, singularity, and N = 2 superconformal field theories
Nanopoulos, Dimitri; Xie, Dan
2010-03-01
We argue that Hitchin’s equation determines not only the low energy effective theory but also describes the UV theory of four dimensional N = 2 superconformal field theories when we compactify six dimensional A N (0, 2) theory on a punctured Riemann surface. We study singular solutions to Hitchin’s equation and the Highs field of equation has a simple pole at the punctures; We show that the massless theory is associated with Higgs field whose residue is a nilpotent element; We identify the flavor symmetry associated with the puncture by studying the singularity of closure of the moduli space of solutions with the appropriate boundary conditions. For mass-deformed theory the residue of the Higgs field is a semi-simple element, we identify the semi-simple element by arguing that the moduli space of solutions of mass-deformed theory must be a deformation of the closure of the moduli space of massless theory. We also study the Seiberg-Witten curve by identifying it as the spectral curve of the Hitchin’s system. The results are all in agreement with Gaiotto’s results derived from studying the Seiberg-Witten curve of four dimensional quiver gauge theory.
Incorporation of generalized uncertainty principle into Lifshitz field theories
Energy Technology Data Exchange (ETDEWEB)
Faizal, Mir, E-mail: f2mir@uwaterloo.ca [Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Majumder, Barun, E-mail: barunbasanta@iitgn.ac.in [Indian Institute of Technology Gandhinagar, Ahmedabad, 382424 (India)
2015-06-15
In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.
Toward a quantum theory of tachyon fields
Schwartz, Charles
2016-03-01
We construct momentum space expansions for the wave functions that solve the Klein-Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than light) particles. We find that we can postulate commutation or anticommutation rules for the operators that lead to physically sensible results: causality, for tachyon fields, means that there is no connection between space-time points separated by a timelike interval. Calculating the conserved charge and four-momentum for these fields allows us to interpret the number operators for particles and antiparticles in a consistent manner; and we see that helicity plays a critical role for the spinor field. Some questions about Lorentz invariance are addressed and some remain unresolved; and we show how to handle the group representation for tachyon spinors.
Toward a Quantum Theory of Tachyon Fields
Schwartz, Charles
2016-01-01
We construct momentum space expansions for the wave functions that solve the Klein-Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than light) particles. We find that we can postulate commutation or anticommutation rules for the operators that lead to physically sensible results: causality, for tachyon fields, means that there is no connection between spacetime points separated by a timelike interval. Calculating the conserved charge and 4-momentum for these fields allows us to interpret the number operators for particles and antiparticles in a consistent manner; and we see that helicity plays a critical role for the spinor field. Some questions about Lorentz invariance are addressed and some remain unresolved; and we show how to handle the group representation for tachyon spinors.
Unorientable Boundary Superstring Field theory with Tachyon field
Viswanathan, K S
2002-01-01
We use the BSFT method to study the unoriented open string theory. The partition function on the Mobius strip is calculated. We find that, at the one-loop level, the divergence coming from planar graph and unoriented graph cancel each other as expected.
Quantum Yang-Mills field theory
Frasca, Marco
2017-01-01
We show that the Dyson-Schwinger set of equations for the Yang-Mills theory can be exactly solved till the two-point function. This is obtained given a set of nonlinear waves solving the classical equations of motion. Translation invariance is maintained by the proper choice of the solution of the equation for the two-point function as devised by Coleman. The computation of the Dyson-Schwinger equations is performed in the same way as devised by Bender, Milton and Savage providing a set of partial differential equations whose proof of existence of the solutions is standard. So, the correlation functions of the theory could be proved to exist and the two-point function manifests a mass gap.
Quantum Field Theories and Prime Numbers Spectrum
Menezes, G
2012-01-01
The Riemann hypothesis states that all nontrivial zeros of the zeta function lie on the critical line $\\Re(s)=1/2$. Hilbert and P\\'olya suggested a possible approach to prove it, based on spectral theory. Within this context, some authors formulated the question: is there a quantum mechanical system related to the sequence of prime numbers? In this Letter we assume that there is a class of hypothetical physical systems described by self-adjoint operators with countable infinite number of degrees of freedom with spectra given by the sequence of primes numbers. We prove a no-go theorem. We show that the generating functional of connected Schwinger functions of such theories cannot be constructed.
Killing vector fields and harmonic superfield theories
Energy Technology Data Exchange (ETDEWEB)
Groeger, Josua, E-mail: groegerj@mathematik.hu-berlin.de [Humboldt-Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, 12489 Berlin (Germany)
2014-09-15
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, also referred to as harmonic, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of this harmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.
Thermo--hydrodynamics As a Field Theory
Jezierski, Jacek
2011-01-01
The field theoretical description of thermo-hydrodynamics is given. It is based on the duality between the physical space--time and the "material space-time" which we construct here. The material space appearing in a natural way in the canonical formulation of the hydrodynamics is completed with a material time playing role of the field potential for temperature. Both Lagrangian and Hamiltonian formulations, the canonical structure, Poisson bracket, N\\"other theorem and conservation laws are discussed.
Quantum tunneling and field electron emission theories
Liang, Shi-Dong
2013-01-01
Quantum tunneling is an essential issue in quantum physics. Especially, the rapid development of nanotechnology in recent years promises a lot of applications in condensed matter physics, surface science and nanodevices, which are growing interests in fundamental issues, computational techniques and potential applications of quantum tunneling. The book involves two relevant topics. One is quantum tunneling theory in condensed matter physics, including the basic concepts and methods, especially for recent developments in mesoscopic physics and computational formulation. The second part is the f
Thermal Renormalons in Scalar Field Theory
Loewe, M
2000-01-01
In the frame of the scalar theory $\\lambda \\phi ^{4}$, we explore the occurrence of thermal renormalons, i. e. temperature dependent singularities in the Borel plane. Using Thermofield Dynamics, we found in fact a series of singularities of this kind, which are located to the right of the well known zero temperature pole, being therefore of a subleading character in the ambiguity of the Borel sum.