Renormalized action improvements

International Nuclear Information System (INIS)

Zachos, C.

1984-01-01

Finite lattice spacing artifacts are suppressed on the renormalized actions. The renormalized action trajectories of SU(N) lattice gauge theories are considered from the standpoint of the Migdal-Kadanoff approximation. The minor renormalized trajectories which involve representations invariant under the center are discussed and quantified. 17 references

Renormalization of non-abelian gauge theories in curved space-time

International Nuclear Information System (INIS)

Freeman, M.D.

1984-01-01

We use indirect, renormalization group arguments to calculate the gravitational counterterms needed to renormalize an interacting non-abelian gauge theory in curved space-time. This method makes it straightforward to calculate terms in the trace anomaly which first appear at high order in the coupling constant, some of which would need a 4-loop calculation to find directly. The role of gauge invariance in the theory is considered, and we discuss briefly the effect of using coordinate-dependent gauge-fixing terms. We conclude by suggesting possible applications of this work to models of the very early universe

Two-and three-dimension Potts magnetism in the renormalization group approximation

International Nuclear Information System (INIS)

Silva, L.R. da.

1985-01-01

Through a real space Renormalization Group (RG) technique we discuss the criticality of various physical systems, calculate order parameters for geometrical problems and analyse convergence aspects of the RG theory. (author) [pt

Zero-temperature renormalization of the 2D transverse Ising model

International Nuclear Information System (INIS)

Kamieniarz, G.

1982-08-01

A zero-temperature real-space renormalization-group method is applied to the transverse Ising model on planar hexagonal, triangular and quadratic lattices. The critical fields and the critical exponents describing low-field large-field transition are calculated. (author)

A simple method for one-loop renormalization in curved space-time

Energy Technology Data Exchange (ETDEWEB)

Markkanen, Tommi [Helsinki Institute of Physics and Department of Physics, P.O. Box 64, FI-00014, University of Helsinki (Finland); Tranberg, Anders, E-mail: tommi.markkanen@helsinki.fi, E-mail: anders.tranberg@uis.no [Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen (Denmark)

2013-08-01

We present a simple method for deriving the renormalization counterterms from the components of the energy-momentum tensor in curved space-time. This method allows control over the finite parts of the counterterms and provides explicit expressions for each term separately. As an example, the method is used for the self-interacting scalar field in a Friedmann-Robertson-Walker metric in the adiabatic approximation, where we calculate the renormalized equation of motion for the field and the renormalized components of the energy-momentum tensor to fourth adiabatic order while including interactions to one-loop order. Within this formalism the trace anomaly, including contributions from interactions, is shown to have a simple derivation. We compare our results to those obtained by two standard methods, finding agreement with the Schwinger-DeWitt expansion but disagreement with adiabatic subtractions for interacting theories.

Generalized Hubbard Hamiltonian: renormalization group approach

International Nuclear Information System (INIS)

Cannas, S.A.; Tamarit, F.A.; Tsallis, C.

1991-01-01

We study a generalized Hubbard Hamiltonian which is closed within the framework of a Quantum Real Space Renormalization Group, which replaces the d-dimensional hypercubic lattice by a diamond-like lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled band case in d = 2 and d = 3. Some evidence for superconductivity is presented. (author). 44 refs., 12 figs., 2 tabs

Fisher's Zeros as the Boundary of Renormalization Group Flows in Complex Coupling Spaces

International Nuclear Information System (INIS)

Denbleyker, A.; Du Daping; Liu Yuzhi; Meurice, Y.; Zou Haiyuan

2010-01-01

We propose new methods to extend the renormalization group transformation to complex coupling spaces. We argue that Fisher's zeros are located at the boundary of the complex basin of attraction of infrared fixed points. We support this picture with numerical calculations at finite volume for two-dimensional O(N) models in the large-N limit and the hierarchical Ising model. We present numerical evidence that, as the volume increases, the Fisher's zeros of four-dimensional pure gauge SU(2) lattice gauge theory with a Wilson action stabilize at a distance larger than 0.15 from the real axis in the complex β=4/g 2 plane. We discuss the implications for proofs of confinement and searches for nontrivial infrared fixed points in models beyond the standard model.

A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY

OpenAIRE

SASAKURA, NAOKI

2010-01-01

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian config...

Gauge-independent renormalization of the N2HDM

Science.gov (United States)

Krause, Marcel; López-Val, David; Mühlleitner, Margarete; Santos, Rui

2017-12-01

The Next-to-Minimal 2-Higgs-Doublet Model (N2HDM) is an interesting benchmark model for a Higgs sector consisting of two complex doublet and one real singlet fields. Like the Next-to-Minimal Supersymmetric extension (NMSSM) it features light Higgs bosons that could have escaped discovery due to their singlet admixture. Thereby, the model allows for various different Higgs-to-Higgs decay modes. Contrary to the NMSSM, however, the model is not subject to supersymmetric relations restraining its allowed parameter space and its phenomenology. For the correct determination of the allowed parameter space, the correct interpretation of the LHC Higgs data and the possible distinction of beyond-the-Standard Model Higgs sectors higher order corrections to the Higgs boson observables are crucial. This requires not only their computation but also the development of a suitable renormalization scheme. In this paper we have worked out the renormalization of the complete N2HDM and provide a scheme for the gauge-independent renormalization of the mixing angles. We discuss the renormalization of the Z_2 soft breaking parameter m 12 2 and the singlet vacuum expectation value v S . Both enter the Higgs self-couplings relevant for Higgs-to-Higgs decays. We apply our renormalization scheme to different sample processes such as Higgs decays into Z bosons and decays into a lighter Higgs pair. Our results show that the corrections may be sizable and have to be taken into account for reliable predictions.

Generalized conditions for the distributional zero-mass limit of renormalized Feynman amplitudes in Minkowski space

International Nuclear Information System (INIS)

Manoukian, E.B.

1986-01-01

Generalized conditions (rules) are set up for the existence of the distributional zero-mass limit of renormalized Feynman amplitudes in Minkowski space. These rules are generalizations of rules that have been set up earlier by us and hence are applicable to a larger class of graphs. The study is very general as the vanishing masses are led to vanish at different rates. All subtractions of renormalization are carried out directly in momentum space, about the origin, with the degree of divergence of a subtraction coinciding with the dimensionality of the corresponding subdiagram

Quantum renormalization group approach to quantum coherence and multipartite entanglement in an XXZ spin chain

Energy Technology Data Exchange (ETDEWEB)

Wu, Wei [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China); Beijing Computational Science Research Center, Beijing 100193 (China); Xu, Jing-Bo, E-mail: xujb@zju.edu.cn [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China)

2017-01-30

We investigate the performances of quantum coherence and multipartite entanglement close to the quantum critical point of a one-dimensional anisotropic spin-1/2 XXZ spin chain by employing the real-space quantum renormalization group approach. It is shown that the quantum criticality of XXZ spin chain can be revealed by the singular behaviors of the first derivatives of renormalized quantum coherence and multipartite entanglement in the thermodynamics limit. Moreover, we find the renormalized quantum coherence and multipartite entanglement obey certain universal exponential-type scaling laws in the vicinity of the quantum critical point of XXZ spin chain. - Highlights: • The QPT of XXZ chain is studied by renormalization group. • The renormalized coherence and multiparticle entanglement is investigated. • Scaling laws of renormalized coherence and multiparticle entanglement are revealed.

Real-space decoupling transformation for quantum many-body systems.

Science.gov (United States)

Evenbly, G; Vidal, G

2014-06-06

We propose a real-space renormalization group method to explicitly decouple into independent components a many-body system that, as in the phenomenon of spin-charge separation, exhibits separation of degrees of freedom at low energies. Our approach produces a branching holographic description of such systems that opens the path to the efficient simulation of the most entangled phases of quantum matter, such as those whose ground state violates a boundary law for entanglement entropy. As in the coarse-graining transformation of Vidal [Phys. Rev. Lett. 99, 220405 (2007).

Improved Epstein-Glaser Renormalization in Coordinate Space I. Euclidean Framework

International Nuclear Information System (INIS)

Gracia-Bondia, Jose M.

2003-01-01

In a series of papers, we investigate the reformulation of Epstein-Glaser renormalization in coordinate space, both in analytic and (Hopf) algebraic terms. This first article deals with analytical aspects. Some of the (historically good) reasons for the divorces of the Epstein-Glaser method, both from mainstream quantum field theory and the mathematical literature on distributions, are made plain; and overcome

Hadamard and minimal renormalizations

International Nuclear Information System (INIS)

Castagnino, M.A.; Gunzig, E.; Nardone, P.; Paz, J.P.

1986-01-01

A common language is introduced to study two, well-known, different methods for the renormalization of the energy-momentum tensor of a scalar neutral quantum field in curved space-time. Different features of the two renormalizations are established and compared

Green's functions for theories with massless particles (in perturbation theory). [Growth properties, momentum space, mass renormalization

Energy Technology Data Exchange (ETDEWEB)

Blanchard, P [European Organization for Nuclear Research, Geneva (Switzerland); Seneor, R [European Organization for Nuclear Research, Geneva (Switzerland); Ecole Polytechnique, 75 - Paris (France). Centre de Physique Theorique)

1975-01-01

With the method of perturbative renormalization developed by Epstein and Glaser it is shown that Green's functions exist for theories with massless particles such as Q.E.D. and lambda:PHI/sup 2n/ theories. Growth properties are given in momentum space. In the case of Q.E.D., it is also shown that one can perform the physical mass renormalization.

Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)

Science.gov (United States)

Lahoche, Vincent; Oriti, Daniele

2017-01-01

We study the renormalization of a general field theory on the homogeneous space (SU(2)/ ≤ft. U(1)\\right){{}× d} with tensorial interaction and gauge invariance under the diagonal action of SU(2). We derive the power counting for arbitrary d. For the case d  =  4, we prove perturbative renormalizability to all orders via multi-scale analysis, study both the renormalized and effective perturbation series, and establish the asymptotic freedom of the model. We also outline a general power counting for the homogeneous space {{≤ft(SO(D)/SO(D-1)\\right)}× d} , of direct interest for quantum gravity models in arbitrary dimension, and point out the obstructions to the direct generalization of our results to these cases.

Regularization and renormalization of quantum field theory in curved space-time

International Nuclear Information System (INIS)

Bernard, C.; Duncan, A.

1977-01-01

It is proposed that field theories quantized in a curved space-time manifold can be conveniently regularized and renormalized with the aid of Pauli-Villars regulator fields. The method avoids the conceptual difficulties of covariant point-separation approaches, by starting always from a manifestly generally covariant action, and the technical limitations of the dimensional reqularization approach, which requires solution of the theory in arbitrary dimension in order to go beyond a weak-field expansion. An action is constructed which renormalizes the weak-field perturbation theory of a massive scalar field in two space-time dimensions--it is shown that the trace anomaly previously found in dimensional regularization and some point-separation calculations also arises in perturbation theory when the theory is Pauli-Villars regulated. One then studies a specific solvable two-dimensional model of a massive scalar field in a Robertson-Walker asymptotically flat universe. It is shown that the action previously considered leads, in this model, to a well defined finite expectation value for the stress-energy tensor. The particle production (less than 0 in/vertical bar/theta/sup mu nu/(x,t)/vertical bar/0 in greater than for t → + infinity) is computed explicitly. Finally, the validity of weak-field perturbation theory (in the appropriate range of parameters) is checked directly in the solvable model, and the trace anomaly computed in the asymptotic regions t→ +- infinity independently of any weak field approximation. The extension of the model to higher dimensions and the renormalization of interacting (scalar) field theories are briefly discussed

BPHZ renormalization in configuration space for the A4-model

Science.gov (United States)

Pottel, Steffen

2018-02-01

Recent developments for BPHZ renormalization performed in configuration space are reviewed and applied to the model of a scalar quantum field with quartic self-interaction. An extension of the results regarding the short-distance expansion and the Zimmermann identity is shown for a normal product, which is quadratic in the field operator. The realization of the equation of motion is computed for the interacting field and the relation to parametric differential equations is indicated.

Non-perturbative renormalization in coordinate space for Nf=2 maximally twisted mass fermions with tree-level Symanzik improved gauge action

International Nuclear Information System (INIS)

Cichy, Krzysztof; Adam Mickiewicz Univ., Poznan; Jansen, Karl; Korcyl, Piotr; Jagiellonian Univ., Krakow

2012-07-01

We present results of a lattice QCD application of a coordinate space renormalization scheme for the extraction of renormalization constants for flavour non-singlet bilinear quark operators. The method consists in the analysis of the small-distance behaviour of correlation functions in Euclidean space and has several theoretical and practical advantages, in particular: it is gauge invariant, easy to implement and has relatively low computational cost. The values of renormalization constants in the X-space scheme can be converted to the MS scheme via 4-loop continuum perturbative formulae. Our results for N f =2 maximally twisted mass fermions with tree-level Symanzik improved gauge action are compared to the ones from the RI-MOM scheme and show full agreement with this method. (orig.)

On mass-shell parametric space renormalization of PHI3 theory in six dimensions

International Nuclear Information System (INIS)

Smith, A.W.

1977-05-01

An on mass shell, parametric space renormalization procedure for phi 3 theory in six dimensions is defined and its formal equivalence to the usual Lagrangian counter procedure demonstrated. Two loop contributions to the self-energy are used as an illustration of the method. (author)

Dynamical renormalization group resummation of finite temperature infrared divergences

International Nuclear Information System (INIS)

Boyanovsky, D.; Vega, H.J. de; Boyanovsky, D.; Simionato, M.; Holman, R.; Simionato, M.

1999-01-01

We introduce the method of dynamical renormalization group to study relaxation and damping out of equilibrium directly in real time and apply it to the study of infrared divergences in scalar QED. This method allows a consistent resummation of infrared effects associated with the exchange of quasistatic transverse photons and leads to anomalous logarithmic relaxation of the form e -αampersandhthinsp;Tampersandhthinsp;tampersandhthinsp;ln[t/t 0 ] for hard momentum charged excitations. This is in contrast with the usual quasiparticle interpretation of charged collective excitations at finite temperature in the sense of exponential relaxation of a narrow width resonance for which the width is the imaginary part of the self-energy on shell. In the case of narrow resonances away from thresholds, this approach leads to the usual exponential relaxation. The hard thermal loop resummation program is incorporated consistently into the dynamical renormalization group yielding a picture of relaxation and damping phenomena in a plasma in real time that transcends the conceptual limitations of the quasiparticle picture and other types of resummation schemes. copyright 1999 The American Physical Society

G-Boson renormalizations and mixed symmetry states

International Nuclear Information System (INIS)

Scholten, O.

1986-01-01

In the IBA model the low-lying collective states are described in terms of a system of interacting s- and d-bosons. A boson can be interpreted as corresponding to collective J=0 or J=2 fermion pair states. As such the IBA model space can be seen as only a small subsector of the full shell model space. For medium heavy nuclei such a truncation of the model space is necessary to make calculations feasible. As is well known truncations of a model space make it necessary to renormalize the model parameters. In this work some renormalizations of the Hamiltonian and the E2 transition operator will be discussed. Special attention will be given to the implication of these renormalizations for the properties of mixed symmetry states. The effects of renormalization are obtained by considering the influence of fermion pair states that have been omitted from the model basis. Here the authors focus attention on the effect of the low-lying two particle J=4 state, referred to as g-boson or G-pair state. Renormalizations of the d-boson energy, the E2 effective charges, and symmetry force are discussed

Photon propagators and the definition and approximation of renormalized stress tensors in curved space-time

International Nuclear Information System (INIS)

Brown, M.R.; Ottewill, A.C.

1986-01-01

We present the symmetric Hadamard representation for scalar and photon Feynman Green's functions. We use these representations to give a simple definition for their associated renormalized stress tensors. We investigate the connection between the accuracy of the WKB approximation and the vanishing of the trace anomaly for these fields. We show that, although for scalars there is a direct connection, this is not true for photons, and we discuss the relevance of these results to the approximation of renormalized stress tensors in static Einstein space-times

Phase diagram of the Hubbard model with arbitrary band filling: renormalization group approach

International Nuclear Information System (INIS)

Cannas, Sergio A.; Cordoba Univ. Nacional; Tsallis, Constantino.

1991-01-01

The finite temperature phase diagram of the Hubbard model in d = 2 and d = 3 is calculated for arbitrary values of the parameter U/t and chemical potential μ using a quantum real space renormalization group. Evidence for a ferromagnetic phase at low temperatures is presented. (author). 15 refs., 5 figs

Momentum-subtraction renormalization techniques in curved space-time

Energy Technology Data Exchange (ETDEWEB)

Foda, O.

1987-10-01

Momentum-subtraction techniques, specifically BPHZ and Zimmermann's Normal Product algorithm, are introduced as useful tools in the study of quantum field theories in the presence of background fields. In a model of a self-interacting massive scalar field, conformally coupled to a general asymptotically-flat curved space-time with a trivial topology, momentum-subtractions are shown to respect invariance under general coordinate transformations. As an illustration, general expressions for the trace anomalies are derived, and checked by explicit evaluation of the purely gravitational contributions in the free field theory limit. Furthermore, the trace of the renormalized energy-momentum tensor is shown to vanish at the Gell-Mann Low eigenvalue as it should.

Momentum-subtraction renormalization techniques in curved space-time

International Nuclear Information System (INIS)

Foda, O.

1987-01-01

Momentum-subtraction techniques, specifically BPHZ and Zimmermann's Normal Product algorithm, are introduced as useful tools in the study of quantum field theories in the presence of background fields. In a model of a self-interacting massive scalar field, conformally coupled to a general asymptotically-flat curved space-time with a trivial topology, momentum-subtractions are shown to respect invariance under general coordinate transformations. As an illustration, general expressions for the trace anomalies are derived, and checked by explicit evaluation of the purely gravitational contributions in the free field theory limit. Furthermore, the trace of the renormalized energy-momentum tensor is shown to vanish at the Gell-Mann Low eigenvalue as it should

A geometric renormalization group in discrete quantum space-time

International Nuclear Information System (INIS)

Requardt, Manfred

2003-01-01

We model quantum space-time on the Planck scale as dynamical networks of elementary relations or time dependent random graphs, the time dependence being an effect of the underlying dynamical network laws. We formulate a kind of geometric renormalization group on these (random) networks leading to a hierarchy of increasingly coarse-grained networks of overlapping lumps. We provide arguments that this process may generate a fixed limit phase, representing our continuous space-time on a mesoscopic or macroscopic scale, provided that the underlying discrete geometry is critical in a specific sense (geometric long range order). Our point of view is corroborated by a series of analytic and numerical results, which allow us to keep track of the geometric changes, taking place on the various scales of the resolution of space-time. Of particular conceptual importance are the notions of dimension of such random systems on the various scales and the notion of geometric criticality

Renormalization and effective lagrangians

International Nuclear Information System (INIS)

Polchinski, J.

1984-01-01

There is a strong intuitive understanding of renormalization, due to Wilson, in terms of the scaling of effective lagrangians. We show that this can be made the basis for a proof of perturbative renormalization. We first study renormalizability in the language of renormalization group flows for a toy renormalization group equation. We then derive an exact renormalization group equation for a four-dimensional lambda PHI 4 theory with a momentum cutoff. We organize the cutoff dependence of the effective lagrangian into relevant and irrelevant parts, and derive a linear equation for the irrelevant part. A lengthy but straightforward argument establishes that the piece identified as irrelevant actually is so in perturbation theory. This implies renormalizability. The method extends immediately to any system in which a momentum-space cutoff can be used, but the principle is more general and should apply for any physical cutoff. Neither Weinberg's theorem nor arguments based on the topology of graphs are needed. (orig.)

Nonequilibrium dynamical renormalization group: Dynamical crossover from weak to infinite randomness in the transverse-field Ising chain

Science.gov (United States)

Heyl, Markus; Vojta, Matthias

2015-09-01

In this work we formulate the nonequilibrium dynamical renormalization group (ndRG). The ndRG represents a general renormalization-group scheme for the analytical description of the real-time dynamics of complex quantum many-body systems. In particular, the ndRG incorporates time as an additional scale which turns out to be important for the description of the long-time dynamics. It can be applied to both translational-invariant and disordered systems. As a concrete application, we study the real-time dynamics after a quench between two quantum critical points of different universality classes. We achieve this by switching on weak disorder in a one-dimensional transverse-field Ising model initially prepared at its clean quantum critical point. By comparing to numerically exact simulations for large systems, we show that the ndRG is capable of analytically capturing the full crossover from weak to infinite randomness. We analytically study signatures of localization in both real space and Fock space.

Absence of renormalization group pathologies near the critical temperature. Two examples

International Nuclear Information System (INIS)

Haller, K.; Kennedy, T.

1996-01-01

We consider real-space renormalization group transformations for Ising-type systems which are formally defined by where T(σ, σ') is a probability kernel, i.e., Σ σ' T(σ, σ') = 1, for every configuration σ. For each choice of the block spin configuration σ', let μ σ' , be the measure on spin configurations σ which is formally given by taking the probability of σ to be proportional to T(σ, σ') exp[ -H(σ)]. We give a condition which is sufficient to imply that the renormalized Hamiltonian H' is defined. Roughly speaking, the condition is that the collection of measures μ σ' is in the high-temperature phase uniformly in the block spin configuration σ'. The proof of this result uses methods of Olivieri and Picco. We use our theorem to prove that the first iteration of the renormalization group transformation is defined in the following two examples: decimation with spacing b = 2 on the square lattice with β c and the Kadanoff transformation with parameter p on the triangular lattice in a subset of the β, p plane that includes values of β greater than β c

Renormalized Lie perturbation theory

International Nuclear Information System (INIS)

Rosengaus, E.; Dewar, R.L.

1981-07-01

A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another

Non-perturbative renormalization in coordinate space for N{sub f}=2 maximally twisted mass fermions with tree-level Symanzik improved gauge action

Energy Technology Data Exchange (ETDEWEB)

Cichy, Krzysztof [DESY, Zeuthen (Germany). NIC; Adam Mickiewicz Univ., Poznan (Poland). Faculty of Physics; Jansen, Karl [DESY, Zeuthen (Germany). NIC; Korcyl, Piotr [DESY, Zeuthen (Germany). NIC; Jagiellonian Univ., Krakow (Poland). M. Smoluchowski Inst. of Physics

2012-07-15

We present results of a lattice QCD application of a coordinate space renormalization scheme for the extraction of renormalization constants for flavour non-singlet bilinear quark operators. The method consists in the analysis of the small-distance behaviour of correlation functions in Euclidean space and has several theoretical and practical advantages, in particular: it is gauge invariant, easy to implement and has relatively low computational cost. The values of renormalization constants in the X-space scheme can be converted to the MS scheme via 4-loop continuum perturbative formulae. Our results for N{sub f}=2 maximally twisted mass fermions with tree-level Symanzik improved gauge action are compared to the ones from the RI-MOM scheme and show full agreement with this method. (orig.)

Renormalization group analysis of a simple hierarchical fermion model

International Nuclear Information System (INIS)

Dorlas, T.C.

1991-01-01

A simple hierarchical fermion model is constructed which gives rise to an exact renormalization transformation in a 2-dimensional parameter space. The behaviour of this transformation is studied. It has two hyperbolic fixed points for which the existence of a global critical line is proven. The asymptotic behaviour of the transformation is used to prove the existence of the thermodynamic limit in a certain domain in parameter space. Also the existence of a continuum limit for these theories is investigated using information about the asymptotic renormalization behaviour. It turns out that the 'trivial' fixed point gives rise to a two-parameter family of continuum limits corresponding to that part of parameter space where the renormalization trajectories originate at this fixed point. Although the model is not very realistic it serves as a simple example of the appliclation of the renormalization group to proving the existence of the thermodynamic limit and the continuum limit of lattice models. Moreover, it illustrates possible complications that can arise in global renormalization group behaviour, and that might also be present in other models where no global analysis of the renormalization transformation has yet been achieved. (orig.)

Renormalization of supersymmetric theories

International Nuclear Information System (INIS)

Pierce, D.M.

1998-06-01

The author reviews the renormalization of the electroweak sector of the standard model. The derivation also applies to the minimal supersymmetric standard model. He discusses regularization, and the relation between the threshold corrections and the renormalization group equations. He considers the corrections to many precision observables, including M W and sin 2 θ eff . He shows that global fits to the data exclude regions of supersymmetric model parameter space and lead to lower bounds on superpartner masses

Break-collapse method for resistor networks-renormalization group applications

International Nuclear Information System (INIS)

Tsallis, C.; Coniglio, A.; Redner, S.

1982-01-01

The break-collapse method recently introduced for the q-state Potts model is adapted for resistor networks. This method greatly simplifies the calculation of the conductance of an arbitrary two-terminal d-dimensional array of conductances, obviating the use of either Kirchhoff's laws or the star-triangle or similiar transformations. Related properties are discussed as well. An illustrative real-space renormalization-group treatment of the random resistor problem on the square lattice is presented; satisfactory results are obtained. (Author) [pt

The metric on field space, functional renormalization, and metric–torsion quantum gravity

International Nuclear Information System (INIS)

Reuter, Martin; Schollmeyer, Gregor M.

2016-01-01

Searching for new non-perturbatively renormalizable quantum gravity theories, functional renormalization group (RG) flows are studied on a theory space of action functionals depending on the metric and the torsion tensor, the latter parameterized by three irreducible component fields. A detailed comparison with Quantum Einstein–Cartan Gravity (QECG), Quantum Einstein Gravity (QEG), and “tetrad-only” gravity, all based on different theory spaces, is performed. It is demonstrated that, over a generic theory space, the construction of a functional RG equation (FRGE) for the effective average action requires the specification of a metric on the infinite-dimensional field manifold as an additional input. A modified FRGE is obtained if this metric is scale-dependent, as it happens in the metric–torsion system considered.

A renormalization group study of persistent current in a quasiperiodic ring

Energy Technology Data Exchange (ETDEWEB)

Dutta, Paramita [Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata-700 064 (India); Maiti, Santanu K., E-mail: santanu.maiti@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata-700 108 (India); Karmakar, S.N. [Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata-700 064 (India)

2014-04-01

We propose a real-space renormalization group approach for evaluating persistent current in a multi-channel quasiperiodic Fibonacci tight-binding ring based on a Green's function formalism. Unlike the traditional methods, the present scheme provides a powerful tool for the theoretical description of persistent current with a very high degree of accuracy in large periodic and quasiperiodic rings, even in the micron scale range, which emphasizes the merit of this work.

Dynamical renormalization group approach to relaxation in quantum field theory

International Nuclear Information System (INIS)

Boyanovsky, D.; Vega, H.J. de

2003-01-01

The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG). Linear response is invoked to set up the renormalized initial value problem to study the dynamics of the expectation value of quantum fields. The perturbative solution of the equations of motion for the field expectation values of quantum fields as well as the evolution of quantum states features secular terms, namely terms that grow in time and invalidate the perturbative expansion for late times. The DRG provides a consistent framework to resum these secular terms and yields a uniform asymptotic expansion at long times. Several relevant cases are studied in detail, including those of threshold infrared divergences which appear in gauge theories at finite temperature and lead to anomalous relaxation. In these cases the DRG is shown to provide a resummation akin to Bloch-Nordsieck but directly in real time and that goes beyond the scope of Bloch-Nordsieck and Dyson resummations. The nature of the resummation program is discussed in several examples. The DRG provides a framework that is consistent, systematic, and easy to implement to study the non-equilibrium relaxational dynamics directly in real time that does not rely on the concept of quasiparticle widths

Differential renormalization of gauge theories

International Nuclear Information System (INIS)

Aguila, F. del; Perez-Victoria, M.

1998-01-01

The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author)

Introduction to the nonequilibrium functional renormalization group

International Nuclear Information System (INIS)

Berges, J.; Mesterházy, D.

2012-01-01

In these lectures we introduce the functional renormalization group out of equilibrium. While in thermal equilibrium typically a Euclidean formulation is adequate, nonequilibrium properties require real-time descriptions. For quantum systems specified by a given density matrix at initial time, a generating functional for real-time correlation functions can be written down using the Schwinger-Keldysh closed time path. This can be used to construct a nonequilibrium functional renormalization group along similar lines as for Euclidean field theories in thermal equilibrium. Important differences include the absence of a fluctuation-dissipation relation for general out-of-equilibrium situations. The nonequilibrium renormalization group takes on a particularly simple form at a fixed point, where the corresponding scale-invariant system becomes independent of the details of the initial density matrix. We discuss some basic examples, for which we derive a hierarchy of fixed point solutions with increasing complexity from vacuum and thermal equilibrium to nonequilibrium. The latter solutions are then associated to the phenomenon of turbulence in quantum field theory.

Differential renormalization of gauge theories

Energy Technology Data Exchange (ETDEWEB)

Aguila, F. del; Perez-Victoria, M. [Dept. de Fisica Teorica y del Cosmos, Universidad de Granada, Granada (Spain)

1998-10-01

The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author) 9 refs, 1 fig., 1 tab

Implementation of rigorous renormalization group method for ground space and low-energy states of local Hamiltonians

Science.gov (United States)

Roberts, Brenden; Vidick, Thomas; Motrunich, Olexei I.

2017-12-01

The success of polynomial-time tensor network methods for computing ground states of certain quantum local Hamiltonians has recently been given a sound theoretical basis by Arad et al. [Math. Phys. 356, 65 (2017), 10.1007/s00220-017-2973-z]. The convergence proof, however, relies on "rigorous renormalization group" (RRG) techniques which differ fundamentally from existing algorithms. We introduce a practical adaptation of the RRG procedure which, while no longer theoretically guaranteed to converge, finds matrix product state ansatz approximations to the ground spaces and low-lying excited spectra of local Hamiltonians in realistic situations. In contrast to other schemes, RRG does not utilize variational methods on tensor networks. Rather, it operates on subsets of the system Hilbert space by constructing approximations to the global ground space in a treelike manner. We evaluate the algorithm numerically, finding similar performance to density matrix renormalization group (DMRG) in the case of a gapped nondegenerate Hamiltonian. Even in challenging situations of criticality, large ground-state degeneracy, or long-range entanglement, RRG remains able to identify candidate states having large overlap with ground and low-energy eigenstates, outperforming DMRG in some cases.

Perturbatively improving RI-MOM renormalization constants

Energy Technology Data Exchange (ETDEWEB)

Constantinou, M.; Costa, M.; Panagopoulos, H. [Cyprus Univ. (Cyprus). Dept. of Physics; Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences; Schhierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2013-03-15

The determination of renormalization factors is of crucial importance in lattice QCD. They relate the observables obtained on the lattice to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. In this paper we investigate a method to suppress these artifacts by subtracting one-loop contributions to renormalization factors calculated in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of contributions proportional to the square of the lattice spacing.

Renormalization and plasma physics

Energy Technology Data Exchange (ETDEWEB)

Krommes, J.A.

1980-02-01

A review is given of modern theories of statistical dynamics as applied to problems in plasma physics. The derivation of consistent renormalized kinetic equations is discussed, first heuristically, later in terms of powerful functional techniques. The equations are illustrated with models of various degrees of idealization, including the exactly soluble stochastic oscillator, a prototype for several important applications. The direct-interaction approximation is described in detail. Applications discussed include test particle diffusion and the justification of quasilinear theory, convective cells, E vector x B vector turbulence, the renormalized dielectric function, phase space granulation, and stochastic magnetic fields.

Renormalization and plasma physics

International Nuclear Information System (INIS)

Krommes, J.A.

1980-02-01

A review is given of modern theories of statistical dynamics as applied to problems in plasma physics. The derivation of consistent renormalized kinetic equations is discussed, first heuristically, later in terms of powerful functional techniques. The equations are illustrated with models of various degrees of idealization, including the exactly soluble stochastic oscillator, a prototype for several important applications. The direct-interaction approximation is described in detail. Applications discussed include test particle diffusion and the justification of quasilinear theory, convective cells, E vector x B vector turbulence, the renormalized dielectric function, phase space granulation, and stochastic magnetic fields

Renormalization-group studies of antiferromagnetic chains. I. Nearest-neighbor interactions

International Nuclear Information System (INIS)

Rabin, J.M.

1980-01-01

The real-space renormalization-group method introduced by workers at the Stanford Linear Accelerator Center (SLAC) is used to study one-dimensional antiferromagnetic chains at zero temperature. Calculations using three-site blocks (for the Heisenberg-Ising model) and two-site blocks (for the isotropic Heisenberg model) are compared with exact results. In connection with the two-site calculation a duality transformation is introduced under which the isotropic Heisenberg model is self-dual. Such duality transformations can be defined for models other than those considered here, and may be useful in various block-spin calculations

Potts ferromagnet correlation length in hypercubic lattices: Renormalization - group approach

International Nuclear Information System (INIS)

Curado, E.M.F.; Hauser, P.R.

1984-01-01

Through a real space renormalization group approach, the q-state Potts ferromagnet correlation length on hierarchical lattices is calculated. These hierarchical lattices are build in order to simulate hypercubic lattices. The high-and-low temperature correlation length asymptotic behaviours tend (in the Ising case) to the Bravais lattice correlation length ones when the size of the hierarchical lattice cells tends to infinity. It is conjectured that the asymptotic behaviours several values of q and d (dimensionality) so obtained are correct. Numerical results are obtained for the full temperature range of the correlation length. (Author) [pt

Negative norm states in de Sitter space and QFT without renormalization procedure

International Nuclear Information System (INIS)

Takook, M.V.

2002-01-01

In recent papers, 1,2 it has been shown that the presence of negative norm states or negative frequency solutions are indispensable for a fully covariant quantization of the minimally coupled scalar field in de Sitter space. Their presence, while leaving unchanged the physical content of the theory, offers the advantage of eliminating any ultraviolet divergence in the vacuum energy 2 and infrared divergence in the two point function. 3 We attempt here to extend this method to the interacting quantum field in Minkowski space-time. As an illustration of the procedure, we consider the λϕ 4 theory in Minkowski space-time. The mathematical consequences of this method is the disappearance of the ultraviolet divergence to the one-loop approximation. This means, the effect of these auxiliary negative norm states is to allow an automatic renormalization of the theory in this approximation. (author)

Renormalization in p-adic quantum field theory

International Nuclear Information System (INIS)

Smirnov, V.A.

1990-01-01

A version of p-adic perturbative Euclidean quantum field theory is presented. It is based on the new type of propagator which happens to be rather natural for p-adic space-time. Low-order Feynamn diagrams are explicity calculated and typical renormalization schemes are introduced: analytic, dimensional and BPHZ renormalizations. The calculations show that in p-adic Feynman integrals only logarithmic divergences appear. 14 refs.; 1 fig

Renormalization of QED with planar binary trees

International Nuclear Information System (INIS)

Brouder, C.

2001-01-01

The Dyson relations between renormalized and bare photon and electron propagators Z 3 anti D(q)=D(q) and Z 2 anti S(q)=S(q) are expanded over planar binary trees. This yields explicit recursive relations for the terms of the expansions. When all the trees corresponding to a given power of the electron charge are summed, recursive relations are obtained for the finite coefficients of the renormalized photon and electron propagators. These relations significantly decrease the number of integrals to carry out, as compared to the standard Feynman diagram technique. In the case of massless quantum electrodynamics (QED), the relation between renormalized and bare coefficients of the perturbative expansion is given in terms of a Hopf algebra structure. (orig.)

Nonperturbative Renormalization of Composite Operators with Overlap Fermions

Energy Technology Data Exchange (ETDEWEB)

J.B. Zhang; N. Mathur; S.J. Dong; T. Draper; I. Horvath; F. X. Lee; D.B. Leinweber; K.F. Liu; A.G. Williams

2005-12-01

We compute non-perturbatively the renormalization constants of composite operators on a quenched 16{sup 3} x 28 lattice with lattice spacing a = 0.20 fm for the overlap fermion by using the regularization independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations Z{sub A} = Z{sub V} and Z{sub S} = Z{sub P} and find that they agree well (less than 1%) above {mu} = 1.6 GeV. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the {ovr MS} scheme. The wave-function renormalization Z{sub {psi}} is determined from the vertex function of the axial current and Z{sub A} from the chiral Ward identity. Finally, we examine the finite quark mass behavior for the renormalization factors of the quark bilinear operators. We find that the (pa){sup 2} errors of the vertex functions are small and the quark mass dependence of the renormalization factors to be quite weak.

Dynamical renormalization group approach to transport in ultrarelativistic plasmas: The electrical conductivity in high temperature QED

International Nuclear Information System (INIS)

Boyanovsky, Daniel; Vega, Hector J. de; Wang Shangyung

2003-01-01

The dc electrical conductivity of an ultrarelativistic QED plasma is studied in real time by implementing the dynamical renormalization group. The conductivity is obtained from the real-time dependence of a dissipative kernel closely related to the retarded photon polarization. Pinch singularities in the imaginary part of the polarization are manifest as secular terms that grow in time in the perturbative expansion of this kernel. The leading secular terms are studied explicitly and it is shown that they are insensitive to the anomalous damping of hard fermions as a result of a cancellation between self-energy and vertex corrections. The resummation of the secular terms via the dynamical renormalization group leads directly to a renormalization group equation in real time, which is the Boltzmann equation for the (gauge invariant) fermion distribution function. A direct correspondence between the perturbative expansion and the linearized Boltzmann equation is established, allowing a direct identification of the self-energy and vertex contributions to the collision term. We obtain a Fokker-Planck equation in momentum space that describes the dynamics of the departure from equilibrium to leading logarithmic order in the coupling. This equation determines that the transport time scale is given by t tr =24 π/e 4 T ln(1/e). The solution of the Fokker-Planck equation approaches asymptotically the steady-state solution as ∼e -t/(4.038...t tr ) . The steady-state solution leads to the conductivity σ=15.698 T/e 2 ln(1/e) to leading logarithmic order. We discuss the contributions beyond leading logarithms as well as beyond the Boltzmann equation. The dynamical renormalization group provides a link between linear response in quantum field theory and kinetic theory

Holographic Renormalization in Dense Medium

International Nuclear Information System (INIS)

Park, Chanyong

2014-01-01

The holographic renormalization of a charged black brane with or without a dilaton field, whose dual field theory describes a dense medium at finite temperature, is investigated in this paper. In a dense medium, two different thermodynamic descriptions are possible due to an additional conserved charge. These two different thermodynamic ensembles are classified by the asymptotic boundary condition of the bulk gauge field. It is also shown that in the holographic renormalization regularity of all bulk fields can reproduce consistent thermodynamic quantities and that the Bekenstein-Hawking entropy is nothing but the renormalized thermal entropy of the dual field theory. Furthermore, we find that the Reissner-Nordström AdS black brane is dual to a theory with conformal matter as expected, whereas a charged black brane with a nontrivial dilaton profile is mapped to a theory with nonconformal matter although its leading asymptotic geometry still remains as AdS space

Effective field renormalization group approach for Ising lattice spin systems

Science.gov (United States)

Fittipaldi, Ivon P.

1994-03-01

A new applicable real-space renormalization group framework (EFRG) for computing the critical properties of Ising lattice spin systems is presented. The method, which follows up the same strategy of the mean-field renormalization group scheme (MFRG), is based on rigorous Ising spin identities and utilizes a convenient differential operator expansion technique. Within this scheme, in contrast with the usual mean-field type of equation of state, all the relevant self-spin correlations are taken exactly into account. The results for the critical coupling and the critical exponent v, for the correlation length, are very satisfactory and it is shown that this technique leads to rather accurate results which represent a remarkable improvement on those obtained from the standard MFRG method. In particular, it is shown that the present EFRG approach correctly distinguishes the geometry of the lattice structure even when employing its simplest size-cluster version. Owing to its simplicity we also comment on the wide applicability of the present method to problems in crystalline and disordered Ising spin systems.

Renormalization Scale-Fixing for Complex Scattering Amplitudes

Energy Technology Data Exchange (ETDEWEB)

Brodsky, Stanley J.; /SLAC; Llanes-Estrada, Felipe J.; /Madrid U.

2005-12-21

We show how to fix the renormalization scale for hard-scattering exclusive processes such as deeply virtual meson electroproduction by applying the BLM prescription to the imaginary part of the scattering amplitude and employing a fixed-t dispersion relation to obtain the scale-fixed real part. In this way we resolve the ambiguity in BLM renormalization scale-setting for complex scattering amplitudes. We illustrate this by computing the H generalized parton distribution at leading twist in an analytic quark-diquark model for the parton-proton scattering amplitude which can incorporate Regge exchange contributions characteristic of the deep inelastic structure functions.

A complete non-perturbative renormalization prescription for quasi-PDFs

Energy Technology Data Exchange (ETDEWEB)

Alexandrou, Constantia [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; The Cyprus Institute, Nicosia (Cyprus); Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Adam Mickiewicz Univ., Poznan (Poland). Faculty of Physics; Constantinou, Martha [Temple Univ., Philadelphia, PA (United States). Dept. of Physics; Hadjiyiannakou, Kyriakos [The Cyprus Institute, Nicosia (Cyprus); Jansen, Karl; Steffens, Fernanda [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Panagopoulos, Haralambos [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Collaboration: European Twisted Mass Collaboration

2017-06-15

In this work we present, for the first time, the non-perturbative renormalization for the unpolarized, helicity and transversity quasi-PDFs, in an RI{sup '} scheme. The proposed prescription addresses simultaneously all aspects of renormalization: logarithmic divergences, finite renormalization as well as the linear divergence which is present in the matrix elements of fermion operators with Wilson lines. Furthermore, for the case of the unpolarized quasi-PDF, we describe how to eliminate the unwanted mixing with the twist-3 scalar operator. We utilize perturbation theory for the one-loop conversion factor that brings the renormalization functions to the MS-scheme at a scale of 2 GeV. We also explain how to improve the estimates on the renormalization functions by eliminating lattice artifacts. The latter can be computed in one-loop perturbation theory and to all orders in the lattice spacing. We apply the methodology for the renormalization to an ensemble of twisted mass fermions with N{sub f}=2+1+1 dynamical quarks, and a pion mass of around 375 MeV.

Dimensional regularization in position space and a forest formula for regularized Epstein-Glaser renormalization

Energy Technology Data Exchange (ETDEWEB)

Keller, Kai Johannes

2010-04-15

The present work contains a consistent formulation of the methods of dimensional regularization (DimReg) and minimal subtraction (MS) in Minkowski position space. The methods are implemented into the framework of perturbative Algebraic Quantum Field Theory (pAQFT). The developed methods are used to solve the Epstein-Glaser recursion for the construction of time-ordered products in all orders of causal perturbation theory. A solution is given in terms of a forest formula in the sense of Zimmermann. A relation to the alternative approach to renormalization theory using Hopf algebras is established. (orig.)

Dimensional regularization in position space and a forest formula for regularized Epstein-Glaser renormalization

International Nuclear Information System (INIS)

Keller, Kai Johannes

2010-04-01

The present work contains a consistent formulation of the methods of dimensional regularization (DimReg) and minimal subtraction (MS) in Minkowski position space. The methods are implemented into the framework of perturbative Algebraic Quantum Field Theory (pAQFT). The developed methods are used to solve the Epstein-Glaser recursion for the construction of time-ordered products in all orders of causal perturbation theory. A solution is given in terms of a forest formula in the sense of Zimmermann. A relation to the alternative approach to renormalization theory using Hopf algebras is established. (orig.)

Simple perturbative renormalization scheme for supersymmetric gauge theories

Energy Technology Data Exchange (ETDEWEB)

Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)

1983-06-30

We show that the manifestly supersymmetric and gauge-invariant results of Supersymmetric Dimensional renormalization (SDR) are reproduceable through a simple, and mathematically consistent perturbative renormalization technique, where regularization is attained via a map that deforms the momentum space Feynman integrands in a specific way. In particular, it introduces a multiplicative factor of ((p+q)/..delta..)/sup -/delta in each momentum-space loop integral, where p is the magnitude of the loop momentum, q is an arbitrary constant to be chosen as will be explained, thus compensating for loss of translation invariance in p, ..lambda.. is a renormalization mass, and delta is a suitable non-integer: the analog of epsilon in dimensional schemes. All Dirac algebra and integration are four-dimensional, and renormalization is achieved by subtracting poles in delta, followed by setting delta->O. The mathematical inconsistencies of SDR are evaded by construction, since the numbers of fermion and boson degrees of freedom remain unchanged but analytic continuation in the number of dimensions is bypassed. Thus, the technique is equally viable in component and in superfield formalisms, and all anomalies are realized. The origin of the chiral anomaly is that no choice of q satisfies both gauge and chiral Ward identities simultaneously.

Transformation of renormalization groups in 2N-component fermion hierarchical model

International Nuclear Information System (INIS)

Stepanov, R.G.

2006-01-01

The 2N-component fermion model on the hierarchical lattice is studied. The explicit formulae for renormalization groups transformation in the space of coefficients setting the Grassmannian-significant density of the free measure are presented. The inverse transformation of the renormalization group is calculated. The definition of immovable points of renormalization groups is reduced to solving the set of algebraic equations. The interesting connection between renormalization group transformations in boson and fermion hierarchical models is found out. It is shown that one transformation is obtained from other one by the substitution of N on -N [ru

Effective-field renormalization-group method for Ising systems

Science.gov (United States)

Fittipaldi, I. P.; De Albuquerque, D. F.

1992-02-01

A new applicable effective-field renormalization-group (ERFG) scheme for computing critical properties of Ising spins systems is proposed and used to study the phase diagrams of a quenched bond-mixed spin Ising model on square and Kagomé lattices. The present EFRG approach yields results which improves substantially on those obtained from standard mean-field renormalization-group (MFRG) method. In particular, it is shown that the EFRG scheme correctly distinguishes the geometry of the lattice structure even when working with the smallest possible clusters, namely N'=1 and N=2.

Percolation with first-and-second neighbour bonds: a renormalization-group calculation of critical exponents

International Nuclear Information System (INIS)

Riera, R.; Oliveira, P.M.C. de; Chaves, C.M.G.F.; Queiroz, S.L.A. de.

1980-04-01

A real-space renormalization group approach for the bond percolation problem in a square lattice with first- and second- neighbour bonds is proposed. The respective probabilities are treated, as independent variables. Two types of cells are constructed. In one of them the lattice is considered as two interpenetrating sublattices, first-neighbour bonds playing the role of intersublattice links. This allows the calculation of both critical exponents ν and γ, without resorting to any external field. Values found for the critical indices are in good agreement with data available in the literature. The phase diagram in parameter space is also obtained in each case. (Author) [pt

Point transformations and renormalization in the unitary gauge. III. Renormalization effects

International Nuclear Information System (INIS)

Sherry, T.N.

1976-06-01

An analysis of two simple gauge theory models is continued using point transformations rather than gauge transformations. The renormalization constants are examined directly in two gauges, the renormalization (Landau) and unitary gauges. The result is that the individual coupling constant renormalizations are identical when calculated in each of the above two gauges, although the wave-function and proper vertex renormalizations differ

Renormalization group critical frontier of the three-dimensional bond-dilute Ising ferromagnet

International Nuclear Information System (INIS)

Chao, N.-C.; Schwaccheim, G.; Tsallis, C.

1981-01-01

The critical frontier (as well as the thermal type critical exponents) associated to the quenched bond-dilute spin - 1/2 Ising ferromagnet in the simple cubic lattice is approximately calculated within a real space renormalization group framework in two different versions. Both lead to qualitatively satisfactory critical frontiers, although one of them provides an unphysical fixed point (which seem to be related to the three-dimensionality of the system) besides the expected pure ones; its effects tend to disappear for increasingly large clusters. Through an extrapolation procedure the (unknown) critical frontier is approximately located. (Author) [pt

Consciousness viewed in the framework of brain phase space dynamics, criticality, and the Renormalization Group

International Nuclear Information System (INIS)

Werner, Gerhard

2013-01-01

The topic of this paper will be addressed in three stages: I will first review currently prominent theoretical conceptualizations of the neurobiology of consciousness and, where appropriate, identify ill-advised and flawed notions in theoretical neuroscience that may impede viewing consciousness as a phenomenon in the physics of brain. In this context, I will also introduce relevant facts that tend not to receive adequate attention in much of the current consciousness discourse. Next, I will review the evidence that accrued in the last decade that identifies the resting brain as being in a state of criticality. In the framework of state phase dynamics of statistical physics, this observational evidence also entails that the resting brain is poised at the brink of a second order phase transition. On this basis, I will in the third stage propose applying the framework of the Renormalization Group to viewing consciousness as a phenomenon in statistical physics. In physics, concepts of phase space transitions and the Renormalization Group are powerful tools for interpreting phenomena involving many scales of length and time in complex systems. The significance of these concepts lies in their accounting for the emergence of different levels of new collective behaviors in complex systems, each level with its distinct macroscopic physics, organization, and laws, as a new pattern of reality. In this framework, I propose to view subjectivity as the symbolic description of the physical brain state of consciousness that emerges as one of the levels of phase transitions of the brain-body-environment system, along the trajectory of Renormalization Group Transformations

NLO renormalization in the Hamiltonian truncation

Science.gov (United States)

Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

2017-09-01

Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.

Covariant Derivatives and the Renormalization Group Equation

Science.gov (United States)

Dolan, Brian P.

The renormalization group equation for N-point correlation functions can be interpreted in a geometrical manner as an equation for Lie transport of amplitudes in the space of couplings. The vector field generating the diffeomorphism has components given by the β functions of the theory. It is argued that this simple picture requires modification whenever any one of the points at which the amplitude is evaluated becomes close to any other. This modification necessitates the introduction of a connection on the space of couplings and new terms appear in the renormalization group equation involving covariant derivatives of the β function and the curvature associated with the connection. It is shown how the connection is related to the operator product expansion coefficients, but there remains an arbitrariness in its definition.

Influence of Inter and Intra-rows Spacing on Yield and Yield ...

African Journals Online (AJOL)

Abyssinia

yield and yield components of fresh market(Bishola) and processing (Cochoro) tomato cultivars. ... row spacing had a significant effect on plan canopy width, above ground dry biomass, ... Poor varietal performance and management practices that includeinter and intra-row spacing ..... of assimilate export from the leaves.

Renormalization Group Reduction of Non Integrable Hamiltonian Systems

International Nuclear Information System (INIS)

Tzenov, Stephan I.

2002-01-01

Based on Renormalization Group method, a reduction of non integratable multi-dimensional Hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density and for the amplitudes of the angular modes have been derived. It has been shown that these equations are precisely the Renormalization Group equations. As an application of the approach developed, the modulational diffusion in one-and-a-half degrees of freedom dynamical system has been studied in detail

Renormalization Methods - A Guide For Beginners

International Nuclear Information System (INIS)

Cardy, J

2004-01-01

The stated goal of this book is to fill a perceived gap between undergraduate texts on critical phenomena and advanced texts on quantum field theory, in the general area of renormalization methods. It is debatable whether this gap really exists nowadays, as a number of books have appeared in which it is made clear that field-theoretic renormalization group methods are not the preserve of particle theory, and indeed are far more easily appreciated in the contexts of statistical and condensed matter physics. Nevertheless, this volume does have a fresh aspect to it, perhaps because of the author's background in fluid dynamics and turbulence theory, rather than through the more traditional migration from particle physics. The book begins at a very elementary level, in an effort to motivate the use of renormalization methods. This is a worthy effort, but it is likely that most of this section will be thought too elementary by readers wanting to get their teeth into the subject, while those for whom this section is apparently written are likely to find the later chapters rather challenging. The author's particular approach then leads him to emphasise the role of renormalized perturbation theory (rather than the renormalization group) in a number of problems, including non-linear systems and turbulence. Some of these ideas will be novel and perhaps even surprising to traditionally trained field theorists. Most of the rest of the book is on far more familiar territory: the momentum-space renormalization group, epsilon-expansion, and so on. This is standard stuff, and, like many other textbooks, it takes a considerable chunk of the book to explain all the formalism. As a result, there is only space to discuss the standard φ 4 field theory as applied to the Ising model (even the N-vector model is not covered) so that no impression is conveyed of the power and extent of all the applications and generalizations of the techniques. It is regrettable that so much space is spent

A simple perturbative renormalization scheme for supersymmetric gauge theories

International Nuclear Information System (INIS)

Foda, O.E.

1983-01-01

We show that the manifestly supersymmetric and gauge-invariant results of Supersymmetric Dimensional renormalization (SDR) are reproduceable through a simple, and mathematically consistent perturbative renormalization technique, where regularization is attained via a map that deforms the momentum space Feynman integrands in a specific way. In particular, it introduces a multiplicative factor of [(p+q)/δ] - delta in each momentum-space loop integral, where p is the magnitude of the loop momentum, q is an arbitrary constant to be chosen as will be explained, thus compensating for loss of translation invariance in p, #betta# is a renormalization mass, and delta is a suitable non-integer: the analog of epsilon in dimensional schemes. All Dirac algebra and integration are four-dimensional, and renormalization is achieved by subtracting poles in delta, followed by setting delta->O. The mathematical inconsistencies of SDR are evaded by construction, since the numbers of fermion and boson degrees of freedom remain unchanged but analytic continuation in the number of dimensions is bypassed. Thus, the technique is equally viable in component and in superfield formalisms, and all anomalies are realized. The origin of the chiral anomaly is that no choice of q satisfies both gauge and chiral Ward identities simultaneously. (orig.)

Nonperturbative renormalization of nonlocal quark bilinears for quasi-PDFs on the lattice using an auxiliary field

Energy Technology Data Exchange (ETDEWEB)

Green, Jeremy; Jansen, Karl; Steffens, Fernanda [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

2017-07-15

Quasi-PDFs provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking, and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the MS scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters we show the effect of renormalization on nucleon matrix elements with pion mass approximately 370 MeV, and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.

Nonperturbative renormalization of nonlocal quark bilinears for quasi-PDFs on the lattice using an auxiliary field

International Nuclear Information System (INIS)

Green, Jeremy; Jansen, Karl; Steffens, Fernanda

2017-07-01

Quasi-PDFs provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking, and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the MS scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters we show the effect of renormalization on nucleon matrix elements with pion mass approximately 370 MeV, and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.

Renormalization constants for 2-twist operators in twisted mass QCD

International Nuclear Information System (INIS)

Alexandrou, C.; Constantinou, M.; Panagopoulos, H.; Stylianou, F.; Korzec, T.

2011-01-01

Perturbative and nonperturbative results on the renormalization constants of the fermion field and the twist-2 fermion bilinears are presented with emphasis on the nonperturbative evaluation of the one-derivative twist-2 vector and axial-vector operators. Nonperturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations have been performed for pion masses in the range of about 450-260 MeV and at three values of the lattice spacing a corresponding to β=3.9, 4.05, 4.20. Subtraction of O(a 2 ) terms is carried out by performing the perturbative evaluation of these operators at 1-loop and up to O(a 2 ). The renormalization conditions are defined in the RI ' -MOM scheme, for both perturbative and nonperturbative results. The renormalization factors, obtained for different values of the renormalization scale, are evolved perturbatively to a reference scale set by the inverse of the lattice spacing. In addition, they are translated to MS at 2 GeV using 3-loop perturbative results for the conversion factors.

Space Weather and Real-Time Monitoring

Directory of Open Access Journals (Sweden)

S Watari

2009-04-01

Full Text Available Recent advance of information and communications technology enables to collect a large amount of ground-based and space-based observation data in real-time. The real-time data realize nowcast of space weather. This paper reports a history of space weather by the International Space Environment Service (ISES in association with the International Geophysical Year (IGY and importance of real-time monitoring in space weather.

Renormalization group flows and fixed points for a scalar field in curved space with nonminimal F (ϕ )R coupling

Science.gov (United States)

Merzlikin, Boris S.; Shapiro, Ilya L.; Wipf, Andreas; Zanusso, Omar

2017-12-01

Using covariant methods, we construct and explore the Wetterich equation for a nonminimal coupling F (ϕ )R of a quantized scalar field to the Ricci scalar of a prescribed curved space. This includes the often considered nonminimal coupling ξ ϕ2R as a special case. We consider the truncations without and with scale- and field-dependent wave-function renormalization in dimensions between four and two. Thereby the main emphasis is on analytic and numerical solutions of the fixed point equations and the behavior in the vicinity of the corresponding fixed points. We determine the nonminimal coupling in the symmetric and spontaneously broken phases with vanishing and nonvanishing average fields, respectively. Using functional perturbative renormalization group methods, we discuss the leading universal contributions to the RG flow below the upper critical dimension d =4 .

Renormalization and scaling behavior of non-Abelian gauge fields in curved spacetime

International Nuclear Information System (INIS)

Leen, T.K.

1983-01-01

In this article we discuss the one loop renormalization and scaling behavior of non-Abelian gauge field theories in a general curved spacetime. A generating functional is constructed which forms the basis for both the perturbation expansion and the Ward identifies. Local momentum space representations for the vector and ghost particles are developed and used to extract the divergent parts of Feynman integrals. The one loop diagram for the ghost propagator and the vector-ghost vertex are shown to have no divergences not present in Minkowski space. The Ward identities insure that this is true for the vector propagator as well. It is shown that the above renormalizations render the three- and four-vector vertices finite. Finally, a renormalization group equation valid in curved spacetimes is derived. Its solution is given and the theory is shown to be asymptotically free as in Minkowski space

Renormalization group in quantum mechanics

International Nuclear Information System (INIS)

Polony, J.

1996-01-01

The running coupling constants are introduced in quantum mechanics and their evolution is described with the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The Hamiltonian and the Lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models. Copyright copyright 1996 Academic Press, Inc

Renormalization group theory of earthquakes

Directory of Open Access Journals (Sweden)

H. Saleur

1996-01-01

Full Text Available We study theoretically the physical origin of the proposed discrete scale invariance of earthquake processes, at the origin of the universal log-periodic corrections to scaling, recently discovered in regional seismic activity (Sornette and Sammis (1995. The discrete scaling symmetries which may be present at smaller scales are shown to be robust on a global scale with respect to disorder. Furthermore, a single complex exponent is sufficient in practice to capture the essential properties of the leading correction to scaling, whose real part may be renormalized by disorder, and thus be specific to the system. We then propose a new mechanism for discrete scale invariance, based on the interplay between dynamics and disorder. The existence of non-linear corrections to the renormalization group flow implies that an earthquake is not an isolated 'critical point', but is accompanied by an embedded set of 'critical points', its foreshocks and any subsequent shocks for which it may be a foreshock.

Renormalization of an abelian gauge theory in stochastic quantization

International Nuclear Information System (INIS)

Chaturvedi, S.; Kapoor, A.K.; Srinivasan, V.

1987-01-01

The renormalization of an abelian gauge field coupled to a complex scalar field is discussed in the stochastic quantization method. The super space formulation of the stochastic quantization method is used to derive the Ward Takahashi identities associated with supersymmetry. These Ward Takahashi identities together with previously derived Ward Takahashi identities associated with gauge invariance are shown to be sufficient to fix all the renormalization constants in terms of scaling of the fields and of the parameters appearing in the stochastic theory. (orig.)

Algebraic renormalization. Perturbative renormalization, symmetries and anomalies

International Nuclear Information System (INIS)

Piguet, O.

1995-01-01

This book is an introduction to the algebraic method in the perturbative renormalization of relativistic quantum field theory. After a general introduction to renormalized perturbation theory the quantum action principle and Ward identities are described. Then Yang-Mills gauge theories are considered. Thereafter the BRS cohomology and descent equations are described. Then nonrenormalization theorems and topological field theories are considered. Finally an application to the bosonic string is described. (HSI)

The Kadanoff lower-bound variational renormalization group applied to an SU(2) lattice spin model

International Nuclear Information System (INIS)

Thorleifsson, G.; Damgaard, P.H.

1990-07-01

We apply the variational lower-bound Renormalization Group transformation of Kadanoff to an SU(2) lattice spin model in 2 and 3 dimensions. Even in the one-hypercube framework of this renormalization group transformation the present model is characterised by having an infinite basis of fundamental operators. We investigate whether the lower-bound variational renormalization group transformation yields results stable under truncations of this operator basis. Our results show that for this particular spin model this is not the case. (orig.)

Renormalization-group analysis of the generalized sine-Gordon model and of the Coulomb gas for d≥3 dimensions

International Nuclear Information System (INIS)

Nandori, I.; Jentschura, U.D.; Soff, G.; Sailer, K.

2004-01-01

Renormalization-group (RG) flow equations have been derived for the generalized sine-Gordon model (GSGM) and the Coulomb gas (CG) in d≥3 of dimensions by means of the Wegner-Houghton method, and by way of the real-space RG approach. The UV scaling laws determined by the leading-order terms of the flow equations are in qualitative agreement for all dimensions d≥3, independent of the dimensionality, and in sharp contrast to the special case d=2. For the 4-dimensional GSGM it is demonstrated explicitly (by numerical calculations) that the blocked potential tends to a constant effective potential in the infrared limit, satisfying the requirements of periodicity and convexity. The comparison of the RG flows for the three-dimensional GSGM, the CG, and the vortex-loop gas reveals a significant dependence on the renormalization schemes and the approximations used

Renormalization-scheme-invariant QCD and QED: The method of effective charges

International Nuclear Information System (INIS)

Grunberg, G.

1984-01-01

We review, extend, and give some further applications of a method recently suggested to solve the renormalization-scheme-dependence problem in perturbative field theories. The use of a coupling constant as a universal expansion parameter is abandoned. Instead, to each physical quantity depending on a single scale variable is associated an effective charge, whose corresponding Stueckelberg--Peterman--Gell-Mann--Low function is identified as the proper object on which perturbation theory applies. Integration of the corresponding renormalization-group equations yields renormalization-scheme-invariant results free of any ambiguity related to the definition of the kinematical variable, or that of the scale parameter Λ, even though the theory is not solved to all orders. As a by-product, a renormalization-group improvement of the usual series is achieved. Extension of these methods to operators leads to the introduction of renormalization-group-invariant Green's function and Wilson coefficients, directly related to effective charges. The case of nonzero fermion masses is discussed, both for fixed masses and running masses in mass-independent renormalization schemes. The importance of the scale-invariant mass m is emphasized. Applications are given to deep-inelastic phenomena, where the use of renormalization-group-invariant coefficient functions allows to perform the factorization without having to introduce a factorization scale. The Sudakov form factor of the electron in QED is discussed as an example of an extension of the method to problems involving several momentum scales

Dimensional renormalization and comparison of renormalization schemes in quantum electrodynamics

International Nuclear Information System (INIS)

Coquereaux, R.

1979-02-01

The method of dimensional renormalization as applied to quantum electrodynamics is discussed. A general method is given which allows one to compare the various quantities like coupling constants and masses that appear in different renormalization schemes

Renormalization techniques applied to the study of density of states in disordered systems

International Nuclear Information System (INIS)

Ramirez Ibanez, J.

1985-01-01

A general scheme for real space renormalization of formal scattering theory is presented and applied to the calculation of density of states (DOS) in some finite width systems. This technique is extended in a self-consistent way, to the treatment of disordered and partially ordered chains. Numerical results of moments and DOS are presented in comparison with previous calculations. In addition, a self-consistent theory for the magnetic order problem in a Hubbard chain is derived and a parametric transition is observed. Properties of localization of the electronic states in disordered chains are studied through various decimation averaging techniques and using numerical simulations. (author) [pt

Renormalization of fermion mixing

International Nuclear Information System (INIS)

Schiopu, R.

2007-01-01

Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by

Renormalization of fermion mixing

Energy Technology Data Exchange (ETDEWEB)

Schiopu, R.

2007-05-11

Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by

g-Boson renormalization effects in the interacting Boson model for nondegenerate orbits

Science.gov (United States)

Duval, P. D.; Pittel, S.; Barrett, B. R.; Druce, C. H.

1983-09-01

A nonperturbative model-space truncation procedure is utilized to include the effects of a single g boson on the parameters of the neutron-proton Interacting Boson Model in the realistic case of nondegenerate single-particle orbits. Particular emphasis is given to the single-boson energies ɛdϱ (ϱ = v, π), with numerical results presented for the even isotopes of Hg. Only part of the observed renormalization is obtained. Possible sources of further renormalizations to ɛdϱ are discussed. Results are also presented for the renormalizations of the boson quadrupole parameters κ and χϱ.

Method of renormalization potential for one model of Hartree-Fock-Slater type

CERN Document Server

Zasorin, Y V

2002-01-01

A new method of the potential renormalization for the quasiclassical model of the Hartree-Fock-Slater real potential is proposed. The method makes it possible to easily construct the wave functions and contrary to the majority od similar methods it does not require the knowledge of the real-type potential

Tadpole renormalization and relativistic corrections in lattice NRQCD

Science.gov (United States)

Shakespeare, Norman H.; Trottier, Howard D.

1998-08-01

We make a detailed comparison of two tadpole renormalization schemes in the context of the quarkonium hyperfine splittings in lattice NRQCD. We renormalize improved gauge-field and NRQCD actions using the mean-link u0,L in the Landau gauge, and using the fourth root of the average plaquette u0,P. Simulations are done for the three quarkonium systems cc¯, bc¯, and bb¯. The hyperfine splittings are computed both at leading [O(MQv4)] and at next-to-leading [O(MQv6)] order in the relativistic expansion, where MQ is the renormalized quark mass, and v2 is the mean-squared velocity. Results are obtained at a large number of lattice spacings, in the range of about 0.14-0.38 fm. A number of features emerge, all of which favor tadpole renormalization using u0,L. This includes a much better scaling behavior of the hyperfine splittings in the three quarkonium systems when u0,L is used. We also find that relativistic corrections to the spin splittings are smaller when u0,L is used, particularly for the cc¯ and bc¯ systems. We also see signs of a breakdown in the NRQCD expansion when the bare quark mass falls below about 1 in lattice units. Simulations with u0,L also appear to be better behaved in this context: the bare quark masses turn out to be larger when u0,L is used, compared to when u0,P is used on lattices with comparable spacings. These results also demonstrate the need to go beyond tree-level tadpole improvement for precision simulations.

Perturbative renormalization of QED via flow equations

International Nuclear Information System (INIS)

Keller, G.; Kopper, C.

1991-01-01

We prove the perturbative renormalizability of euclidean QED 4 with a small photon mass in the framework of effective lagrangians due to Wilson and Polchinski. In particular we show that the QED identities, which become violated by our momentum space regularization at intermediate stages, are restored in the renormalized theory. (orig.)

Renormalization group coupling flow of SU(3) gauge theory

OpenAIRE

QCDTARO Collaboration

1998-01-01

We present our new results on the renormalization group coupling flow obtained i n 3 dimensional coupling space $(\\beta_{11},\\beta_{12},\\beta_{twist})$. The value of $\\beta_{twist}$ turns out to be small and the coupling flow projected on $(\\beta_{11},\\beta_{12})$ plane is very similar with the previous result obtained in the 2 dimensional coupling space.

Non-Perturbative Renormalization

CERN Document Server

Mastropietro, Vieri

2008-01-01

The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providi

Perturbative renormalization of QED via flow equations

Energy Technology Data Exchange (ETDEWEB)

Keller, G. (Max-Planck-Inst. fuer Physik, Werner-Heisenberg-Inst., Munich (Germany)); Kopper, C. (Max-Planck-Inst. fuer Physik, Werner-Heisenberg-Inst., Munich (Germany) Inst. fuer Theoretische Physik, Univ. Goettingen (Germany))

1991-12-19

We prove the perturbative renormalizability of euclidean QED{sub 4} with a small photon mass in the framework of effective lagrangians due to Wilson and Polchinski. In particular we show that the QED identities, which become violated by our momentum space regularization at intermediate stages, are restored in the renormalized theory. (orig.).

Spectral functions and transport coefficients from the functional renormalization group

Energy Technology Data Exchange (ETDEWEB)

Tripolt, Ralf-Arno

2015-06-03

In this thesis we present a new method to obtain real-time quantities like spectral functions and transport coefficients at finite temperature and density using the Functional Renormalization Group approach. Our non-perturbative method is thermodynamically consistent, symmetry preserving and based on an analytic continuation from imaginary to real time on the level of the flow equations. We demonstrate the applicability of this method by calculating mesonic spectral functions as well as the shear viscosity for the quark-meson model. In particular, results are presented for the pion and sigma spectral function at finite temperature and chemical potential, with a focus on the regime near the critical endpoint in the phase diagram of the quark-meson model. Moreover, the different time-like and space-like processes, which give rise to a complex structure of the spectral functions, are discussed. Finally, based on the momentum dependence of the spectral functions, we calculate the shear viscosity and the shear viscosity to entropy density ratio using the corresponding Green-Kubo formula.

Distribution of the minimum path on percolation clusters: A renormalization group calculation

International Nuclear Information System (INIS)

Hipsh, Lior.

1993-06-01

This thesis uses the renormalization group for the research of the chemical distance or the minimal path on percolation clusters on a 2 dimensional square lattice. Our aims are to calculate analytically (iterative calculation) the fractal dimension of the minimal path. d min. , and the distributions of the minimum paths, l min for different lattice sizes and for different starting densities (including the threshold value p c ). For the distributions. We seek for an analytic form which describes them. The probability to get a minimum path for each linear size L is calculated by iterating the distribution of l min for the basic cell of size 2*2 to the next scale sizes, using the H cell renormalization group. For the threshold value of p and for values near to p c . We confirm a scaling in the form: P(l,L) =f1/l(l/(L d min ). L - the linear size, l - the minimum path. The distribution can be also represented in the Fourier space, so we will try to solve the renormalization group equations in this space. A numerical fitting is produced and compared to existing numerical results. In order to improve the agreement between the renormalization group and the numerical simulations, we also present attempts to generalize the renormalization group by adding more parameters, e.g. correlations between bonds in different directions or finite densities for occupation of bonds and sites. (author) 17 refs

Real space process algebra

NARCIS (Netherlands)

Bergstra, J.A.; Baeten, J.C.M.

1993-01-01

The real time process algebra of Baeten and Bergstra [Formal Aspects of Computing, 3, 142-188 (1991)] is extended to real space by requiring the presence of spatial coordinates for each atomic action, in addition to the required temporal attribute. It is found that asynchronous communication

Excited state TBA and renormalized TCSA in the scaling Potts model

Science.gov (United States)

Lencsés, M.; Takács, G.

2014-09-01

We consider the field theory describing the scaling limit of the Potts quantum spin chain using a combination of two approaches. The first is the renormalized truncated conformal space approach (TCSA), while the second one is a new thermodynamic Bethe Ansatz (TBA) system for the excited state spectrum in finite volume. For the TCSA we investigate and clarify several aspects of the renormalization procedure and counter term construction. The TBA system is first verified by comparing its ultraviolet limit to conformal field theory and the infrared limit to exact S matrix predictions. We then show that the TBA and the renormalized TCSA match each other to a very high precision for a large range of the volume parameter, providing both a further verification of the TBA system and a demonstration of the efficiency of the TCSA renormalization procedure. We also discuss the lessons learned from our results concerning recent developments regarding the low-energy scattering of quasi-particles in the quantum Potts spin chain.

Mutual information, neural networks and the renormalization group

Science.gov (United States)

Koch-Janusz, Maciej; Ringel, Zohar

2018-06-01

Physical systems differing in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the powerful renormalization group (RG) procedure, which systematically retains `slow' degrees of freedom and integrates out the rest. However, the important degrees of freedom may be difficult to identify. Here we demonstrate a machine-learning algorithm capable of identifying the relevant degrees of freedom and executing RG steps iteratively without any prior knowledge about the system. We introduce an artificial neural network based on a model-independent, information-theoretic characterization of a real-space RG procedure, which performs this task. We apply the algorithm to classical statistical physics problems in one and two dimensions. We demonstrate RG flow and extract the Ising critical exponent. Our results demonstrate that machine-learning techniques can extract abstract physical concepts and consequently become an integral part of theory- and model-building.

The Implementation of the Renormalized Complex MSSM in FeynArts and FormCalc

CERN Document Server

Fritzsche, T; Heinemeyer, S; Rzehak, H; Schappacher, C

2014-01-01

We describe the implementation of the renormalized complex MSSM (cMSSM) in the diagram generator FeynArts and the calculational tool FormCalc. This extension allows to perform UV-finite one-loop calculations of cMSSM processes almost fully automatically. The Feynman rules for the cMSSM with counterterms are available as a new model file for FeynArts. Also included are default definitions of the renormalization constants; this fixes the renormalization scheme. Beyond that all model parameters are generic, e.g. we do not impose any relations to restrict the number of input parameters. The model file has been tested extensively for several non-trivial decays and scattering reactions. Our renormalization scheme has been shown to give stable results over large parts of the cMSSM parameter space.

Critical behavior of the anisotropic Heisenberg model by effective-field renormalization group

Science.gov (United States)

de Sousa, J. Ricardo; Fittipaldi, I. P.

1994-05-01

A real-space effective-field renormalization-group method (ERFG) recently derived for computing critical properties of Ising spins is extended to treat the quantum spin-1/2 anisotropic Heisenberg model. The formalism is based on a generalized but approximate Callen-Suzuki spin relation and utilizes a convenient differential operator expansion technique. The method is illustrated in several lattice structures by employing its simplest approximation version in which clusters with one (N'=1) and two (N=2) spins are used. The results are compared with those obtained from the standard mean-field (MFRG) and Migdal-Kadanoff (MKRG) renormalization-group treatments and it is shown that this technique leads to rather accurate results. It is shown that, in contrast with the MFRG and MKRG predictions, the EFRG, besides correctly distinguishing the geometries of different lattice structures, also provides a vanishing critical temperature for all two-dimensional lattices in the isotropic Heisenberg limit. For the simple cubic lattice, the dependence of the transition temperature Tc with the exchange anisotropy parameter Δ [i.e., Tc(Δ)], and the resulting value for the critical thermal crossover exponent φ [i.e., Tc≂Tc(0)+AΔ1/φ ] are in quite good agreement with results available in the literature in which more sophisticated treatments are used.

Introduction to the functional renormalization group

International Nuclear Information System (INIS)

Kopietz, Peter; Bartosch, Lorenz; Schuetz, Florian

2010-01-01

This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals. In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step. Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given. Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics. (orig.)

Nonthermal fixed points and the functional renormalization group

International Nuclear Information System (INIS)

Berges, Juergen; Hoffmeister, Gabriele

2009-01-01

Nonthermal fixed points represent basic properties of quantum field theories, in addition to vacuum or thermal equilibrium fixed points. The functional renormalization group on a closed real-time path provides a common framework for their description. For the example of an O(N) symmetric scalar theory it reveals a hierarchy of fixed point solutions, with increasing complexity from vacuum and thermal equilibrium to nonequilibrium

Two-loop renormalization in the standard model, part II. Renormalization procedures and computational techniques

Energy Technology Data Exchange (ETDEWEB)

Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)

2006-12-15

In part I general aspects of the renormalization of a spontaneously broken gauge theory have been introduced. Here, in part II, two-loop renormalization is introduced and discussed within the context of the minimal Standard Model. Therefore, this paper deals with the transition between bare parameters and fields to renormalized ones. The full list of one- and two-loop counterterms is shown and it is proven that, by a suitable extension of the formalism already introduced at the one-loop level, two-point functions suffice in renormalizing the model. The problem of overlapping ultraviolet divergencies is analyzed and it is shown that all counterterms are local and of polynomial nature. The original program of 't Hooft and Veltman is at work. Finite parts are written in a way that allows for a fast and reliable numerical integration with all collinear logarithms extracted analytically. Finite renormalization, the transition between renormalized parameters and physical (pseudo-)observables, are discussed in part III where numerical results, e.g. for the complex poles of the unstable gauge bosons, are shown. An attempt is made to define the running of the electromagnetic coupling constant at the two-loop level. (orig.)

Renormalization group and asymptotic freedom

International Nuclear Information System (INIS)

Morris, J.R.

1978-01-01

Several field theoretic models are presented which allow exact expressions of the renormalization constants and renormalized coupling constants. These models are analyzed as to their content of asymptotic free field behavior through the use of the Callan-Symanzik renormalization group equation. It is found that none of these models possesses asymptotic freedom in four dimensions

Renormalization in few body nuclear physics

Energy Technology Data Exchange (ETDEWEB)

Tomio, L.; Biswas, R. [Instituto de Fisica Teorica, UNESP, 01405-900 Sao Paulo (Brazil); Delfino, A. [Instituto de Fisica, Universidade Federal Fluminenese, Niteroi (Brazil); Frederico, T. [Instituto Tecnologico de Aeronautica, CTA 12228-900 Sao Jose dos Campos (Brazil)

2001-09-01

Full text: Renormalized fixed-point Hamiltonians are formulated for systems described by interactions that originally contain point-like singularities (as the Dirac delta and/or its derivatives). The approach was developed considering a renormalization scheme for a few-nucleon interaction, that relies on a subtracted T-matrix equation. The fixed-point Hamiltonian contains the renormalized coefficients/operators that carry the physical information of the quantum mechanical system, as well as all the necessary counterterms that make finite the scattering amplitude. It is also behind the renormalization group invariance of quantum mechanics. The renormalization procedure, via subtracted kernel, was first applied to the one-pion-exchange potential supplemented by contact interactions. The singlet and triplet scattering lengths are given to fix the renormalized strengths of the contact interactions. Considering only one scaling parameter, the results that were obtained show an overall very good agreement with neutron-proton data, particularly for the observables related to the triplet channel. In this example, we noticed that the mixing parameter of the {sup 3}S{sub l} -{sup 3} D{sub 1} states is the most sensible observable related to the renormalization scale. The above approach, where the nonrelativistic scattering equation with singular interaction is renormalized through a subtraction procedure at a given energy scale, lead us to propose a scheme to formulate renormalized (fixed- point) Hamiltonians in quantum mechanics. We illustrate the numerical diagonalization of the regularized form of the fixed-point Hamiltonian for a two-body system with a Yukawa plus a Dirac-delta interaction. The eigenvalues for the system are shown to be stable in the infinite momentum cutoff. In another example, we also derive the explicit form of the renormalized potential for an example of four-term singular bare interaction. Application of this renormalization scheme to three

Renormalization in few body nuclear physics

International Nuclear Information System (INIS)

Tomio, L.; Biswas, R.; Delfino, A.; Frederico, T.

2001-01-01

Full text: Renormalized fixed-point Hamiltonians are formulated for systems described by interactions that originally contain point-like singularities (as the Dirac delta and/or its derivatives). The approach was developed considering a renormalization scheme for a few-nucleon interaction, that relies on a subtracted T-matrix equation. The fixed-point Hamiltonian contains the renormalized coefficients/operators that carry the physical information of the quantum mechanical system, as well as all the necessary counterterms that make finite the scattering amplitude. It is also behind the renormalization group invariance of quantum mechanics. The renormalization procedure, via subtracted kernel, was first applied to the one-pion-exchange potential supplemented by contact interactions. The singlet and triplet scattering lengths are given to fix the renormalized strengths of the contact interactions. Considering only one scaling parameter, the results that were obtained show an overall very good agreement with neutron-proton data, particularly for the observables related to the triplet channel. In this example, we noticed that the mixing parameter of the 3 S l - 3 D 1 states is the most sensible observable related to the renormalization scale. The above approach, where the nonrelativistic scattering equation with singular interaction is renormalized through a subtraction procedure at a given energy scale, lead us to propose a scheme to formulate renormalized (fixed- point) Hamiltonians in quantum mechanics. We illustrate the numerical diagonalization of the regularized form of the fixed-point Hamiltonian for a two-body system with a Yukawa plus a Dirac-delta interaction. The eigenvalues for the system are shown to be stable in the infinite momentum cutoff. In another example, we also derive the explicit form of the renormalized potential for an example of four-term singular bare interaction. Application of this renormalization scheme to three-body halo nuclei is also

Critical Dynamics of the Xy-Model on the One-Dimensional Superlattice by Position Space Renormalization Group

Science.gov (United States)

Lima, J. P. De; Gonçalves, L. L.

The critical dynamics of the isotropic XY-model on the one-dimensional superlattice is considered in the framework of the position space renormalization group theory. The decimation transformation is introduced by considering the equations of motion of the operators associated to the excitations of the system, and it corresponds to an extension of the procedure introduced by Stinchcombe and dos Santos (J. Phys. A18, L597 (1985)) for the homogeneous lattice. The dispersion relation is obtained exactly and the static and dynamic scaling forms are explicitly determined. The dynamic critical exponent is also obtained and it is shown that it is identical to the one of the XY-model on the homogeneous chain.

Bundles over Quantum RealWeighted Projective Spaces

Directory of Open Access Journals (Sweden)

Tomasz Brzeziński

2012-09-01

Full Text Available The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1-bundles over quantum real weighted projective spaces are constructed. As the spaces in question fall into two separate classes, the negative or odd class that generalises quantum real projective planes and the positive or even class that generalises the quantum disc, so do the constructed principal bundles. In the negative case the principal bundle is proven to be non-trivial and associated projective modules are described. In the positive case the principal bundles turn out to be trivial, and so all the associated modules are free. It is also shown that the circle (coactions on the quantum Seifert manifold that define quantum real weighted projective spaces are almost free.

Renormalization group procedure for potential −g/r2

Directory of Open Access Journals (Sweden)

S.M. Dawid

2018-02-01

Full Text Available Schrödinger equation with potential −g/r2 exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at r=0. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of g.

Renormalized plasma turbulence theory: A quasiparticle picture

International Nuclear Information System (INIS)

DuBois, D.F.

1981-01-01

A general renormalized statistical theory of Vlasov turbulence is given which proceeds directly from the Vlasov equation and does not assume prior knowledge of sophisticated field-theoretic techniques. Quasiparticles are the linear excitations of the turbulent system away from its instantaneous mean (ensemble-averaged) state or background; the properties of this background state ''dress'' or renormalize the quasiparticle responses. It is shown that all two-point responses (including the dielectric) and all two-point correlation functions can be completely described by the mean distribution function and three fundamental quantities. Two of these are the quasiparticle responses: the propagator and the potential source: which measure, respectively, the separate responses of the mean distribution function and the mean electrostatic potential to functional changes in an external phase-space source added to Vlasov's equation. The third quantity is the two-point correlation function of the incoherent part of the phase-space density which acts as a self-consistent source of quasiparticle and potential fluctuations. This theory explicitly takes into account the self-consistent nature of the electrostatic-field fluctuations which introduces new effects not found in the usual ''test-particle'' theories. Explicit equations for the fundamental quantities are derived in the direct interaction approximation. Special attention is paid to the two-point correlations and the relation to theories of phase-space granulation

Differential regularization and renormalization: a new method of calculation in quantum field theory

International Nuclear Information System (INIS)

Freedman, D.Z.; Johnson, K.; Latorre, J.I.

1992-01-01

Most primitively divergent Feynman diagrams are well defined in x-space but too singular at short distances for transformation to p-space. A new method of regularization is developed in which singular functions are written as derivatives of less singular functions which contain a logarithmic mass scale. The Fourier transform is then defined by formal integration by parts. The procedure is extended to graphs with divergent subgraphs. No explicit cutoff or counterterms are required, and the method automatically delivers renormalized amplitudes which satisfy Callan-Symanzik equations. These features are thoroughly explored in massless φ 4 theory through 3-loop order, and the method yields explicit functional forms for all amplitudes with less difficulty than conventional methods which use dimensional regularization in p-space. The procedure also appears to be compatible with gauge invariance and the chiral structure of the standard model. This aspect is tested in extensive 1-loop calculations which include the Ward identity in quantum electrodynamics, the chiral anomaly, and the background field algorithm in non-abelian gauge theories. (orig.)

Unambiguity of renormalization group calculations in QCD

International Nuclear Information System (INIS)

Vladimirov, A.A.

1979-01-01

A detailed analysis of the reduction of ambiguities determined by an arbitrary renormalization scheme is presented for the renormalization group calculations of physical quantities in quantum chromodynamics (QCD). Some basic formulas concerning the renormalization-scheme dependence of Green's and renormalization group functions are given. A massless asymptotically free theory with one coupling constant g is considered. In conclusion, several rules for renormalization group calculations in QCD are formulated

Renormalization group fixed points of foliated gravity-matter systems

Energy Technology Data Exchange (ETDEWEB)

Biemans, Jorn [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands); Platania, Alessia [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands); Department of Physics and Astronomy, University of Catania,Via S. Sofia 63, 95123 Catania (Italy); INFN, Catania section,Via S. Sofia 64, 95123, Catania (Italy); INAF, Catania Astrophysical Observatory,Via S. Sofia 78, 95123, Catania (Italy); Saueressig, Frank [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands)

2017-05-17

We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a lapse function, shift vector, and spatial metric equips spacetime with a preferred (Euclidean) “time”-direction. In this work, we provide a detailed derivation of the renormalization group flow of Newton’s constant and the cosmological constant on a flat Friedmann-Robertson-Walker background. Adding matter fields, it is shown that their contribution to the flow is the same as in the covariant formulation and can be captured by two parameters d{sub g}, d{sub λ}. We classify the resulting fixed point structure as a function of these parameters finding that the existence of non-Gaussian renormalization group fixed points is rather generic. In particular the matter content of the standard model and its most common extensions gives rise to one non-Gaussian fixed point with real critical exponents suitable for Asymptotic Safety. Moreover, we find non-Gaussian fixed points for any number of scalar matter fields, making the scenario attractive for cosmological model building.

Constructive renormalization theory

International Nuclear Information System (INIS)

Rivasseau, Vincent

2000-01-01

These notes are the second part of a common course on Renormalization Theory given with Professor P. da Veiga. I emphasize here the rigorous non-perturbative or constructive aspects of the theory. The usual formalism for the renormalization group in field theory or statistical mechanics is reviewed, together with its limits. The constructive formalism is introduced step by step. Taylor forest formulas allow to perform easily the cluster and Mayer expansions which are needed for a single step of the renormalization group in the case of Bosonic theories. The iteration of this single step leads to further difficulties whose solution is briefly sketched. The second part of the course is devoted to Fermionic models. These models are easier to treat on the constructive level so they are very well suited to beginners in constructive theory. It is shown how the Taylor forest formulas allow to reorganize perturbation theory nicely in order to construct the Gross-Neveu 2 model without any need for cluster or Mayer expansions. Finally applications of this technique to condensed matter and renormalization group around Fermi surface are briefly reviewed. (author)

Algebraic renormalization perturbative twisted considerations on topological Yang-Mills theory and on N=2 supersymmetric gauge theories

International Nuclear Information System (INIS)

Fucito, F.; Tanzini, A.; Sorella, S.P.

1997-07-01

The aim of these notes is to provide a simple and pedagogical (as much as possible) introduction to what is nowadays commonly called Algebraic Renormalization. As the same itself let it understand, the Algebraic Renormalization gives a systematic set up in order to analyse the quantum extension of a given set of classical symmetries. The framework is purely algebraic, yielding a complete characterization of all possible anomalies and invariant counterterms without making use of any explicit computation of the Feynman diagrams. This goal is achieved by collecting, with the introduction of suitable ghost fields, all the symmetries into a unique operation summarized by a generalized Slavnov-Taylor (or master equation) identity which is the starting point for the quantum analysis. The Slavnov-Taylor identity allows to define a nilpotent operator whose cohomology classes in the space of the integrated local polynomials in the fields and their derivatives with dimensions bounded by power counting give all nontrivial anomalies and counterterms. I other words, the proof of the renormalizability is reduced to the computation of some cohomology classes. (author)

The real meaning of complex Minkowski-space world-lines

Energy Technology Data Exchange (ETDEWEB)

Adamo, T M [University of Oxford, Mathematical Institute, 24-29 St Giles, Oxford, OX1 3LB (United Kingdom); Newman, E T, E-mail: newman@pitt.ed [University of Pittsburgh, Department of Physics and Astronomy, Pittsburgh, PA 15213 (United States)

2010-04-07

In connection with the study of shear-free null geodesics in Minkowski space, we investigate the real geometric effects in real Minkowski space that are induced by and associated with complex world-lines in complex Minkowski space. It was already known, in a formal manner, that complex analytic curves in complex Minkowski space induce shear-free null geodesic congruences. Here we look at the direct geometric connections of the complex line and the real structures. Among other items, we show, in particular, how a complex world-line projects into the real Minkowski space in the form of a real shear-free null geodesic congruence.

The real meaning of complex Minkowski-space world-lines

International Nuclear Information System (INIS)

Adamo, T M; Newman, E T

2010-01-01

In connection with the study of shear-free null geodesics in Minkowski space, we investigate the real geometric effects in real Minkowski space that are induced by and associated with complex world-lines in complex Minkowski space. It was already known, in a formal manner, that complex analytic curves in complex Minkowski space induce shear-free null geodesic congruences. Here we look at the direct geometric connections of the complex line and the real structures. Among other items, we show, in particular, how a complex world-line projects into the real Minkowski space in the form of a real shear-free null geodesic congruence.

Comparative study of standard space and real space analysis of quantitative MR brain data.

Science.gov (United States)

Aribisala, Benjamin S; He, Jiabao; Blamire, Andrew M

2011-06-01

To compare the robustness of region of interest (ROI) analysis of magnetic resonance imaging (MRI) brain data in real space with analysis in standard space and to test the hypothesis that standard space image analysis introduces more partial volume effect errors compared to analysis of the same dataset in real space. Twenty healthy adults with no history or evidence of neurological diseases were recruited; high-resolution T(1)-weighted, quantitative T(1), and B(0) field-map measurements were collected. Algorithms were implemented to perform analysis in real and standard space and used to apply a simple standard ROI template to quantitative T(1) datasets. Regional relaxation values and histograms for both gray and white matter tissues classes were then extracted and compared. Regional mean T(1) values for both gray and white matter were significantly lower using real space compared to standard space analysis. Additionally, regional T(1) histograms were more compact in real space, with smaller right-sided tails indicating lower partial volume errors compared to standard space analysis. Standard space analysis of quantitative MRI brain data introduces more partial volume effect errors biasing the analysis of quantitative data compared to analysis of the same dataset in real space. Copyright © 2011 Wiley-Liss, Inc.

The homogeneous geometries of real hyperbolic space

DEFF Research Database (Denmark)

Castrillón López, Marco; Gadea, Pedro Martínez; Swann, Andrew Francis

We describe the holonomy algebras of all canonical connections of homogeneous structures on real hyperbolic spaces in all dimensions. The structural results obtained then lead to a determination of the types, in the sense of Tricerri and Vanhecke, of the corresponding homogeneous tensors. We use...... our analysis to show that the moduli space of homogeneous structures on real hyperbolic space has two connected components....

Renormalization Group Theory

International Nuclear Information System (INIS)

Stephens, C. R.

2006-01-01

In this article I give a brief account of the development of research in the Renormalization Group in Mexico, paying particular attention to novel conceptual and technical developments associated with the tool itself, rather than applications of standard Renormalization Group techniques. Some highlights include the development of new methods for understanding and analysing two extreme regimes of great interest in quantum field theory -- the ''high temperature'' regime and the Regge regime

Similarity renormalization group evolution of N N interactions within a subtractive renormalization scheme

Directory of Open Access Journals (Sweden)

Durães F.O.

2010-04-01

Full Text Available We apply the similarity renormalization group (SRG approach to evolve a nucleon-nucleon (N N interaction in leading-order (LO chiral effective field theory (ChEFT, renormalized within the framework of the subtracted kernel method (SKM. We derive a fixed-point interaction and show the renormalization group (RG invariance in the SKM approach. We also compare the evolution of N N potentials with the subtraction scale through a SKM RG equation in the form of a non-relativistic Callan-Symanzik (NRCS equation and the evolution with the similarity cutoff through the SRG transformation.

Computing the effective action with the functional renormalization group

Energy Technology Data Exchange (ETDEWEB)

Codello, Alessandro [CP3-Origins and the Danish IAS University of Southern Denmark, Odense (Denmark); Percacci, Roberto [SISSA, Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy); Rachwal, Leslaw [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Tonero, Alberto [ICTP-SAIFR and IFT, Sao Paulo (Brazil)

2016-04-15

The ''exact'' or ''functional'' renormalization group equation describes the renormalization group flow of the effective average action Γ{sub k}. The ordinary effective action Γ{sub 0} can be obtained by integrating the flow equation from an ultraviolet scale k = Λ down to k = 0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity. (orig.)

Compositeness condition in the renormalization group equation

International Nuclear Information System (INIS)

Bando, Masako; Kugo, Taichiro; Maekawa, Nobuhiro; Sasakura, Naoki; Watabiki, Yoshiyuki; Suehiro, Kazuhiko

1990-01-01

The problems in imposing compositeness conditions as boundary conditions in renormalization group equations are discussed. It is pointed out that one has to use the renormalization group equation directly in cutoff theory. In some cases, however, it can be approximated by the renormalization group equation in continuum theory if the mass dependent renormalization scheme is adopted. (orig.)

Finite cluster renormalization and new two step renormalization group for Ising model

International Nuclear Information System (INIS)

Benyoussef, A.; El Kenz, A.

1989-09-01

New types of renormalization group theory using the generalized Callen identities are exploited in the study of the Ising model. Another type of two-step renormalization is proposed. Critical couplings and critical exponents y T and y H are calculated by these methods for square and simple cubic lattices, using different size clusters. (author). 17 refs, 2 tabs

Renormalization group flows and continual Lie algebras

International Nuclear Information System (INIS)

Bakas, Ioannis

2003-01-01

We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by (d/dt;1), with anti-symmetric Cartan kernel K(t,t') = δ'(t-t'); as such, it coincides with the Cartan matrix of the superalgebra sl(N vertical bar N+1) in the large-N limit. The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time, t. We provide the general solution of the renormalization group flows in terms of free fields, via Baecklund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Z n to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra (d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown. (author)

Impact of Inter-Row Spacing on Yield and Yield Components of several Annual Medics Species

Directory of Open Access Journals (Sweden)

Mahnaz BAGHERI

2010-12-01

Full Text Available A field study was conducted in Faculty of Agriculture, Tarbiat Modares University, Tehran, Iran to evaluate the effects of three within-row spacing treatments (20, 30 and 40 cm on forage and seed production of five species of annual medics (Medicago scutellata cv. Sava; M. littoralis cv. Herald; M. polymorpha cv. Santiago; M. minima cv. Orion and M. truncatula cv. Mogul. The experiment was carried out in Faculty of Agriculture, Tarbiat Modares University, Tehran, Iran. The results of the experiment indicated that M. polymorpha had the highest forage yield out of the highest plant population. Latter with average 443.09 Kg ha-1 and M. scutellata with average 409.99 Kg ha-1 produced the highest seed yield. Also, the last species with 1306.78 Kg ha-1 had the highest pod yields. The highest seed yield and pod yield were produced at 20 cm within-row spacing because there were not adequate plants for maximum seed and pod yields in 30 and 40 cm within-row spacing. The tested plant densities did not affect on seeds number per pod, 1000 seeds weight and seeds to burr pod weight ratio. The M. truncatula and M. minima have the highest seeds number per pod. In addition, M. scutellata had the highest 1000 seeds weight with an average of 12.57 g. The highest seeds to burr pod ratio was observed in M. polymorpha. The most pod numbers were obtained in 20 and 30 cm within-row spacing and M. polymorpha while, the least pod numbers was observed in M. scutellata. Plant densities did not affect on pod numbers of the mentioned species. The highest dry forage yield was produced in 20 cm within-row spacing. Among the tested tested species, M. truncatula had the highest forage yield with average 870.07 Kg ha-1. This experiment indicated that there is possibility for seed and forage production of tested annual medics in the mentioned zone with the considering suitable plant densities.

Bose-Einstein condensation in real space

International Nuclear Information System (INIS)

Valencia, J.J.; Llano, M. de; Solis, M.A.

2004-01-01

We show how Bose-Einstein condensation (BEC) occurs not only in momentum space but also in coordinate (or real) space. Analogies between the isotherms of a van der Waals classical gas of extended (or finite-diameter) identical atoms and the point (or zero-diameter) particles of an ideal BE gas allow concluding that, in contrast with the classical case, the volume per particle vanishes in the pure BE condensate phase precisely because the boson diameters are zero. Thus a BE condensate forms in real space without exhibiting a liquid branch as does the classical gas. (Author)

Two-loop renormalization in the standard model, part III. Renormalization equations and their solutions

Energy Technology Data Exchange (ETDEWEB)

Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)

2006-12-15

In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)

Two-loop renormalization in the standard model, part III. Renormalization equations and their solutions

International Nuclear Information System (INIS)

Actis, S.; Passarino, G.

2006-12-01

In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)

Fixed point of the parabolic renormalization operator

CERN Document Server

Lanford III, Oscar E

2014-01-01

This monograph grew out of the authors' efforts to provide a natural geometric description for the class of maps invariant under parabolic renormalization and for the Inou-Shishikura fixed point itself as well as to carry out a computer-assisted study of the parabolic renormalization operator. It introduces a renormalization-invariant class of analytic maps with a maximal domain of analyticity and rigid covering properties and presents a numerical scheme for computing parabolic renormalization of a germ, which is used to compute the Inou-Shishikura renormalization fixed point.   Inside, readers will find a detailed introduction into the theory of parabolic bifurcation,  Fatou coordinates, Écalle-Voronin conjugacy invariants of parabolic germs, and the definition and basic properties of parabolic renormalization.   The systematic view of parabolic renormalization developed in the book and the numerical approach to its study will be interesting to both experts in the field as well as graduate students wishi...

Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory.

Science.gov (United States)

Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic

2010-01-14

We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu(2)O(2)](2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu(2)O(2)](2+).

Scaling algebras and renormalization group in algebraic quantum field theory

International Nuclear Information System (INIS)

Buchholz, D.; Verch, R.

1995-01-01

For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary spacetime manifolds and provides a framework for the systematic analysis of the short distance properties of local quantum field theories. It is shown that every theory has a (possibly non-unique) scaling limit which can be classified according to its classical or quantum nature. Dilation invariant theories are stable under the action of the renormalization group. Within this framework the problem of wedge (Bisognano-Wichmann) duality in the scaling limit is discussed and some of its physical implications are outlined. (orig.)

Extending the random-phase approximation for electronic correlation energies: the renormalized adiabatic local density approximation

DEFF Research Database (Denmark)

Olsen, Thomas; Thygesen, Kristian S.

2012-01-01

The adiabatic connection fluctuation-dissipation theorem with the random phase approximation (RPA) has recently been applied with success to obtain correlation energies of a variety of chemical and solid state systems. The main merit of this approach is the improved description of dispersive forces...... while chemical bond strengths and absolute correlation energies are systematically underestimated. In this work we extend the RPA by including a parameter-free renormalized version of the adiabatic local-density (ALDA) exchange-correlation kernel. The renormalization consists of a (local) truncation...... of the ALDA kernel for wave vectors q > 2kF, which is found to yield excellent results for the homogeneous electron gas. In addition, the kernel significantly improves both the absolute correlation energies and atomization energies of small molecules over RPA and ALDA. The renormalization can...

Singlet vs Nonsinglet Perturbative Renormalization factors of Staggered Fermion Bilinears

Science.gov (United States)

Panagopoulos, Haralambos; Spanoudes, Gregoris

2018-03-01

In this paper we present the perturbative computation of the difference between the renormalization factors of flavor singlet (Σfψ¯fΓψf', f : flavor index) and nonsinglet (ψ¯f1Γψf2,f1 ≠ f2) bilinear quark operators (where Γ = 𝟙, γ5, γ µ, γ5 γ µ, γ5 σµv on the lattice. The computation is performed to two loops and to lowest order in the lattice spacing, using Symanzik improved gluons and staggered fermions with twice stout-smeared links. The stout smearing procedure is also applied to the definition of bilinear operators. A significant part of this work is the development of a method for treating some new peculiar divergent integrals stemming from the staggered formalism. Our results can be combined with precise simulation results for the renormalization factors of the nonsinglet operators, in order to obtain an estimate of the renormalization factors for the singlet operators. The results have been published in Physical Review D [1].

Application of dimensional regularization to single chain polymer static properties: Conformational space renormalization of polymers. III

International Nuclear Information System (INIS)

Oono, Y.; Ohta, T.; Freed, K.F.

1981-01-01

A dimensional regularization approach to the renormalization group treatment of polymer excluded volume is formulated in chain conformation space where monomers are specified by their spatial positions and their positions along the chain and the polymers may be taken to be monodisperse. The method utilizes basic scale invariance considerations. First, it is recognized that long wavelength macroscopic descriptions must be well defined in the limit that the minimum atomic or molecular scale L is set to zero. Secondly, the microscopic theory is independent of the conveniently chosen macroscopic scale of length k. The freedom of choice of k is exploited along with the assumed renormalizability of the theory to provide the renormalization group equations which directly imply the universal scaling laws for macroscopic properties. The renormalizability of the model implies the existence of the general relations between the basic macroparameters, such as chain length, excluded volume, etc., and their microscopic counterparts in the microscopic model for the system. These macro--micro relations are defined through the condition that macroscopic quantities be well defined for polymer chains for any spatial dimensionality. The method is illustrated by calculating the end vector distribution function for all values of end vectors R. The evaluation of this distribution function currently requires the use of expansions in e = 4-d. In this case our distribution reduces to known limits for R→0 or infinity. Subsequent papers will present calculations of the polymer coherent scattering function, the monomer spatial distribution function, and concentration dependent properties

On renormalization of axial anomaly

International Nuclear Information System (INIS)

Efremov, A.V.; Teryaev, O.V.

1989-01-01

It is shown that multiplicative renormalization of the axial singlet current results in renormalization of the axial anomaly in all orders of perturbation theory. It is a necessary condition for the Adler - Bardeen theorem being valid. 10 refs.; 2 figs

The density-matrix renormalization group: a short introduction.

Science.gov (United States)

Schollwöck, Ulrich

2011-07-13

The density-matrix renormalization group (DMRG) method has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. The DMRG is a method that shares features of a renormalization group procedure (which here generates a flow in the space of reduced density operators) and of a variational method that operates on a highly interesting class of quantum states, so-called matrix product states (MPSs). The DMRG method is presented here entirely in the MPS language. While the DMRG generally fails in larger two-dimensional systems, the MPS picture suggests a straightforward generalization to higher dimensions in the framework of tensor network states. The resulting algorithms, however, suffer from difficulties absent in one dimension, apart from a much more unfavourable efficiency, such that their ultimate success remains far from clear at the moment.

Interactive Space(s) -- the CTSG: bridging the real and virtual

NARCIS (Netherlands)

Eliëns, A.P.W.; Mao, W.; Vermeersch, L

2010-01-01

In this paper, ideas will be presented how to realize games or playful activities in interactive space(s), having a real (spatial) component as well as a representation in virtual 2D or 3D space, by means of web pages and/or online games. Apart from general design criteria, the paper discusses a

Renormalization and Interaction in Quantum Field Theory

International Nuclear Information System (INIS)

RATSIMBARISON, H.M.

2008-01-01

This thesis works on renormalization in quantum field theory (QFT), in order to show the relevance of some mathematical structures as C*-algebraic and probabilistic structures. Our work begins with a study of the path integral formalism and the Kreimer-Connes approach in perturbative renormalization, which allows to situate the statistical nature of QFT and to appreciate the ultra-violet divergence problem of its partition function. This study is followed by an emphasis of the presence of convolution products in non perturbative renormalisation, through the construction of the Wilson effective action and the Legendre effective action. Thanks to these constructions and the definition of effective theories according J. Polchinski, the non perturbative renormalization shows in particular the general approach of regularization procedure. We begin the following chapter with a C*-algebraic approach of the scale dependence of physical theories by showing the existence of a hierarchy of commutative spaces of states and its compatibility with the fiber bundle formulation of classical field theory. Our Hierarchy also allows us to modelize the notion of states and particles. Finally, we develop a probabilistic construction of interacting theories starting from simple model, a Bernoulli random processes. We end with some arguments on the applicability of our construction -such as the independence between the free and interacting terms and the possibility to introduce a symmetry group wich will select the type of interactions in quantum field theory. [fr

The quantum-field renormalization group in the problem of a growing phase boundary

International Nuclear Information System (INIS)

Antonov, N.V.; Vasil'ev, A.N.

1995-01-01

Within the quantum-field renormalization-group approach we examine the stochastic equation discussed by S.I. Pavlik in describing a randomly growing phase boundary. We show that, in contrast to Pavlik's assertion, the model is not multiplicatively renormalizable and that its consistent renormalization-group analysis requires introducing an infinite number of counterterms and the respective coupling constants (open-quotes chargeclose quotes). An explicit calculation in the one-loop approximation shows that a two-dimensional surface of renormalization-group points exits in the infinite-dimensional charge space. If the surface contains an infrared stability region, the problem allows for scaling with the nonuniversal critical dimensionalities of the height of the phase boundary and time, δ h and δ t , which satisfy the exact relationship 2 δ h = δ t + d, where d is the dimensionality of the phase boundary. 23 refs., 1 tab

Renormalization group treatment of bond percolation in anisotropic and 'inhomogeneous' planar lattices

International Nuclear Information System (INIS)

Magalhaes, A.C.N. de; Tsallis, C.; Schwaccheim, G.

1980-04-01

The uncorrelated bond percolation problem is studied in three planar systems where there are two distinct occupancy probabilities. Two different real space renormalization group approaches (referred as the 'canonical' (CRG) and the 'parametric' (PRG) ones) are applied to the anisotropic first-neighbour square lattice, and both of them exhibit the expected tendency towards the exactly known phase boundary (p+q=1). Then, within the context of PRG calculations for increasingly large cells, an extrapolation method is introduced, which leads to analytic proposals for the other two lattices, namely p+q = 1/2 for the first-and second-neighbour square lattice (p and q are, respectively, the first and second neighbour occupancy probabilities), and 3 (p-1/2) = 4 [(1-q) 2 + (1-q) 3 ] (p and q are, respectively, the occupancy probabilities of the topologically different bonds which are in a 1:2 ratio) for the 4- 8 lattice. (Author) [pt

Thermal expansion of an amorphous alloy. Reciprocal-space versus real-space distribution functions

International Nuclear Information System (INIS)

Louzguine-Luzgin, Dmitri V.; Inoue, Akihisa

2007-01-01

This paper describes the relation between the change in the position of the first X-ray diffraction maximum in reciprocal space and the first maximum of the distribution function in real space for the Ge 50 Al 40 Cr 10 amorphous alloy. It is also shown that the first diffraction maximum of the interference function carries the most significant information about the interatomic distances in real space while the subsequent peaks of the interference function are responsible for the shoulders of the main peak of the real-space distribution function. The results are used to support validity of the method previously used to monitor thermal expansion of the glassy alloys using an X-ray diffraction profile

Renormalization group flow of scalar models in gravity

International Nuclear Information System (INIS)

Guarnieri, Filippo

2014-01-01

In this Ph.D. thesis we study the issue of renormalizability of gravitation in the context of the renormalization group (RG), employing both perturbative and non-perturbative techniques. In particular, we focus on different gravitational models and approximations in which a central role is played by a scalar degree of freedom, since their RG flow is easier to analyze. We restrict our interest in particular to two quantum gravity approaches that have gained a lot of attention recently, namely the asymptotic safety scenario for gravity and the Horava-Lifshitz quantum gravity. In the so-called asymptotic safety conjecture the high energy regime of gravity is controlled by a non-Gaussian fixed point which ensures non-perturbative renormalizability and finiteness of the correlation functions. We then investigate the existence of such a non trivial fixed point using the functional renormalization group, a continuum version of the non-perturbative Wilson's renormalization group. In particular we quantize the sole conformal degree of freedom, which is an approximation that has been shown to lead to a qualitatively correct picture. The question of the existence of a non-Gaussian fixed point in an infinite-dimensional parameter space, that is for a generic f(R) theory, cannot however be studied using such a conformally reduced model. Hence we study it by quantizing a dynamically equivalent scalar-tensor theory, i.e. a generic Brans-Dicke theory with ω=0 in the local potential approximation. Finally, we investigate, using a perturbative RG scheme, the asymptotic freedom of the Horava-Lifshitz gravity, that is an approach based on the emergence of an anisotropy between space and time which lifts the Newton's constant to a marginal coupling and explicitly preserves unitarity. In particular we evaluate the one-loop correction in 2+1 dimensions quantizing only the conformal degree of freedom.

Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions

Science.gov (United States)

Rose, F.; Dupuis, N.

2018-05-01

We present an approximation scheme of the nonperturbative renormalization group that preserves the momentum dependence of correlation functions. This approximation scheme can be seen as a simple improvement of the local potential approximation (LPA) where the derivative terms in the effective action are promoted to arbitrary momentum-dependent functions. As in the LPA, the only field dependence comes from the effective potential, which allows us to solve the renormalization-group equations at a relatively modest numerical cost (as compared, e.g., to the Blaizot-Mendéz-Galain-Wschebor approximation scheme). As an application we consider the two-dimensional quantum O(N ) model at zero temperature. We discuss not only the two-point correlation function but also higher-order correlation functions such as the scalar susceptibility (which allows for an investigation of the "Higgs" amplitude mode) and the conductivity. In particular, we show how, using Padé approximants to perform the analytic continuation i ωn→ω +i 0+ of imaginary frequency correlation functions χ (i ωn) computed numerically from the renormalization-group equations, one can obtain spectral functions in the real-frequency domain.

Renormalization group flow of entanglement entropy on spheres

Energy Technology Data Exchange (ETDEWEB)

Ben-Ami, Omer; Carmi, Dean [Raymond and Beverly Sackler Faculty of Exact Sciences School of Physics and Astronomy,Tel-Aviv University, Ramat-Aviv 69978 (Israel); Smolkin, Michael [Center for Theoretical Physics and Department of Physics,University of California, Berkeley, CA 94720 (United States)

2015-08-12

We explore entanglement entropy of a cap-like region for a generic quantum field theory residing in the Bunch-Davies vacuum on de Sitter space. Entanglement entropy in our setup is identical with the thermal entropy in the static patch of de Sitter, and we derive a simple relation between the vacuum expectation value of the energy-momentum tensor trace and the RG flow of entanglement entropy. In particular, renormalization of the bare couplings and logarithmic divergence of the entanglement entropy are interrelated in our setup. We confirm our findings by recovering known universal contributions for a free field theory deformed by a mass operator as well as obtain correct universal behaviour at the fixed points. Simple examples of entanglement entropy flows are elaborated in d=2,3,4. In three dimensions we find that while the renormalized entanglement entropy is stationary at the fixed points, it is not monotonic. We provide a computational evidence that the universal ‘area law’ for a conformally coupled scalar is different from the known result in the literature, and argue that this difference survives in the limit of flat space. Finally, we carry out the spectral decomposition of entanglement entropy flow and discuss its application to the F-theorem.

A key heterogeneous structure of fractal networks based on inverse renormalization scheme

Science.gov (United States)

Bai, Yanan; Huang, Ning; Sun, Lina

2018-06-01

Self-similarity property of complex networks was found by the application of renormalization group theory. Based on this theory, network topologies can be classified into universality classes in the space of configurations. In return, through inverse renormalization scheme, a given primitive structure can grow into a pure fractal network, then adding different types of shortcuts, it exhibits different characteristics of complex networks. However, the effect of primitive structure on networks structural property has received less attention. In this paper, we introduce a degree variance index to measure the dispersion of nodes degree in the primitive structure, and investigate the effect of the primitive structure on network structural property quantified by network efficiency. Numerical simulations and theoretical analysis show a primitive structure is a key heterogeneous structure of generated networks based on inverse renormalization scheme, whether or not adding shortcuts, and the network efficiency is positively correlated with degree variance of the primitive structure.

Renormalized semiclassical quantization for rescalable Hamiltonians

International Nuclear Information System (INIS)

Takahashi, Satoshi; Takatsuka, Kazuo

2004-01-01

A renormalized semiclassical quantization method for rescalable Hamiltonians is proposed. A classical Hamilton system having a potential function that consists of homogeneous polynomials like the Coulombic potential can have a scale invariance in its extended phase space (phase space plus time). Consequently, infinitely many copies of a single trajectory constitute a one-parameter family that is characterized in terms of a scaling factor. This scaling invariance in classical dynamics is lost in quantum mechanics due to the presence of the Planck constant. It is shown that in a system whose classical motions have a self-similarity in the above sense, classical trajectories adopted in the semiclassical scheme interact with infinitely many copies of their own that are reproduced by the relevant scaling procedure, thereby undergoing quantum interference among themselves to produce a quantized spectrum

Real Space Approach to CMB deboosting

CERN Document Server

Yoho, Amanda; Starkman, Glenn D.; Pereira, Thiago S.

2013-01-01

The effect of our Galaxy's motion through the Cosmic Microwave Background rest frame, which aberrates and Doppler shifts incoming photons measured by current CMB experiments, has been shown to produce mode-mixing in the multipole space temperature coefficients. However, multipole space determinations are subject to many difficulties, and a real-space analysis can provide a straightforward alternative. In this work we describe a numerical method for removing Lorentz- boost effects from real-space temperature maps. We show that to deboost a map so that one can accurately extract the temperature power spectrum requires calculating the boost kernel at a finer pixelization than one might naively expect. In idealized cases that allow for easy comparison to analytic results, we have confirmed that there is indeed mode mixing among the spherical harmonic coefficients of the temperature. We find that using a boost kernel calculated at Nside=8192 leads to a 1% bias in the binned boosted power spectrum at l~2000, while ...

The renormalization of the electroweak standard model

International Nuclear Information System (INIS)

Boehm, M.; Spiesberger, H.; Hollik, W.

1984-03-01

A renormalization scheme for the electroweak standard model is presented in which the electric charge and the masses of the gauge bosons, Higgs particle and fermions are used as physical parameters. The photon is treated such that quantum electrodynamics is contained in the usual form. Field renormalization respecting the gauge symmetry gives finite Green functions. The Ward identities between the Green functions of the unphysical sector allow a renormalization that maintains the simple pole structure of the propagators. Explicit results for the renormalization self energies and vertex functions are given. They can be directly used as building blocks for the evaluation of l-loop radiative corrections. (orig.)

Dealing with chemical reaction pathways and electronic excitations in molecular systems via renormalized and active-space coupled-cluster methods

Energy Technology Data Exchange (ETDEWEB)

Piecuch, Piotr; Li, Wei; Lutz, Jesse J. [Department of Chemistry, Michigan State University, East Lansing, MI 48824 (United States); Włoch, Marta [Department of Chemistry, Michigan Technological University, Houghton, Michigan 49931 (United States); Gour, Jeffrey R. [Department of Chemistry, Michigan State University, East Lansing, MI 48824, USA and Department of Chemistry, Stanford University, Stanford, California 94305 (United States)

2015-01-22

Coupled-cluster (CC) theory has become the de facto standard for high-accuracy molecular calculations, but the widely used CC and equation-of-motion (EOM) CC approaches, such as CCSD(T) and EOMCCSD, have difficulties with capturing stronger electron correlations that characterize multi-reference molecular problems. This presentation demonstrates that many of these difficulties can be addressed by exploiting the completely renormalized (CR) CC and EOMCC approaches, such as CR-CC(2,3), CR-EOMCCSD(T), and CR-EOMCC(2,3), and their local correlation counterparts applicable to systems with hundreds of atoms, and the active-space CC/EOMCC approaches, such as CCSDt and EOMCCSDt, and their extensions to valence systems via the electron-attached and ionized formalisms.

Renormalization of the inflationary perturbations revisited

Science.gov (United States)

Markkanen, Tommi

2018-05-01

In this work we clarify aspects of renormalization on curved backgrounds focussing on the potential ramifications on the amplitude of inflationary perturbations. We provide an alternate view of the often used adiabatic prescription by deriving a correspondence between the adiabatic subtraction terms and traditional renormalization. Specifically, we show how adiabatic subtraction can be expressed as a set of counter terms that are introduced by redefining the bare parameters of the action. Our representation of adiabatic subtraction then allows us to easily find other renormalization prescriptions differing only in the finite parts of the counter terms. As our main result, we present for quadratic inflation how one may consistently express the renormalization of the spectrum of perturbations from inflation as a redefinition of the bare cosmological constant and Planck mass such that the observable predictions coincide with the unrenormalized result.

The renormalization group and lattice QCD

International Nuclear Information System (INIS)

Gupta, R.

1989-01-01

This report discusses the following topics: scaling of thermodynamic quantities and critical exponents; scaling relations; block spin idea of Kadanoff; exact RG solution of the 1-d Ising model; Wilson's formulation of the renormalization group; linearized transformation matrix and classification of exponents; derivation of exponents from the eigenvalues of Τ αβ ; simple field theory: the gaussian model; linear renormalization group transformations; numerical methods: MCRG; block transformations for 4-d SU(N) LGT; asymptotic freedom makes QCD simple; non-perturbative β-function and scaling; and the holy grail: the renormalized trajectory

Renormalization methods in solid state physics

Energy Technology Data Exchange (ETDEWEB)

Nozieres, P [Institut Max von Laue - Paul Langevin, 38 - Grenoble (France)

1976-01-01

Renormalization methods in various solid state problems (e.g., the Kondo effect) are analyzed from a qualitative vantage point. Our goal is to show how the renormalization procedure works, and to uncover a few simple general ideas (universality, phenomenological descriptions, etc...).

Aspects of renormalization in finite-density field theory

Energy Technology Data Exchange (ETDEWEB)

Fitzpatrick, A. Liam; Torroba, Gonzalo; Wang, Huajia

2015-05-26

We study the renormalization of the Fermi surface coupled to a massless boson near three spatial dimensions. For this, we set up a Wilsonian RG with independent decimation procedures for bosons and fermions, where the four-fermion interaction “Landau parameters” run already at tree level. Our explicit one-loop analysis resolves previously found obstacles in the renormalization of finite-density field theory, including logarithmic divergences in nonlocal interactions and the appearance of multilogarithms. The key aspects of the RG are the above tree-level running, and a UV-IR mixing between virtual bosons and fermions at the quantum level, which is responsible for the renormalization of the Fermi velocity. We apply this approach to the renormalization of 2 k F singularities, and to Fermi surface instabilities in a companion paper, showing how multilogarithms are properly renormalized. We end with some comments on the renormalization of finite-density field theory with the inclusion of Landau damping of the boson.

Renormalization of quark propagator, vertex functions, and twist-2 operators from twisted-mass lattice QCD at Nf=4

Science.gov (United States)

Blossier, Benoît.; Brinet, Mariane; Guichon, Pierre; Morénas, Vincent; Pène, Olivier; Rodríguez-Quintero, Jose; Zafeiropoulos, Savvas

2015-06-01

We present a precise nonperturbative determination of the renormalization constants in the mass independent RI'-MOM scheme. The lattice implementation uses the Iwasaki gauge action and four degenerate dynamical twisted-mass fermions. The gauge configurations are provided by the ETM Collaboration. Renormalization constants for scalar, pseudoscalar, vector and axial operators, as well as the quark propagator renormalization, are computed at three different values of the lattice spacing, two volumes and several twisted-mass parameters. The method we developed allows for a precise cross-check of the running, thanks to the particular proper treatment of hypercubic artifacts. Results for the twist-2 operator O44 are also presented.

Perturbative and constructive renormalization

International Nuclear Information System (INIS)

Veiga, P.A. Faria da

2000-01-01

These notes are a survey of the material treated in a series of lectures delivered at the X Summer School Jorge Andre Swieca. They are concerned with renormalization in Quantum Field Theories. At the level of perturbation series, we review classical results as Feynman graphs, ultraviolet and infrared divergences of Feynman integrals. Weinberg's theorem and Hepp's theorem, the renormalization group and the Callan-Symanzik equation, the large order behavior and the divergence of most perturbation series. Out of the perturbative regime, as an example of a constructive method, we review Borel summability and point out how it is possible to circumvent the perturbation diseases. These lectures are a preparation for the joint course given by professor V. Rivasseau at the same school, where more sophisticated non-perturbative analytical methods based on rigorous renormalization group techniques are presented, aiming at furthering our understanding about the subject and bringing field theoretical models to a satisfactory mathematical level. (author)

Real-variable theory of Musielak-Orlicz Hardy spaces

CERN Document Server

Yang, Dachun; Ky, Luong Dang

2017-01-01

The main purpose of this book is to give a detailed and complete survey of recent progress related to the real-variable theory of Musielak–Orlicz Hardy-type function spaces, and to lay the foundations for further applications. The real-variable theory of function spaces has always been at the core of harmonic analysis. Recently, motivated by certain questions in analysis, some more general Musielak–Orlicz Hardy-type function spaces were introduced. These spaces are defined via growth functions which may vary in both the spatial variable and the growth variable. By selecting special growth functions, the resulting spaces may have subtler and finer structures, which are necessary in order to solve various endpoint or sharp problems. This book is written for graduate students and researchers interested in function spaces and, in particular, Hardy-type spaces.

Critical phenomena and renormalization group transformations

International Nuclear Information System (INIS)

Castellani, C.; Castro, C. di

1980-01-01

Our main goal is to guide the reader to find out the common rational behind the various renormalization procedures which have been proposed in the last ten years. In the first part of these lectures old arguments on universality and scaling will be briefly recalled. To our opinion these introductory remarks allow one to stress the physical origin of the two majore renormalization procedures, which have been used in the theory of critical phenomena: the Wilson and the field theoretic approach. All the general properties of a ''good'' renormalization transformation will also come out quite naturally. (author)

Non-perturbative quark mass renormalization

CERN Document Server

Capitani, S.; Luescher, M.; Sint, S.; Sommer, R.; Weisz, P.; Wittig, H.

1998-01-01

We show that the renormalization factor relating the renormalization group invariant quark masses to the bare quark masses computed in lattice QCD can be determined non-perturbatively. The calculation is based on an extension of a finite-size technique previously employed to compute the running coupling in quenched QCD. As a by-product we obtain the $\\Lambda$--parameter in this theory with completely controlled errors.

Renormalization-group flows and charge transmutation in string theory

International Nuclear Information System (INIS)

Orlando, D.; Petropoulos, P.M.; Sfetsos, K.

2006-01-01

We analyze the behaviour of heterotic squashed-Wess-Zumino-Witten backgrounds under renormalization-group flow. The flows we consider are driven by perturbation creating extra gauge fluxes. We show how the conformal point acts as an attractor from both the target-space and world-sheet points of view. We also address the question of instabilities created by the presence of closed time-like curves in string backgrounds. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

The Background-Field Method and Noninvariant Renormalization

International Nuclear Information System (INIS)

Avdeev, L.V.; Kazakov, D.I.; Kalmykov, M.Yu.

1994-01-01

We investigate the consistency of the background-field formalism when applying various regularizations and renormalization schemes. By an example of a two-dimensional σ model it is demonstrated that the background-field method gives incorrect results when the regularization (and/or renormalization) is noninvariant. In particular, it is found that the cut-off regularization and the differential renormalization belong to this class and are incompatible with the background-field method in theories with nonlinear symmetries. 17 refs

Applying MDA to SDR for Space to Model Real-time Issues

Science.gov (United States)

Blaser, Tammy M.

2007-01-01

NASA space communications systems have the challenge of designing SDRs with highly-constrained Size, Weight and Power (SWaP) resources. A study is being conducted to assess the effectiveness of applying the MDA Platform-Independent Model (PIM) and one or more Platform-Specific Models (PSM) specifically to address NASA space domain real-time issues. This paper will summarize our experiences with applying MDA to SDR for Space to model real-time issues. Real-time issues to be examined, measured, and analyzed are: meeting waveform timing requirements and efficiently applying Real-time Operating System (RTOS) scheduling algorithms, applying safety control measures, and SWaP verification. Real-time waveform algorithms benchmarked with the worst case environment conditions under the heaviest workload will drive the SDR for Space real-time PSM design.

Golden mean Siegel disk universality and renormalization

OpenAIRE

Gaidashev, Denis; Yampolsky, Michael

2016-01-01

We provide a computer-assisted proof of one of the central open questions in one-dimensional renormalization theory -- universality of the golden-mean Siegel disks. We further show that for every function in the stable manifold of the golden-mean renormalization fixed point the boundary of the Siegel disk is a quasicircle which coincides with the closure of the critical orbit, and that the dynamics on the boundary of the Siegel disk is rigid. Furthermore, we extend the renormalization from on...

The analytic renormalization group

Directory of Open Access Journals (Sweden)

Frank Ferrari

2016-08-01

Full Text Available Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients Gk, k∈Z, associated with the Matsubara frequencies νk=2πk/β. We show that analyticity implies that the coefficients Gk must satisfy an infinite number of model-independent linear equations that we write down explicitly. In particular, we construct “Analytic Renormalization Group” linear maps Aμ which, for any choice of cut-off μ, allow to express the low energy Fourier coefficients for |νk|<μ (with the possible exception of the zero mode G0, together with the real-time correlators and spectral functions, in terms of the high energy Fourier coefficients for |νk|≥μ. Operating a simple numerical algorithm, we show that the exact universal linear constraints on Gk can be used to systematically improve any random approximate data set obtained, for example, from Monte-Carlo simulations. Our results are illustrated on several explicit examples.

Holographic renormalization and supersymmetry

Energy Technology Data Exchange (ETDEWEB)

Genolini, Pietro Benetti [Mathematical Institute, University of Oxford,Woodstock Road, Oxford OX2 6GG (United Kingdom); Cassani, Davide [LPTHE, Sorbonne Universités UPMC Paris 6 and CNRS, UMR 7589,F-75005, Paris (France); Martelli, Dario [Department of Mathematics, King’s College London,The Strand, London, WC2R 2LS (United Kingdom); Sparks, James [Mathematical Institute, University of Oxford,Woodstock Road, Oxford OX2 6GG (United Kingdom)

2017-02-27

Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N=2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges.

Analysis of coined quantum walks with renormalization

Science.gov (United States)

Boettcher, Stefan; Li, Shanshan

2018-01-01

We introduce a framework to analyze quantum algorithms with the renormalization group (RG). To this end, we present a detailed analysis of the real-space RG for discrete-time quantum walks on fractal networks and show how deep insights into the analytic structure as well as generic results about the long-time behavior can be extracted. The RG flow for such a walk on a dual Sierpinski gasket and a Migdal-Kadanoff hierarchical network is obtained explicitly from elementary algebraic manipulations, after transforming the unitary evolution equation into Laplace space. Unlike for classical random walks, we find that the long-time asymptotics for the quantum walk requires consideration of a diverging number of Laplace poles, which we demonstrate exactly for the closed-form solution available for the walk on a one-dimensional loop. In particular, we calculate the probability of the walk to overlap with its starting position, which oscillates with a period that scales as NdwQ/df with system size N . While the largest Jacobian eigenvalue λ1 of the RG flow merely reproduces the fractal dimension, df=log2λ1 , the asymptotic analysis shows that the second Jacobian eigenvalue λ2 becomes essential to determine the dimension of the quantum walk via dwQ=log2√{λ1λ2 } . We trace this fact to delicate cancellations caused by unitarity. We obtain identical relations for other networks, although the details of the RG analysis may exhibit surprisingly distinct features. Thus, our conclusions—which trivially reproduce those for regular lattices with translational invariance with df=d and dwQ=1 —appear to be quite general and likely apply to networks beyond those studied here.

Effects of Row Spacing and Plant Density on Yield and Yield Components of Sweet Corn in Climatic Conditions of Isfahan

Directory of Open Access Journals (Sweden)

N. Khodaeian

2013-06-01

Full Text Available To evaluate the effects of row spacing and plant density on yield and yield components of sweet corn, variety KSC403, an experiment was conducted in Research Farm of Isfahan University of Technology, Isfahan, Iran, in 2007, as randomized complete block design with a split-plot layout and three replications. The main plots were allocated to two row spacing (60 and 75 cm and the sub-plots accommodated four levels of plant density (50000, 70000, 90000 and 110000 plants per ha. There was significant increase in leaf area index, shoot dry weight, 100-grain fresh weight and grain fresh yield, as row width was decreased from 75 to 60 cm but the plant height was decreased. There was no significant effect of row spacing on number of rows per ear, number of grains per row and number of grains per ear. Plant height, leaf area index, shoot dry weight per m2 and number of ears per m2 were increased with an increase in plant density. The number of rows per ear, number of grains per row, number of grains per ear, 100-grain fresh weight and grain fresh yield were significantly higher under plant densities of 90000 and 110000 as compared to 50000 and 70000 plants per ha. There was significant interaction between row spacing and plant density for leaf area index, shoot dry weight, number of grains per ear, 100-grain fresh weight and grain fresh yield. Under all plant densities, the grain fresh yield was higher in 60-cm row width compared to 70-cm row width. However, the difference between these two row spacing was not significant in plant densities of 50000 and 110000 plants per ha. The highest grain fresh yield (33940 kg/ha was achieved under row spacing 60 cm and 70000 plants per ha and the least grain fresh yield (20750 kg/ha was obtained in under 75 cm row width and 110000 plants per ha. Considering the obtained results of this experiment, to have maximum grain fresh yield of sweet corn under Isfahan climate, the row spacing of 60 cm and plant density of

Renormalization Group and Phase Transitions in Spin, Gauge, and QCD Like Theories

Energy Technology Data Exchange (ETDEWEB)

Liu, Yuzhi [Univ. of Iowa, Iowa City, IA (United States)

2013-08-01

In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG).

Tourism in Real and Virtual Space

Directory of Open Access Journals (Sweden)

Alireza Dehghan

2009-07-01

Full Text Available During these two decades, according to the expansion of communication, there is a deep transformation in individuals’ conception of space. As space plays an important role in tourism, either real or virtual, this transformation happens in the field too. The present study attempts to show how tourism in the contemporary virtualized world, or as some authors name: the dual globalized situation, occurs.

Dimensional regularization and renormalization of Coulomb gauge quantum electrodynamics

International Nuclear Information System (INIS)

Heckathorn, D.

1979-01-01

Quantum electrodynamics is renormalized in the Coulomb gauge with covariant counter terms and without momentum-dependent wave-function renormalization constants. It is shown how to dimensionally regularize non-covariant integrals occurring in this guage, and prove that the 'minimal' subtraction prescription excludes non-covariant counter terms. Motivated by the need for a renormalized Coulomb gauge formalism in certain practical calculations, the author introduces a convenient prescription with physical parameters. The renormalization group equations for the Coulomb gauge are derived. (Auth.)

Sigma models and renormalization of string loops

International Nuclear Information System (INIS)

Tseytlin, A.A.

1989-05-01

An extension of the ''σ-model β-functions - string equations of motion'' correspondence to the string loop level is discussed. Special emphasis is made on how the renormalization group acts in string loops and, in particular, on the renormalizability property of the generating functional Z-circumflex for string amplitudes (related to the σ model partition function integrated over moduli). Renormalization of Z-circumflex at one and two loop order is analyzed in some detail. We also discuss an approach to renormalization based on operators of insertion of topological fixtures. (author). 70 refs

Effective AdS/renormalized CFT

OpenAIRE

Fan, JiJi

2011-01-01

For an effective AdS theory, we present a simple prescription to compute the renormalization of its dual boundary field theory. In particular, we define anomalous dimension holographically as the dependence of the wave-function renormalization factor on the radial cutoff in the Poincare patch of AdS. With this definition, the anomalous dimensions of both single- and double- trace operators are calculated. Three different dualities are considered with the field theory being CFT, CFT with a dou...

The two-loop renormalization of general quantum field theories

International Nuclear Information System (INIS)

Damme, R.M.J. van.

1984-01-01

This thesis provides a general method to compute all first order corrections to the renormalization group equations. This requires the computation of the first perturbative corrections to the renormalization group β-functions. These corrections are described by Feynman diagrams with two loops. The two-loop renormalization is treated for an arbitrary renormalization field theory. Two cases are considered: 1. the Yukawa sector; 2. the gauge coupling and the scalar potential. In a final section, the breakdown of unitarity in the dimensional reduction scheme is discussed. (Auth.)

Technical fine-tuning problem in renormalized perturbation theory

International Nuclear Information System (INIS)

Foda, O.E.

1983-01-01

The technical - as opposed to physical - fine tuning problem, i.e. the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a number of different models is studied. These include softly-broken supersymmetric models, and non-supersymmetric ones with a hierarchy of spontaneously-broken gauge symmetries. The models are renormalized using the BPHZ prescription, with momentum subtractions. Explicit calculations indicate that the tree-level hierarchy is not upset by the radiative corrections, and consequently no further fine-tuning is required to maintain it. Furthermore, this result is shown to run counter to that obtained via Dimensional Renormalization, (the only scheme used in previous literature on the subject). The discrepancy originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Within fully-renormalized perturbation theory the answer to the technical fine-tuning question (in the sense of whether the radiative corrections will ''readily'' respect the tree level gauge hierarchy or not) is contingent on the renormalization scheme used to define the model at the quantum level, rather than on the model itself. In other words, the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes

Technical fine-tuning problem in renormalized perturbation theory

Energy Technology Data Exchange (ETDEWEB)

Foda, O.E.

1983-01-01

The technical - as opposed to physical - fine tuning problem, i.e. the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a number of different models is studied. These include softly-broken supersymmetric models, and non-supersymmetric ones with a hierarchy of spontaneously-broken gauge symmetries. The models are renormalized using the BPHZ prescription, with momentum subtractions. Explicit calculations indicate that the tree-level hierarchy is not upset by the radiative corrections, and consequently no further fine-tuning is required to maintain it. Furthermore, this result is shown to run counter to that obtained via Dimensional Renormalization, (the only scheme used in previous literature on the subject). The discrepancy originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Within fully-renormalized perturbation theory the answer to the technical fine-tuning question (in the sense of whether the radiative corrections will ''readily'' respect the tree level gauge hierarchy or not) is contingent on the renormalization scheme used to define the model at the quantum level, rather than on the model itself. In other words, the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes.

Higher derivatives and renormalization in quantum cosmology

International Nuclear Information System (INIS)

Mazzitelli, F.D.

1991-10-01

In the framework of the canonical quantization of general relativity, quantum field theory on a fixed background formally arises in an expansion in powers of the Planck length. In order to renormalize the theory, quadratic terms in the curvature must be included in the gravitational action from the beginning. These terms contain higher derivatives which change the Hamiltonian structure of the theory completely, making the relation between the renormalized-theory and the original one not clear. We show that it is possible to avoid this problem. We replace the higher derivative theory by a second order one. The classical solutions of the latter are also solutions of the former. We quantize the theory, renormalize the infinities and show that there is a smooth limit between the classical and the renormalized theories. We work in a Robertson Walker minisuperspace with a quantum scalar field. (author). 32 refs

Renormalization in general theories with inter-generation mixing

International Nuclear Information System (INIS)

Kniehl, Bernd A.; Sirlin, Alberto

2011-11-01

We derive general and explicit expressions for the unrenormalized and renormalized dressed propagators of fermions in parity-nonconserving theories with inter-generation mixing. The mass eigenvalues, the corresponding mass counterterms, and the effect of inter-generation mixing on their determination are discussed. Invoking the Aoki-Hioki-Kawabe-Konuma-Muta renormalization conditions and employing a number of very useful relations from Matrix Algebra, we show explicitly that the renormalized dressed propagators satisfy important physical properties. (orig.)

On the renormalization group equations of quantum electrodynamics

International Nuclear Information System (INIS)

Hirayama, Minoru

1980-01-01

The renormalization group equations of quantum electrodynamics are discussed. The solution of the Gell-Mann-Low equation is presented in a convenient form. The interrelation between the Nishijima-Tomozawa equation and the Gell-Mann-Low equation is clarified. The reciprocal effective charge, so to speak, turns out to play an important role to discuss renormalization group equations. Arguments are given that the reciprocal effective charge vanishes as the renormalization momentum tends to infinity. (author)

Renormalization: infinity in today microscopic physics

International Nuclear Information System (INIS)

Zinn-Justin, J.

2000-01-01

The expectations put in quantum electrodynamics were deceived when first calculations showed that divergencies, due to the pinpoint aspect of the electron, continued to exist. Later, as a consequence of new experimental data and theoretical progress, an empirical method called renormalization was proposed to allow the evaluation of expressions involving infinite terms. The development of this method opened the way to the theory of re-normalizing fields and gave so successful results that it was applied to all fundamental interactions except gravity. This theory allowed the standard model in weak, electromagnetic and strong interactions to be confronted successfully with experimental data during more than 25 years. This article presents the progressive evolution of ideas in the concept of renormalization. (A.C.)

Renormalized modes in cuprate superconductors

Science.gov (United States)

Gupta, Anushri; Kumari, Anita; Verma, Sanjeev K.; Indu, B. D.

2018-04-01

The renormalized mode frequencies are obtained with the help of quantum dynamical approach of many body phonon Green's function technique via a general Hamiltonian (excluding BCS Hamiltonian) including the effects of phonons and electrons, anharmonicities and electron-phonon interactions. The numerical estimates have been carried out to study the renormalized mode frequency of high temperature cuprate superconductor (HTS) YBa2Cu3O7-δ using modified Born-Mayer-Huggins interaction potential (MBMHP) best applicable to study the dynamical properties of all HTS.

Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence

Science.gov (United States)

Rubinstein, Robert

1994-01-01

Bolgiano scaling in Boussinesq turbulence is analyzed using the Yakhot-Orszag renormalization group. For this purpose, an isotropic model is introduced. Scaling exponents are calculated by forcing the temperature equation so that the temperature variance flux is constant in the inertial range. Universal amplitudes associated with the scaling laws are computed by expanding about a logarithmic theory. Connections between this formalism and the direct interaction approximation are discussed. It is suggested that the Yakhot-Orszag theory yields a lowest order approximate solution of a regularized direct interaction approximation which can be corrected by a simple iterative procedure.

Renormalized thermodynamic entropy of black holes in higher dimensions

International Nuclear Information System (INIS)

Kim, S.P.; Kim, S.K.; Soh, K.; Yee, J.H.

1997-01-01

We study the ultraviolet divergent structures of the matter (scalar) field in a higher D-dimensional Reissner-Nordstroem black hole and compute the matter field contribution to the Bekenstein-Hawking entropy by using the Pauli-Villars regularization method. We find that the matter field contribution to the black hole entropy does not, in general, yield the correct renormalization of the gravitational coupling constants. In particular, we show that the matter field contribution in odd dimensions does not give the term proportional to the area of the black hole event horizon. copyright 1997 The American Physical Society

Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review

Science.gov (United States)

Wu, Xing-Gang; Ma, Yang; Wang, Sheng-Quan; Fu, Hai-Bing; Ma, Hong-Hao; Brodsky, Stanley J.; Mojaza, Matin

2015-12-01

A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme—this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. In a previous review, we provided a general introduction to the various scale setting approaches suggested in the literature. As a step forward, in the present review, we present a discussion in depth of two well-established scale-setting methods based on RGI. One is the ‘principle of maximum conformality’ (PMC) in which the terms associated with the β-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the ‘principle of minimum sensitivity’ (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables R e+e- and Γ(H\\to b\\bar{b}) up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: the PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. PMC predictions also have the property that any residual dependence on

Renormalization group in modern physics

International Nuclear Information System (INIS)

Shirkov, D.V.

1988-01-01

Renormalization groups used in diverse fields of theoretical physics are considered. The discussion is based upon functional formulation of group transformations. This attitude enables development of a general method by using the notion of functional self-similarity which generalizes the usual self-similarity connected with power similarity laws. From this point of view the authors present a simple derivation of the renorm-group (RG) in QFT liberated from ultra-violet divergences philosophy, discuss the RG approach in other fields of physics and compare different RG's

Optimization of renormalization group transformations in lattice gauge theory

International Nuclear Information System (INIS)

Lang, C.B.; Salmhofer, M.

1988-01-01

We discuss the dependence of the renormalization group flow on the choice of the renormalization group transformation (RGT). An optimal choice of the transformation's parameters should lead to a renormalized trajectory close to a few-parameter action. We apply a recently developed method to determine an optimal RGT to SU(2) lattice gauge theory and discuss the achieved improvement. (orig.)

Maximum-entropy data restoration using both real- and Fourier-space analysis

International Nuclear Information System (INIS)

Anderson, D.M.; Martin, D.C.; Thomas, E.L.

1989-01-01

An extension of the maximum-entropy (ME) data-restoration method is presented that is sensitive to periodic correlations in data. The method takes advantage of the higher signal-to-noise ratio for periodic information in Fourier space, thus enhancing statistically significant frequencies in a manner which avoids the user bias inherent in conventional Fourier filtering. This procedure incorporates concepts underlying new approaches in quantum mechanics that consider entropies in both position and momentum spaces, although the emphasis here is on data restoration rather than quantum physics. After a fast Fourier transform of the image, the phases are saved and the array of Fourier moduli are restored using the maximum-entropy criterion. A first-order continuation method is introduced that speeds convergence of the ME computation. The restored moduli together with the original phases are then Fourier inverted to yield a new image; traditional real-space ME restoration is applied to this new image completing one stage in the restoration process. In test cases improvement can be obtained from two to four stages of iteration. It is shown that in traditional Fourier filtering spurious features can be induced by selection or elimination of Fourier components without regard to their statistical significance. With the present approach there is no such freedom for the user to exert personal bias, so that features present in the final image and power spectrum are those which have survived the tests of statistical significance in both real and Fourier space. However, it is still possible for periodicities to 'bleed' across sharp boundaries. An 'uncertainty' relation is derived describing the inverse relationship between the resolution of these boundaries and the level of noise that can be eliminated. (orig./BHO)

Influence of Inter-Intra Row Spacing on Yield Losses of Tomato ...

African Journals Online (AJOL)

Data on major yield loss agents such as, blossom end rot, decay, insect, disease, sunburn, crack, catface and others minor disorders were collected; as well as total yield, percent of marketable and unmarketable fruit yield parameters were analyzed. Results of the study showed that inter-intra row spacing and cultivar had a ...

Two-loop renormalization in the standard model, part I. Prolegomena

Energy Technology Data Exchange (ETDEWEB)

Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Ferroglia, A. [Albert-Ludwigs-Univ., Freiburg (Germany). Fakultat fur Phys.]|[Zuerich Univ. (Switzerland). Inst. fuer Theoretische Physik; Passera, M. [Padua Univ. (Italy). Dipt. di Fisica]|[INFN, Sezione di Padova (Italy); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica]|[INFN, Sezione di Torino (Italy)

2006-12-15

In this paper the building blocks for the two-loop renormalization of the Standard Model are introduced with a comprehensive discussion of the special vertices induced in the Lagrangian by a particular diagonalization of the neutral sector and by two alternative treatments of the Higgs tadpoles. Dyson resummed propagators for the gauge bosons are derived, and two-loop Ward-Slavnov-Taylor identities are discussed. In part II, the complete set of counterterms needed for the two-loop renormalization will be derived. In part III, a renormalization scheme will be introduced, connecting the renormalized quantities to an input parameter set of (pseudo-)experimental data, critically discussing renormalization of a gauge theory with unstable particles. (orig.)

Renormalization of g-boson effects under weak coupling condition

International Nuclear Information System (INIS)

Zhang Zhanjun; Yang Jie; Liu Yong; Sang Jianping

1998-01-01

An approach based on perturbation theory is proposed to renormalized g-boson effects for sdgIBM system, which modifies that presented earlier by Druce et al. The weak coupling condition as the usage premise of the two approaches is proved to be satisfied. Two renormalization spectra are calculated for comparison and analyses. Results show that the g-boson effects are renormalized more completely by the approach proposed

Keeping it real: revisiting a real-space approach to running ensembles of cosmological N-body simulations

International Nuclear Information System (INIS)

Orban, Chris

2013-01-01

In setting up initial conditions for ensembles of cosmological N-body simulations there are, fundamentally, two choices: either maximizing the correspondence of the initial density field to the assumed fourier-space clustering or, instead, matching to real-space statistics and allowing the DC mode (i.e. overdensity) to vary from box to box as it would in the real universe. As a stringent test of both approaches, I perform ensembles of simulations using power law and a ''powerlaw times a bump'' model inspired by baryon acoustic oscillations (BAO), exploiting the self-similarity of these initial conditions to quantify the accuracy of the matter-matter two-point correlation results. The real-space method, which was originally proposed by Pen 1997 [1] and implemented by Sirko 2005 [2], performed well in producing the expected self-similar behavior and corroborated the non-linear evolution of the BAO feature observed in conventional simulations, even in the strongly-clustered regime (σ 8 ∼>1). In revisiting the real-space method championed by [2], it was also noticed that this earlier study overlooked an important integral constraint correction to the correlation function in results from the conventional approach that can be important in ΛCDM simulations with L box ∼ −1 Gpc and on scales r∼>L box /10. Rectifying this issue shows that the fourier space and real space methods are about equally accurate and efficient for modeling the evolution and growth of the correlation function, contrary to previous claims. An appendix provides a useful independent-of-epoch analytic formula for estimating the importance of the integral constraint bias on correlation function measurements in ΛCDM simulations

A low-cost approach to electronic excitation energies based on the driven similarity renormalization group

Science.gov (United States)

Li, Chenyang; Verma, Prakash; Hannon, Kevin P.; Evangelista, Francesco A.

2017-08-01

We propose an economical state-specific approach to evaluate electronic excitation energies based on the driven similarity renormalization group truncated to second order (DSRG-PT2). Starting from a closed-shell Hartree-Fock wave function, a model space is constructed that includes all single or single and double excitations within a given set of active orbitals. The resulting VCIS-DSRG-PT2 and VCISD-DSRG-PT2 methods are introduced and benchmarked on a set of 28 organic molecules [M. Schreiber et al., J. Chem. Phys. 128, 134110 (2008)]. Taking CC3 results as reference values, mean absolute deviations of 0.32 and 0.22 eV are observed for VCIS-DSRG-PT2 and VCISD-DSRG-PT2 excitation energies, respectively. Overall, VCIS-DSRG-PT2 yields results with accuracy comparable to those from time-dependent density functional theory using the B3LYP functional, while VCISD-DSRG-PT2 gives excitation energies comparable to those from equation-of-motion coupled cluster with singles and doubles.

Quantum fields in curved space

International Nuclear Information System (INIS)

Birrell, N.D.; Davies, P.C.W.

1982-01-01

The book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Quantum field theory in Minkowski space, quantum field theory in curved spacetime, flat spacetime examples, curved spacetime examples, stress-tensor renormalization, applications of renormalization techniques, quantum black holes and interacting fields are all discussed in detail. (U.K.)

Zeta Functions, Renormalization Group Equations, and the Effective Action

International Nuclear Information System (INIS)

Hochberg, D.; Perez-Mercader, J.; Molina-Paris, C.; Visser, M.

1998-01-01

We demonstrate how to extract all the one-loop renormalization group equations for arbitrary quantum field theories from knowledge of an appropriate Seeley-DeWitt coefficient. By formally solving the renormalization group equations to one loop, we renormalization group improve the classical action and use this to derive the leading logarithms in the one-loop effective action for arbitrary quantum field theories. copyright 1998 The American Physical Society

Renormalization group approach in the turbulence theory

International Nuclear Information System (INIS)

Adzhemyan, L.Ts.; Vasil'ev, A.N.; Pis'mak, Yu.M.

1983-01-01

In the framework of the renormalization groUp approach in the turbulence theory sUggested in another paper, the problem of renormalization and evaluation of critical dimensions of composite operators is discussed. Renormalization of a system of operators of canonical dimension equal to 4, including the operator F=phiΔphi (where phi is the velocity field), is considered. It is shown that the critical dimension Δsub(F)=0. The appendice includes the brief proofs of two theorems: 1) the theorem on the equivalence between the arbitrary stochastic problem and quantum field theory; 2) the theorem which determines the reduction of Green functions of the stochastic problem to the hypersurface of coinciding times

Non-perturbative renormalization of three-quark operators

Energy Technology Data Exchange (ETDEWEB)

Goeckeler, Meinulf [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Horsley, Roger [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Kaltenbrunner, Thomas [Regensburg Univ. (DE). Inst. fuer Theoretische Physik] (and others)

2008-10-15

High luminosity accelerators have greatly increased the interest in semi-exclusive and exclusive reactions involving nucleons. The relevant theoretical information is contained in the nucleon wavefunction and can be parametrized by moments of the nucleon distribution amplitudes, which in turn are linked to matrix elements of local three-quark operators. These can be calculated from first principles in lattice QCD. Defining an RI-MOM renormalization scheme, we renormalize three-quark operators corresponding to low moments non-perturbatively and take special care of the operator mixing. After performing a scheme matching and a conversion of the renormalization scale we quote our final results in the MS scheme at {mu}=2 GeV. (orig.)

Studies in the renormalization-prescription dependence of perturbative calculations

International Nuclear Information System (INIS)

Celmaster, W.; Sivers, D.

1981-01-01

Now that the quantitative testing of perturbative quantum chromodynamics (QCD) has become a major experimental and theoretical effort, it is important to understand the renormalization-prescription dependence of perturbative calculations. We stress the phenomenological importance of finding a definition of the QCD expansion parameter which reduces the magnitude of high-order corrections. We give explicit arguments suggesting that a choice of coupling based on momentum-space subtraction can be phenomenologically useful. Examples from QCD and QED are used to illustrate these arguments, and we also discuss possibilities for refining them

Effects of renormalizing the chiral SU(2) quark-meson model

Science.gov (United States)

Zacchi, Andreas; Schaffner-Bielich, Jürgen

2018-04-01

We investigate the restoration of chiral symmetry at finite temperature in the SU(2) quark-meson model, where the mean field approximation is compared to the renormalized version for quarks and mesons. In a combined approach at finite temperature, all the renormalized versions show a crossover transition. The inclusion of different renormalization scales leave the order parameter and the mass spectra nearly untouched but strongly influence the thermodynamics at low temperatures and around the phase transition. We find unphysical results for the renormalized version of mesons and the combined one.

The renormalization scale-setting problem in QCD

Energy Technology Data Exchange (ETDEWEB)

Wu, Xing-Gang [Chongqing Univ. (China); Brodsky, Stanley J. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Mojaza, Matin [SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of Southern Denmark, Odense (Denmark)

2013-09-01

A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this ad hoc procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of the scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scale ambiguity and show how to obtain renormalization scheme- and scale-independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the scheme- and scale-dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, i.e., the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky–Lepage–Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance. Using the PMC, all non-conformal terms associated with the β-function in the perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC provides the principle underlying the BLM method, since it gives the general rule for extending

Renormalization group and fixed points in quantum field theory

International Nuclear Information System (INIS)

Hollowood, Timothy J.

2013-01-01

This Brief presents an introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics. Emphasis is placed on gaining a physical understanding of the running of the couplings. The Wilsonian version of the renormalization group is related to conventional perturbative calculations with dimensional regularization and minimal subtraction. An introduction is given to some of the remarkable renormalization group properties of supersymmetric theories.

Renormalizing Entanglement Distillation

Science.gov (United States)

Waeldchen, Stephan; Gertis, Janina; Campbell, Earl T.; Eisert, Jens

2016-01-01

Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, which are needed to transmit entanglement over arbitrary distances in order to realize quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are identically and independently distributed and are uncorrelated with each other, an assumption that might not be reasonable at all in any entanglement generation process involving memory channels. Here, we introduce a framework that captures entanglement distillation in the presence of natural correlations arising from memory channels. Conceptually, we bring together ideas from condensed-matter physics—ideas from renormalization and matrix-product states and operators—with those of local entanglement manipulation, Markov chain mixing, and quantum error correction. We identify meaningful parameter regions for which we prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow.

Renormalization and 3-manifolds which fiber over the circle (AM-142)

CERN Document Server

McMullen, Curtis T

2014-01-01

Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitativ

The renormalized theory of beam-beam interaction

International Nuclear Information System (INIS)

Chin, Yong Ho.

1988-06-01

A new approach to calculate analytically the particle distribution in the presence of beam-beam interaction and synchrotron radiation effects for an electron-positron colliding beam storage ring is presented. The method is based on correct calculation of the Green's function which includes the full effect of the beam-beam force on the distortion of particle orbits, borrowing the renormalization technique of quantum field therory. By this way, the theory is applicable to any level of beam-beam interaction, no matter whether chaos ensues in phase space or not. This paper is devoted mostly to verificaiton of the theory by comparison with the results of computer simulations. Fairly good agreements are obtained. 5 refs., 3 figs

Source Localization by Entropic Inference and Backward Renormalization Group Priors

Directory of Open Access Journals (Sweden)

Nestor Caticha

2015-04-01

Full Text Available A systematic method of transferring information from coarser to finer resolution based on renormalization group (RG transformations is introduced. It permits building informative priors in finer scales from posteriors in coarser scales since, under some conditions, RG transformations in the space of hyperparameters can be inverted. These priors are updated using renormalized data into posteriors by Maximum Entropy. The resulting inference method, backward RG (BRG priors, is tested by doing simulations of a functional magnetic resonance imaging (fMRI experiment. Its results are compared with a Bayesian approach working in the finest available resolution. Using BRG priors sources can be partially identified even when signal to noise ratio levels are up to ~ -25dB improving vastly on the single step Bayesian approach. For low levels of noise the BRG prior is not an improvement over the single scale Bayesian method. Analysis of the histograms of hyperparameters can show how to distinguish if the method is failing, due to very high levels of noise, or if the identification of the sources is, at least partially possible.

Phases of renormalized lattice gauge theories with fermions

International Nuclear Information System (INIS)

Caracciolo, S.; Menotti, P.; and INFN Sezione di Pisa, Italy)

1979-01-01

Starting from the formulation of gauge theories on a lattice we derive renormalization group transformation of the Migdal-Kadanoff type in the presence of fermions. We consider the effect of the fermion vacuum polarization on the gauge Lagrangian but we neglect fermion mass renormalization. We work out the weak coupling and strong coupling expansion in the same framework. Asymptotic freedom is recovered for the non-Abelian case provided the number of fermion multiplets is lower than a critical number. Fixed points are determined both for the U (1) and SU (2) case. We determine the renormalized trajectories and the phases of the theory

Modeling solvation effects in real-space and real-time within density functional approaches

Energy Technology Data Exchange (ETDEWEB)

Delgado, Alain [Istituto Nanoscienze - CNR, Centro S3, via Campi 213/A, 41125 Modena (Italy); Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear, Calle 30 # 502, 11300 La Habana (Cuba); Corni, Stefano; Pittalis, Stefano; Rozzi, Carlo Andrea [Istituto Nanoscienze - CNR, Centro S3, via Campi 213/A, 41125 Modena (Italy)

2015-10-14

The Polarizable Continuum Model (PCM) can be used in conjunction with Density Functional Theory (DFT) and its time-dependent extension (TDDFT) to simulate the electronic and optical properties of molecules and nanoparticles immersed in a dielectric environment, typically liquid solvents. In this contribution, we develop a methodology to account for solvation effects in real-space (and real-time) (TD)DFT calculations. The boundary elements method is used to calculate the solvent reaction potential in terms of the apparent charges that spread over the van der Waals solute surface. In a real-space representation, this potential may exhibit a Coulomb singularity at grid points that are close to the cavity surface. We propose a simple approach to regularize such singularity by using a set of spherical Gaussian functions to distribute the apparent charges. We have implemented the proposed method in the OCTOPUS code and present results for the solvation free energies and solvatochromic shifts for a representative set of organic molecules in water.

Renormalization of the γ-ray strength functions of light nuclei

International Nuclear Information System (INIS)

Canbula, B.; Ersan, S.; Babacan, H.

2015-01-01

γ-ray strength function is the key input for the photonuclear reactions, which have a special astrophysical importance, and should be renormalized by using the nuclear level density for calculating the theoretical average radiative capture width, but performing such renormalization is challenging for light nuclei. With this motivation, recently introduced level density parameter formula including collective effects is used to calculate the average radiative capture width of light nuclei, and therefore to renormalize their γ-ray strength functions. Obtained normalization factors are tested in (n, γ) reactions for the necessity of renormalization for light nuclei. (author)

Unique determination of the effective potential in terms of renormalization group functions

International Nuclear Information System (INIS)

Chishtie, F. A.; Hanif, T.; McKeon, D. G. C.; Steele, T. G.

2008-01-01

The perturbative effective potential V in the massless λφ 4 model with a global O(N) symmetry is uniquely determined to all orders by the renormalization group functions alone when the Coleman-Weinberg renormalization condition (d 4 V/dφ 4 )| φ=μ =λ is used, where μ represents the renormalization scale. Systematic methods are developed to express the n-loop effective potential in the Coleman-Weinberg scheme in terms of the known n-loop minimal-subtraction (MS) renormalization group functions. Moreover, it also proves possible to sum the leading- and subsequent-to-leading-logarithm contributions to V. An essential element of this analysis is a conversion of the renormalization group functions in the Coleman-Weinberg scheme to the renormalization group functions in the MS scheme. As an example, the explicit five-loop effective potential is obtained from the known five-loop MS renormalization group functions and we explicitly sum the leading-logarithm, next-to-leading-logarithm, and further subleading-logarithm contributions to V. Extensions of these results to massless scalar QED are also presented. Because massless scalar QED has two couplings, conversion of the renormalization group functions from the MS scheme to the Coleman-Weinberg scheme requires the use of multiscale renormalization group methods.

Spaces an introduction to real analysis

CERN Document Server

Lindstrøm, Tom L

2017-01-01

Spaces is a modern introduction to real analysis at the advanced undergraduate level. It is forward-looking in the sense that it first and foremost aims to provide students with the concepts and techniques they need in order to follow more advanced courses in mathematical analysis and neighboring fields. The only prerequisites are a solid understanding of calculus and linear algebra. Two introductory chapters will help students with the transition from computation-based calculus to theory-based analysis. The main topics covered are metric spaces, spaces of continuous functions, normed spaces, differentiation in normed spaces, measure and integration theory, and Fourier series. Although some of the topics are more advanced than what is usually found in books of this level, care is taken to present the material in a way that is suitable for the intended audience: concepts are carefully introduced and motivated, and proofs are presented in full detail. Applications to differential equations and Fourier analysis ...

Investigation of renormalization effects in high temperature cuprate superconductors

International Nuclear Information System (INIS)

Zabolotnyy, Volodymyr B.

2008-01-01

It has been found that the self-energy of high-T C cuprates indeed exhibits a well pronounced structure, which is currently attributed to coupling of the electrons either to lattice vibrations or to collective magnetic excitations in the system. To clarify this issue, the renormalization effects and the electronic structure of two cuprate families Bi 2 Sr 2 CaCu 2 O 8+δ and YBa 2 Cu 3 O 7-δ were chosen as the main subject for this thesis. With a simple example of an electronic system coupled to a collective mode unusual renormalization features observed in the photoemission spectra are introduced. It is shown that impurity substitution in general leads to suppression of the unusual renormalization. Finally an alternative possibility to obtain a purely superconducting surface of Y-123 via partial substitution of Y atoms with Ca is introduced. It is shown that renormalization in the superconducting Y-123 has similar strong momentum dependence as in the Bi-2212 family. It is also shown that in analogy to Bi-2212 the renormalization appears to have strong dependence on the doping level (no kinks for the overdoped component) and practically vanishes above T C suggesting that coupling to magnetic excitations fits much better than competing scenarios, according to which the unusual renormalization in ARPES spectra is caused by the coupling to single or multiple phononic modes. (orig.)

The Renormalization Group in Nuclear Physics

International Nuclear Information System (INIS)

Furnstahl, R.J.

2012-01-01

Modern techniques of the renormalization group (RG) combined with effective field theory (EFT) methods are revolutionizing nuclear many-body physics. In these lectures we will explore the motivation for RG in low-energy nuclear systems and its implementation in systems ranging from the deuteron to neutron stars, both formally and in practice. Flow equation approaches applied to Hamiltonians both in free space and in the medium will be emphasized. This is a conceptually simple technique to transform interactions to more perturbative and universal forms. An unavoidable complication for nuclear systems from both the EFT and flow equation perspective is the need to treat many-body forces and operators, so we will consider these aspects in some detail. We'll finish with a survey of current developments and open problems in nuclear RG.

Renormalization and effective actions for general relativity

International Nuclear Information System (INIS)

Neugebohrn, F.

2007-05-01

Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the program of renormalization with flow equations is reviewed and then extended to effective field theories that have a finite UV cutoff. This is done for a scalar field theory by imposing additional renormalization conditions for some of the nonrenormalizable couplings. It turns out that one so obtains a statement on the predictivity of the effective theory at scales far below the UV cutoff. In particular, nonrenormalizable theories can be treated without problems in the proposed framework. In the second part, the standard covariant BRS quantization program for Euclidean Einstein gravity is applied. A momentum cutoff regularization is imposed and the resulting violation of the Slavnov-Taylor identities is discussed. Deriving Polchinski's renormalization group equation for Euclidean quantum gravity, the predictivity of effective quantum gravity at scales far below the Planck scale is investigated with flow equations. A fine-tuning procedure for restoring the violated Slavnov-Taylor identities is proposed and it is argued that in the effective quantum gravity context, the restoration will only be accomplished with finite accuracy. Finally, the no-cutoff limit of Euclidean quantum gravity is analyzed from the viewpoint of the Polchinski method. It is speculated whether a limit with nonvanishing gravitational constant might exist where the latter would ultimatively be determined by the cosmological constant and the masses of the elementary particles. (orig.)

Renormalization and effective actions for general relativity

Energy Technology Data Exchange (ETDEWEB)

Neugebohrn, F.

2007-05-15

Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the program of renormalization with flow equations is reviewed and then extended to effective field theories that have a finite UV cutoff. This is done for a scalar field theory by imposing additional renormalization conditions for some of the nonrenormalizable couplings. It turns out that one so obtains a statement on the predictivity of the effective theory at scales far below the UV cutoff. In particular, nonrenormalizable theories can be treated without problems in the proposed framework. In the second part, the standard covariant BRS quantization program for Euclidean Einstein gravity is applied. A momentum cutoff regularization is imposed and the resulting violation of the Slavnov-Taylor identities is discussed. Deriving Polchinski's renormalization group equation for Euclidean quantum gravity, the predictivity of effective quantum gravity at scales far below the Planck scale is investigated with flow equations. A fine-tuning procedure for restoring the violated Slavnov-Taylor identities is proposed and it is argued that in the effective quantum gravity context, the restoration will only be accomplished with finite accuracy. Finally, the no-cutoff limit of Euclidean quantum gravity is analyzed from the viewpoint of the Polchinski method. It is speculated whether a limit with nonvanishing gravitational constant might exist where the latter would ultimatively be determined by the cosmological constant and the masses of the elementary particles. (orig.)

Renormalization in the complete Mellin representation of Feynman amplitudes

International Nuclear Information System (INIS)

Calan, C. de; David, F.; Rivasseau, V.

1981-01-01

The Feynmann amplitudes are renormalized in the formalism of the CM representation. This Mellin-Barnes type integral representation, previously introduced for the study of asymptotic behaviours, is shown to have the following interesting property: in contrast with the usual subtraction procedures, the renormalization leaves the CM intergrand unchanged, and only results into translations of the integration path. The explicit CM representation of the renormalized amplitudes is given. In addition, the dimensional regularization and the extension to spinor amplitudes are sketched. (orig.)

Quantum field theory and phase transitions: universality and renormalization group

International Nuclear Information System (INIS)

Zinn-Justin, J.

2003-08-01

In the quantum field theory the problem of infinite values has been solved empirically through a method called renormalization, this method is satisfying only in the framework of renormalization group. It is in the domain of statistical physics and continuous phase transitions that these issues are the easiest to discuss. Within the framework of a course in theoretical physics the author introduces the notions of continuous limits and universality in stochastic systems operating with a high number of freedom degrees. It is shown that quasi-Gaussian and mean field approximation are unable to describe phase transitions in a satisfying manner. A new concept is required: it is the notion of renormalization group whose fixed points allow us to understand universality beyond mean field. The renormalization group implies the idea that long distance correlations near the transition temperature might be described by a statistical field theory that is a quantum field in imaginary time. Various forms of renormalization group equations are presented and solved in particular boundary limits, namely for fields with high numbers of components near the dimensions 4 and 2. The particular case of exact renormalization group is also introduced. (A.C.)

Wetting transitions: A functional renormalization-group approach

International Nuclear Information System (INIS)

Fisher, D.S.; Huse, D.A.

1985-01-01

A linear functional renormalization group is introduced as a framework in which to treat various wetting transitions of films on substrates. A unified treatment of the wetting transition in three dimensions with short-range interactions is given. The results of Brezin, Halperin, and Leibler in their three different regimes are reproduced along with new results on the multicritical behavior connecting the various regimes. In addition, the critical behavior as the coexistence curve is approached at complete wetting is analyzed. Wetting in the presence of long-range substrate-film interactions that fall off as power laws is also studied. The possible effects of the nonlinear terms in the renormalization group are examined briefly and it appears that they do not alter the critical behavior found using the truncated linear renormalization group

Superconformal gravity in Hamiltonian form: another approach to the renormalization of gravitation

International Nuclear Information System (INIS)

Kaku, M.

1983-01-01

We reexpress superconformal gravity in Hamiltonian form, explicitly displaying all 24 generators of the group as Dirac constraints on the Hilbert space. From this, we can establish a firm foundation for the canonical quantization of superconformal gravity. The purpose of writing down the Hamiltonian form of the theory is to reexamine the question of renormalization and unitarity. Usually, we start with unitary theories of gravity, such as the Einstein-Hilbert action or supergravity, both of which are probably not renormalizable. In this series of papers, we take the opposite approach and start with a theory which is renormalizable but has problems with unitarity. Conformal and superconformal gravity are both plagued with dipole ghosts when we use perturbation theory to quantize the theories. It is difficult to interpret the results of perturbation theory because the asymptotic states have zero norm and the potential between particles grows linearly with the separation distance. The purpose of writing the Hamiltonian form of these theories is to approach the question of unitarity from a different point of view. For example, a strong-coupling approach to these theories may yield a totally different perturbation expansion. We speculate that canonically quantizing the theory by power expanding in the strong-coupling regime may yield a different set of asymptotic states, somewhat similar to the situation in gauge theories. In this series of papers, we wish to reopen the question of the unitarity of conformal theories. We conjecture that ghosts are ''confined.''

First-principles real-space tight-binding LMTO calculation of electronic structures for atomic clusters

International Nuclear Information System (INIS)

Xie, Z.L.; Dy, K.S.; Wu, S.Y.

1997-01-01

A real-space scheme has been developed for a first-principles calculation of electronic structures and total energies of atomic clusters. The scheme is based on the combination of the tight-binding linear muffin-tin orbital (TBLMTO) method and the method of real-space Green close-quote s function. With this approach, the local electronic density of states can be conveniently determined from the real-space Green close-quote s function. Furthermore, the full electron density of a cluster can be directly calculated in real space. The scheme has been shown to be very efficient due to the incorporation of the method of real-space Green close-quote s function and Delley close-quote s method of evaluating multicenter integrals. copyright 1996 The American Physical Society

Real hypersurfaces of a complex projective space

Indian Academy of Sciences (India)

Kaehler manifolds of con- stant holomorphic sectional curvature c) is a very interesting and active area of research. The ambient space ¯M(c), specially in the case c = 0 imposes quite significant restrictions on the geometry of its real hypersurfaces.

Seeing real-space dynamics of liquid water through inelastic x-ray scattering.

Science.gov (United States)

Iwashita, Takuya; Wu, Bin; Chen, Wei-Ren; Tsutsui, Satoshi; Baron, Alfred Q R; Egami, Takeshi

2017-12-01

Water is ubiquitous on earth, but we know little about the real-space motion of molecules in liquid water. We demonstrate that high-resolution inelastic x-ray scattering measurement over a wide range of momentum and energy transfer makes it possible to probe real-space, real-time dynamics of water molecules through the so-called Van Hove function. Water molecules are found to be strongly correlated in space and time with coupling between the first and second nearest-neighbor molecules. The local dynamic correlation of molecules observed here is crucial to a fundamental understanding of the origin of the physical properties of water, including viscosity. The results also suggest that the quantum-mechanical nature of hydrogen bonds could influence its dynamics. The approach used here offers a powerful experimental method for investigating real-space dynamics of liquids.

Investigation of renormalization effects in high temperature cuprate superconductors

Energy Technology Data Exchange (ETDEWEB)

Zabolotnyy, Volodymyr B.

2008-04-16

It has been found that the self-energy of high-T{sub C} cuprates indeed exhibits a well pronounced structure, which is currently attributed to coupling of the electrons either to lattice vibrations or to collective magnetic excitations in the system. To clarify this issue, the renormalization effects and the electronic structure of two cuprate families Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} and YBa{sub 2}Cu{sub 3}O{sub 7-{delta}} were chosen as the main subject for this thesis. With a simple example of an electronic system coupled to a collective mode unusual renormalization features observed in the photoemission spectra are introduced. It is shown that impurity substitution in general leads to suppression of the unusual renormalization. Finally an alternative possibility to obtain a purely superconducting surface of Y-123 via partial substitution of Y atoms with Ca is introduced. It is shown that renormalization in the superconducting Y-123 has similar strong momentum dependence as in the Bi-2212 family. It is also shown that in analogy to Bi-2212 the renormalization appears to have strong dependence on the doping level (no kinks for the overdoped component) and practically vanishes above T{sub C} suggesting that coupling to magnetic excitations fits much better than competing scenarios, according to which the unusual renormalization in ARPES spectra is caused by the coupling to single or multiple phononic modes. (orig.)

A simple proof of renormalization group equation in the minimal subtraction scheme

International Nuclear Information System (INIS)

Chetyrkin, K.G.

1989-04-01

We give a simple combinatorial proof of the renormalization group equation in the minimal subtraction scheme. Being mathematically rigorous, the proof avoids both the notorious complexity of techniques using parametric representations of Feynman diagrams and heuristic arguments of usual ''proofs'' calling up bare fields living in the space-time of complex dimension. It also copes easily with the general case of Green functions of arbitrary number of composite fields. (author). 24 refs

Renormalization using the background-field method

International Nuclear Information System (INIS)

Ichinose, S.; Omote, M.

1982-01-01

Renormalization using the background-field method is examined in detail. The subtraction mechanism of subdivergences is described with reference to multi-loop diagrams and one- and two-loop counter-term formulae are explicitly given. The original one-loop counter-term formula of 't Hooft is thereby improved. The present method of renormalization is far easier to manage than the usual one owing to the fact only gauge-invariant quantities are to be considered when worked in an appropriate gauge. Gravity and Yang-Mills theories are studied as examples. (orig.)

Field renormalization in photonic crystal waveguides

DEFF Research Database (Denmark)

Colman, Pierre

2015-01-01

A novel strategy is introduced in order to include variations of the nonlinearity in the nonlinear Schro¨dinger equation. This technique, which relies on renormalization, is in particular well adapted to nanostructured optical systems where the nonlinearity exhibits large variations up to two...... orders of magnitude larger than in bulk material. We show that it takes into account in a simple and efficient way the specificity of the nonlinearity in nanostructures that is determined by geometrical parameters like the effective mode area and the group index. The renormalization of the nonlinear...

Real-space Berry phases: Skyrmion soccer (invited)

Science.gov (United States)

Everschor-Sitte, Karin; Sitte, Matthias

2014-05-01

Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects.

Real-space Berry phases: Skyrmion soccer (invited)

Energy Technology Data Exchange (ETDEWEB)

Everschor-Sitte, Karin, E-mail: karin@physics.utexas.edu; Sitte, Matthias [The University of Texas at Austin, Department of Physics, 2515 Speedway, Austin, Texas 78712 (United States)

2014-05-07

Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects.

Real-space Berry phases: Skyrmion soccer (invited)

International Nuclear Information System (INIS)

Everschor-Sitte, Karin; Sitte, Matthias

2014-01-01

Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects

Renormalization of the new trajectory in the unitarized conventional dual model

International Nuclear Information System (INIS)

Quiros, M.

1978-08-01

The contribution of one-loop planar diagrams to the two-reggeon two-particle amplitude is derived. Its regge limit splits into two separate contributions which must be interpreted as renormalization effects, to order g 2 , of the α and β trajectories. It is shown that the Neveu-Scherk renormalization prescription is able to render finite both contributions. The intercept of the β trajectory is shifted from its bare value by the renormalization procedure, whereas that of the α trajectrory is not renormalized as it was required by the gauge invariance of dual theories

Renormalization, conformal ward identities and the origin of a conformal anomaly pole

Science.gov (United States)

Corianò, Claudio; Maglio, Matteo Maria

2018-06-01

We investigate the emergence of a conformal anomaly pole in conformal field theories in the case of the TJJ correlator. We show how it comes to be generated in dimensional renormalization, using a basis of 13 form factors (the F-basis), where only one of them requires renormalization (F13), extending previous studies. We then combine recent results on the structure of the non-perturbative solutions of the conformal Ward identities (CWI's) for the TJJ in momentum space, expressed in terms of a minimal set of 4 form factors (A-basis), with the properties of the F-basis, and show how the singular behaviour of the corresponding form factors in both basis can be related. The result proves the centrality of such massless effective interactions induced by the anomaly, which have recently found realization in solid state, in the theory of topological insulators and of Weyl semimetals. This pattern is confirmed in massless abelian and nonabelian theories (QED and QCD) investigated at one-loop.

Non-perturbative renormalization of left-left four-fermion operators in quenched lattice QCD

CERN Document Server

Guagnelli, M; Peña, C; Sint, S; Vladikas, A

2006-01-01

We define a family of Schroedinger Functional renormalization schemes for the four-quark multiplicatively renormalizable operators of the $\\Delta F = 1$ and $\\Delta F = 2$ effective weak Hamiltonians. Using the lattice regularization with quenched Wilson quarks, we compute non-perturbatively the renormalization group running of these operators in the continuum limit in a large range of renormalization scales. Continuum limit extrapolations are well controlled thanks to the implementation of two fermionic actions (Wilson and Clover). The ratio of the renormalization group invariant operator to its renormalized counterpart at a low energy scale, as well as the renormalization constant at this scale, is obtained for all schemes.

Real-Time Inhibitor Recession Measurements in Two Space Shuttle Reusable Solid Rocket Motors

Science.gov (United States)

McWhorter, B. B.; Ewing, M. E.; Bolton, D. E.; Albrechtsen, K. U.; Earnest, T. E.; Noble, T. C.; Longaker, M.

2003-01-01

Real-time internal motor insulation char line recession measurements have been evaluated for two full-scale static tests of the Space Shuttle Reusable Solid Rocket Motor (RSRM). These char line recession measurements were recorded on the forward facing propellant grain inhibitors to better understand the thermal performance of these inhibitors. The RSRM propellant grain inhibitors are designed to erode away during motor operation, thus making it difficult to use post-fire observations to determine inhibitor thermal performance. Therefore, this new internal motor instrumentation is invaluable in establishing an accurate understanding of inhibitor recession versus motor operation time. The data for the first test was presented at the 37th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit (AIAA 2001-3280) in July 2001. Since that time, a second full scale static test has delivered additional real-time data on inhibitor thermal performance. The evaluation of this data is presented in this paper. The second static test, in contrast to the first test, used a slightly different arrangement of instrumentation in the inhibitors. This instrumentation has yielded a better understanding of the inhibitor time dependent inboard tip recession. Graphs of inhibitor recession profiles with time are presented. Inhibitor thermal ablation models have been created from theoretical principals. The model predictions compare favorably with data from both tests. This verified modeling effort is important to support new inhibitor designs for a five segment Space Shuttle solid rocket motor. The internal instrumentation project on RSRM static tests is providing unique opportunities for other real-time internal motor measurements that could not otherwise be directly quantified.

Effects Of Organic Fertilizer And Spacing On Growth And Yield Of ...

African Journals Online (AJOL)

NIHORT), Ibadan to investigate the effects of maize-stover compost fertilizer and plant spacing on the growth and shoot yield of Celosia argentea L. var. TLV8. Plants were spaced 15x 15cm; 20 x 20cm and 25 x 25cm and the compost fertilizer was ...

On renormalization-invariant masses

International Nuclear Information System (INIS)

Fleming, H.; Furuya, K.

1978-02-01

It is shown that spontaneous generation of renormalization invariant mass is possible in infra-red stable theories with more than one coupling constant. If relations among the coupling constants are permitted the effect can be made compatible with pertubation theory

The functional renormalization group for interacting quantum systems with spin-orbit interaction

International Nuclear Information System (INIS)

Grap, Stephan Michael

2013-01-01

We studied the influence of spin-orbit interaction (SOI) in interacting low dimensional quantum systems at zero temperature within the framework of the functional renormalization group (fRG). Among the several types of spin-orbit interaction the so-called Rashba spin-orbit interaction is especially intriguing for future spintronic applications as it may be tuned via external electric fields. We investigated its effect on the low energy physics of an interacting quantum wire in an applied Zeeman field which is modeled as a generalization of the extended Hubbard model. To this end we performed a renormalization group study of the two particle interaction, including the SOI and the Zeeman field exactly on the single particle level. Considering the resulting two band model, we formulated the RG equations for the two particle vertex keeping the full band structure as well as the non trivial momentum dependence of the low energy two particle scattering processes. In order to solve these equations numerically we defined criteria that allowed us to classify whether a given set of initial conditions flows towards the strongly coupled regime. We found regions in the models parameter space where a weak coupling method as the fRG is applicable and it is possible to calculate additional quantities of interest. Furthermore we analyzed the effect of the Rashba SOI on the properties of an interacting multi level quantum dot coupled to two semi in nite leads. Of special interest was the interplay with a Zeeman field and its orientation with respect to the SOI term. We found a renormalization of the spin-orbit energy which is an experimental quantity used to asses SOI effects in transport measurements, as well as renormalized effective g factors used to describe the Zeeman field dependence. In particular in asymmetrically coupled systems the large parameter space allows for rich physics which we studied by means of the linear conductance obtained via the generalized Landauer

Optical Real-Time Space Radiation Monitor, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — Real-time dosimetry is needed to provide immediate feedback, so astronauts can minimize their exposure to ionizing radiation during periods of high solar activity....

The Obstruction criterion for non existence of Invariant Circles and Renormalization.

CERN Document Server

De la Llave, R

2003-01-01

We formulate a conjecture which supplements the standard renormalization scenario for the breakdown of golden circle in twist maps. We show rigorously that if the conjecture was true then: a) The stable manifold of the non-trivial fixed point would indeed be a boundary between the existence of smooth invariant tori and hyperbolic orbits with golden mean rotation number. In particular, the boundary of the set of twist maps with a torus with a golden mean rotation number would include a smooth submanifold in the space of analytic mappings. b) The obstruction criterion of [Olvera-Simo] would be sharp in the universality class of the renormalization group. c) The criterion of [Greene-79] for existence of invariant circles if and only if there the residues of approximating orbits are finite would be valid for maps in the universality class. d) If there is no invariant circle, there are hyperbolic sets with golden mean rotation number. We also provide numerical evidence which suggests that the conjecture is true an...

Trace and axial anomalies in dimensional renormalization through Zimmermann-like identities

International Nuclear Information System (INIS)

Bonneau, G.

1980-01-01

The problem of anomalies is solved in dimensional renormalization in two steps. Firstly one shows that trace and γ 5 anomalies can be expressed as the anomalous normal product N[gsub(μ rho)Osub(μ rho lambda)...(x)] where gsub(μ rho) is the metric tensor in D-4 dimensions (D being the space-time dimension) and Osub(μ rho lambda)...(x) a monomial in the fields and their derivatives. Then, with techniques similar to those used in a previous work to study N[(4-D)Osub(μ rho lambda)(x)], we prove a Zimmermann-like identity that gives the decomposition of such anomalous normal product on 'usual' normal products, the coefficients being explicitly given as residues of the simple pole in v = 4-D of definite proper Green functions where the overall subtraction has not been done. We apply the above formalism to obtain the renormalization group as a consequence of trace anomalies in the dilatation current and to derive the Adler-Bardeen theorem for massive QED. (orig.)

Asynchronous communication in real space process algebra

NARCIS (Netherlands)

Baeten, J.C.M.; Bergstra, J.A.

1991-01-01

A version of classical real space process algebra is given in which messages travel with constant speed through a three-dimensional medium. It follows that communication is asynchronous and has a broadcasting character. A state operator is used to describe asynchronous message transfer and a

Asynchronous communication in real space process algebra

NARCIS (Netherlands)

Bergstra, J.A.; Baeten, J.C.M.

1992-01-01

A version of classical real space process algebra is given in which messages travel with constant speed through a three-dimensional medium. It follows that communication is asynchronous and has a broadcasting character. A state operator is used to describe asynchronous message transfer and a

Fine-tuning problem in renormalized perturbation theory: Spontaneously-broken gauge models

Energy Technology Data Exchange (ETDEWEB)

Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)

1983-04-28

We study the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a model with spontaneously-broken gauge symmetries. We confirm previous results indicating that if the model is renormalized using BPHZ, then the tree-level hierarchy is not upset by the radiative corrections. Consequently, no fine-tuning of the initial parameters is required to maintain it, in contrast to the result obtained using Dimensional Renormalization. This verifies the conclusion that the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes.

Renormalization in self-consistent approximation schemes at finite temperature I: theory

International Nuclear Information System (INIS)

Hees, H. van; Knoll, J.

2001-07-01

Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local counter-terms defined at the vacuum level. The requirements are that the underlying theory is renormalizable and that the self-consistent scheme follows Baym's Φ-derivable concept. The scheme generates both, the renormalized self-consistent equations of motion and the closed equations for the infinite set of counter terms. At the same time the corresponding 2PI-generating functional and the thermodynamic potential can be renormalized, in consistency with the equations of motion. This guarantees the standard Φ-derivable properties like thermodynamic consistency and exact conservation laws also for the renormalized approximation scheme to hold. The proof uses the techniques of BPHZ-renormalization to cope with the explicit and the hidden overlapping vacuum divergences. (orig.)

Renormalization of Hamiltonian QCD

International Nuclear Information System (INIS)

Andrasi, A.; Taylor, John C.

2009-01-01

We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.

Extending the range of real time density matrix renormalization group simulations

Science.gov (United States)

Kennes, D. M.; Karrasch, C.

2016-03-01

We discuss a few simple modifications to time-dependent density matrix renormalization group (DMRG) algorithms which allow to access larger time scales. We specifically aim at beginners and present practical aspects of how to implement these modifications within any standard matrix product state (MPS) based formulation of the method. Most importantly, we show how to 'combine' the Schrödinger and Heisenberg time evolutions of arbitrary pure states | ψ 〉 and operators A in the evaluation of 〈A〉ψ(t) = 〈 ψ | A(t) | ψ 〉 . This includes quantum quenches. The generalization to (non-)thermal mixed state dynamics 〈A〉ρ(t) =Tr [ ρA(t) ] induced by an initial density matrix ρ is straightforward. In the context of linear response (ground state or finite temperature T > 0) correlation functions, one can extend the simulation time by a factor of two by 'exploiting time translation invariance', which is efficiently implementable within MPS DMRG. We present a simple analytic argument for why a recently-introduced disentangler succeeds in reducing the effort of time-dependent simulations at T > 0. Finally, we advocate the python programming language as an elegant option for beginners to set up a DMRG code.

Cohomology and renormalization of BFYM theory in three dimensions

International Nuclear Information System (INIS)

Accardi, A.; Belli, A.; Zeni, M.

1997-01-01

The first-order formalism for the 3D Yang-Mills theory is considered and two different formulations are introduced, in which the gauge theory appears to be a deformation of the topological BF theory. We perform the quantization and the algebraic analysis of the renormalization of both the models, which are found to be anomaly free. We discuss also their stability against radiative corrections, giving the full structure of possible counterterms, requiring an involved matricial renormalization of fields and sources. Both models are then proved to be equivalent to the Yang-Mills theory at the renormalized level. (orig.)

Non-perturbative renormalization of HQET and QCD

International Nuclear Information System (INIS)

Sommer, Rainer

2003-01-01

We discuss the necessity of non-perturbative renormalization in QCD and HQET and explain the general strategy for solving this problem. A few selected topics are discussed in some detail, namely the importance of off shell improvement in the MOM-scheme on the lattice, recent progress in the implementation of finite volume schemes and then particular emphasis is put on the recent idea to carry out a non-perturbative renormalization of the Heavy Quark Effective Theory (HQET)

Renormalization transformation of periodic and aperiodic lattices

International Nuclear Information System (INIS)

Macia, Enrique; Rodriguez-Oliveros, Rogelio

2006-01-01

In this work we introduce a similarity transformation acting on transfer matrices describing the propagation of elementary excitations through either periodic or Fibonacci lattices. The proposed transformation can act at two different scale lengths. At the atomic scale the transformation allows one to express the systems' global transfer matrix in terms of an equivalent on-site model one. Correlation effects among different hopping terms are described by a series of local phase factors in that case. When acting on larger scale lengths, corresponding to short segments of the original lattice, the similarity transformation can be properly regarded as describing an effective renormalization of the chain. The nature of the resulting renormalized lattice significantly depends on the kind of order (i.e., periodic or quasiperiodic) of the original lattice, expressing a delicate balance between chemical complexity and topological order as a consequence of the renormalization process

Electroweak vacuum instability and renormalized Higgs field vacuum fluctuations in the inflationary universe

Energy Technology Data Exchange (ETDEWEB)

Kohri, Kazunori [Institute of Particle and Nuclear Studies, KEK, 1-1 Oho, Tsukuba 305-0801 (Japan); Matsui, Hiroki, E-mail: kohri@post.kek.jp, E-mail: matshiro@post.kek.jp [The Graduate University for Advanced Studies (SOKENDAI), 1-1 Oho, Tsukuba 305-0801 (Japan)

2017-08-01

In this work, we investigated the electroweak vacuum instability during or after inflation. In the inflationary Universe, i.e., de Sitter space, the vacuum field fluctuations < δ φ {sup 2} > enlarge in proportion to the Hubble scale H {sup 2}. Therefore, the large inflationary vacuum fluctuations of the Higgs field < δ φ {sup 2} > are potentially catastrophic to trigger the vacuum transition to the negative-energy Planck-scale vacuum state and cause an immediate collapse of the Universe. However, the vacuum field fluctuations < δ φ {sup 2} >, i.e., the vacuum expectation values have an ultraviolet divergence, and therefore a renormalization is necessary to estimate the physical effects of the vacuum transition. Thus, in this paper, we revisit the electroweak vacuum instability from the perspective of quantum field theory (QFT) in curved space-time, and discuss the dynamical behavior of the homogeneous Higgs field φ determined by the effective potential V {sub eff}( φ ) in curved space-time and the renormalized vacuum fluctuations < δ φ {sup 2} >{sub ren} via adiabatic regularization and point-splitting regularization. We simply suppose that the Higgs field only couples the gravity via the non-minimal Higgs-gravity coupling ξ(μ). In this scenario, the electroweak vacuum stability is inevitably threatened by the dynamical behavior of the homogeneous Higgs field φ, or the formations of AdS domains or bubbles unless the Hubble scale is small enough H < Λ {sub I} .

Renormalization as an extension problem on the Count our ordered formalism in FFTF

Energy Technology Data Exchange (ETDEWEB)

Franco, D.H.T. [Centro de Estudos de Fisica Teorica (CEFT), Belo Horizonte, MG (Brazil); Acebal, J.L. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Teoria de Campos e Particulas; Grupo de Fisica Teorica Jose Leite Lopes (GFT-JLL), Petropolis, RJ (Brazil)

2003-06-01

From a distributional-theoretical framework, we make efforts in order to fill a gap in the series of studies which discuss the inheritance of the renormalization behaviour of a finite temperature field theory (FTFT) from the analogous version in quantum field theory (QFT) at T=0. Renormalization is treated as a distributional extension problem having the mathematical structure disentangled as much as possible from the physical aspects. The purely technical details essential for the discussion are briefly reviewed in a handle manner for further theoretical physics applications. The analysis elucidates some qualitative and quantitative distinctions concerning the divergences in the perturbation series when it is considered the FTFT version associated to a given QFT. Despite the differences, it turns clear the reason why the leading ultraviolet behaviour keeps unaffected when it is considered the FTFT version associated to a given QFT. The study is model independent and the approach allows one to consider the FTFT both imaginary and real time formalism at once in a unified way in the contour ordered formalism. (author)

Renormalization of Supersymmetric QCD on the Lattice

Science.gov (United States)

Costa, Marios; Panagopoulos, Haralambos

2018-03-01

We perform a pilot study of the perturbative renormalization of a Supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider Supersymmetric N=1 QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green's functions using both dimensional and lattice regularizations. Our lattice formulation involves theWilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naive discretization. The gauge group that we consider is SU(Nc), while the number of colors, Nc, the number of flavors, Nf, and the gauge parameter, α, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant (Zg) and of the quark (ZΨ), gluon (Zu), gluino (Zλ), squark (ZA±), and ghost (Zc) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.

All-order renormalization of propagator matrix for fermionic system with flavor mixing

Energy Technology Data Exchange (ETDEWEB)

Kniehl, Bernd A. [California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics

2013-08-15

We consider a mixed system of Dirac fermions in a general parity-nonconserving theory and renormalize the propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. We present closed analytic all-order expressions for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions. We identify residual degrees of freedom in the WFR matrices and propose an additional renormalization condition to exhaust them. We then explain how our results may be generalized to the case of unstable fermions, in which we encounter the phenomenon of WFR bifurcation. In the special case of a solitary unstable fermion, the all-order-renormalized propagator is presented in a particularly compact form.

Setting the renormalization scale in QCD: The principle of maximum conformality

DEFF Research Database (Denmark)

Brodsky, S. J.; Di Giustino, L.

2012-01-01

A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale mu of the running coupling alpha(s)(mu(2)). The purpose of the running coupling in any gauge theory is to sum all terms involving the beta function; in fact, when the renormali......A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale mu of the running coupling alpha(s)(mu(2)). The purpose of the running coupling in any gauge theory is to sum all terms involving the beta function; in fact, when...... the renormalization scale is set properly, all nonconformal beta not equal 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with beta...... = 0. The resulting scale-fixed predictions using the principle of maximum conformality (PMC) are independent of the choice of renormalization scheme-a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale setting in the Abelian limit...

Non-perturbative renormalization on the lattice

International Nuclear Information System (INIS)

Koerner, Daniel

2014-01-01

Strongly-interacting theories lie at the heart of elementary particle physics. Their distinct behaviour shapes our world sui generis. We are interested in lattice simulations of supersymmetric models, but every discretization of space-time inevitably breaks supersymmetry and allows renormalization of relevant susy-breaking operators. To understand the role of such operators, we study renormalization group trajectories of the nonlinear O(N) Sigma model (NLSM). Similar to quantum gravity, it is believed to adhere to the asymptotic safety scenario. By combining the demon method with blockspin transformations, we compute the global flow diagram. In two dimensions, we reproduce asymptotic freedom and in three dimensions, asymptotic safety is demonstrated. Essential for these results is the application of a novel optimization scheme to treat truncation errors. We proceed with a lattice simulation of the supersymmetric nonlinear O(3) Sigma model. Using an original discretization that requires to fine tune only a single operator, we argue that the continuum limit successfully leads to the correct continuum physics. Unfortunately, for large lattices, a sign problem challenges the applicability of Monte Carlo methods. Consequently, the last chapter of this thesis is spent on an assessment of the fermion-bag method. We find that sign fluctuations are thereby significantly reduced for the susy NLSM. The proposed discretization finally promises a direct confirmation of supersymmetry restoration in the continuum limit. For a complementary analysis, we study the one-flavor Gross-Neveu model which has a complex phase problem. However, phase fluctuations for Wilson fermions are very small and no conclusion can be drawn regarding the potency of the fermion-bag approach for this model.

Renorming c0 and closed, bounded, convex sets with fixed point property for affine nonexpansive mappings

Science.gov (United States)

Nezir, Veysel; Mustafa, Nizami

2017-04-01

In 2008, P.K. Lin provided the first example of a nonreflexive space that can be renormed to have fixed point property for nonexpansive mappings. This space was the Banach space of absolutely summable sequences l1 and researchers aim to generalize this to c0, Banach space of null sequences. Before P.K. Lin's intriguing result, in 1979, Goebel and Kuczumow showed that there is a large class of non-weak* compact closed, bounded, convex subsets of l1 with fixed point property for nonexpansive mappings. Then, P.K. Lin inspired by Goebel and Kuczumow's ideas to give his result. Similarly to P.K. Lin's study, Hernández-Linares worked on L1 and in his Ph.D. thesis, supervisored under Maria Japón, showed that L1 can be renormed to have fixed point property for affine nonexpansive mappings. Then, related questions for c0 have been considered by researchers. Recently, Nezir constructed several equivalent norms on c0 and showed that there are non-weakly compact closed, bounded, convex subsets of c0 with fixed point property for affine nonexpansive mappings. In this study, we construct a family of equivalent norms containing those developed by Nezir as well and show that there exists a large class of non-weakly compact closed, bounded, convex subsets of c0 with fixed point property for affine nonexpansive mappings.

EDITORIAL: From reciprocal space to real space in surface science From reciprocal space to real space in surface science

Science.gov (United States)

Bartels, Ludwig; Ernst, Karl-Heinz

2012-09-01

This issue is dedicated to Karl-Heinz Rieder on the occasion of his 70th birthday. It contains contributions written by his former students and colleagues from all over the world. Experimental techniques based on free electrons, such as photoelectron spectroscopy, electron microscopy and low energy electron diffraction (LEED), were foundational to surface science. While the first revealed the band structures of materials, the second provided nanometer scale imagery and the latter elucidated the atomic scale periodicity of surfaces. All required an (ultra-)high vacuum, and LEED illustrated impressively that adsorbates, such as carbon monoxide, hydrogen or oxygen, can markedly and periodically restructure surfaces from their bulk termination, even at pressures ten orders of magnitude or more below atmospheric. Yet these techniques were not generally able to reveal atomic scale surface defects, nor could they faithfully show adsorption of light atoms such as hydrogen. Although a complete atom, helium can also be regarded as a wave with a de Broglie wavelength that allows the study of surface atomic periodicities at a delicateness and sensitivity exceeding that of electrons-based techniques. In combination, these and other techniques generated insight into the periodicity of surfaces and their vibrational properties, yet were limited to simple and periodic surface setups. All that changed with the advent of scanning tunneling microscopy (STM) roughly 30 years ago, allowing real space access to surface defects and individual adsorbates. Applied at low temperatures, not only can STM establish a height profile of surfaces, but can also perform spectroscopy and serve as an actuator capable of rearranging individual species at atomic scale resolution. The direct and intuitive manner in which STM provided access as a spectator and as an actor to the atomic scale was foundational to today's surface science and to the development of the concepts of nanoscience in general. The

Renormalization group-theoretic approach to electron localization in disordered systems

International Nuclear Information System (INIS)

Kumar, N.; Heinrichs, J.

1977-06-01

The localization problem for the Anderson tight-binding model with site-diagonal (gaussian) disorder is studied, using a previously established analogy between this problem and the statistical mechanics of a zero-component classical field. The equivalent free-energy functional turns out to have complex coefficients in the bilinear terms but involves a real repulsive quartic interaction. The averaged one-electron propagator corresponds to the two-point correlation function for the equivalent statistical problem and the critical point gives the mobility edge, which is identified with the (real) fixed point energy of the associated renormalization group. Since for convergence reasons the conventional perturbative treatment of Wilson's formula is invalid, it is resorted to a non-perturbative approach which leads to a physical fixed point corresponding to a repulsive quartic interaction. The results for the mobility edge in three dimensions and for the critical disorder for an Anderson transition in two dimensions agree well with previous detailed predictions. The critical indices describing the approach of the transition at the mobility edge of various physical quantities, within the epsilon-expansion are also discussed. The more general problem where both diagonal and off-diagonal disorder is present in the Anderson hamiltonian is considered. In this case it is shown that the Hamilton function for the equivalent zero-component classical field model involves an additional biquadratic exchange term. From a simple generalization of Wilson's recursion relation and its non-perturbative solution explicit expressions for the mobility edges for weak diagonal and off-diagonal disorder in two and three dimensions are obtained. Our treatment casts doubts on the validity of recent conclusions about electron localization based on the renormalization group study of the nm-component spin model

Fock representation of the renormalized higher powers of White noise and the centreless Virasoro (or Witt)-Zamolodchikov-w∞*-Lie algebra

International Nuclear Information System (INIS)

Accardi, Luigi; Boukas, Andreas

2008-01-01

The identification of the *-Lie algebra of the renormalized higher powers of White noise (RHPWN) and the analytic continuation of the second quantized centreless Virasoro (or Witt)-Zamolodchikov-w ∞ *-Lie algebra of conformal field theory and high-energy physics, was recently established on results obtained. In the present paper, we show how the RHPWN Fock kernels must be truncated in order to be positive semi-definite and we obtain a Fock representation of the two algebras. We show that the truncated renormalized higher powers of White noise (TRHPWN) Fock spaces of order ≥2 host the continuous binomial and beta processes

Renormalization of the nonlinear O(3) model with θ-term

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Flore, Raphael, E-mail: raphael.flore@uni-jena.de [Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, D-07743 Jena (Germany)

2013-05-11

The renormalization of the topological term in the two-dimensional nonlinear O(3) model is studied by means of the Functional Renormalization Group. By considering the topological charge as a limit of a more general operator, it is shown that a finite multiplicative renormalization occurs in the extreme infrared. In order to compute the effects of the zero modes, a specific representation of the Clifford algebra is developed which allows to reformulate the bosonic problem in terms of Dirac operators and to employ the index theorem.

Renormalization Group in different fields of theoretical physics

International Nuclear Information System (INIS)

Shirkov, D.V.

1992-02-01

A very simple and general approach to the symmetry that is widely known as a Renormalization Group symmetry is presented. It essentially uses a functional formulation of group transformations that can be considered as a generalization of self-similarity transformations well known in mathematical physics since last century. This generalized Functional Self-Similarity symmetry and corresponding group transformations are discussed first for a number of simple physical problems taken from diverse fields of classical physics as well as for QED. Then we formulate the Renorm-Group Method as a regular procedure that essentially improves the approximate solutions near the singularity. After that we discuss relations between different formulations of Renormalization Group as they appear in various parts of a modern theoretical physics. Finally we present several topics of RGM application in modern QFT. (author)

Hypercuboidal renormalization in spin foam quantum gravity

Science.gov (United States)

Bahr, Benjamin; Steinhaus, Sebastian

2017-06-01

In this article, we apply background-independent renormalization group methods to spin foam quantum gravity. It is aimed at extending and elucidating the analysis of a companion paper, in which the existence of a fixed point in the truncated renormalization group flow for the model was reported. Here, we repeat the analysis with various modifications and find that both qualitative and quantitative features of the fixed point are robust in this setting. We also go into details about the various approximation schemes employed in the analysis.

Renormalization of a distorted gauge: invariant theory

International Nuclear Information System (INIS)

Hsu, J.P.; Underwood, J.A.

1976-02-01

A new type of renormalizable theory involving massive Yang-Mills fields whose mass is generated by an intrinsic breakdown of the usual local gauge symmetry is considered. However, the Lagrangian has a distorted gauge symmetry which leads to the Ward-Takahashi (W-T) identities. Also, the theory is independent of the gauge parameter xi. An explicit renormalization at the oneloop level is completely carried out by exhibiting counter terms, defining the physical parameters and computing all renormalization constants to check the W-T identities

Renormalization theory of stationary homogeneous strong turbulence in a collisionless plasma

International Nuclear Information System (INIS)

Zhang, Y.Z.

1984-01-01

A renormalization procedure for the perturbation expansion of the Vlasov-Poisson equation is presented to describe stationary homogeneous turbulence. By using the diagramatic scheme the theory is shown to be renormalizable to any order. The expressions for the renormalized propagator, the renormalized dielectric function, and the intrinsically incoherent source are given. The renormalization leads to a complete separation of the fluctuating distribution function f/sub k/ into two parts, the coherent part, which is proved to represent the dielectric effect of the medium, and the intrinsically incoherent part, which represents the effect of nonlinear source. The turbulent collisional operator in the transport equation is proved equal to GAMMA 0 , the frequency broadening when k = 0

Real-space formulation of the electrostatic potential and total energy of solids

International Nuclear Information System (INIS)

Pask, J E; Sterne, P A

2004-01-01

We develop expressions for the electrostatic potential and total energy of crystalline solids which are amenable to direct evaluation in real space. Unlike conventional reciprocal space formulations, no Fourier transforms or reciprocal lattice summations are required, and the formulation is well suited for large-scale, parallel computations. The need for reciprocal space expressions is eliminated by replacing long-range potentials by equivalent localized charge distributions and incorporating long-range interactions into boundary conditions on the unit cell. In so doing, a simplification of the conventional reciprocal space formalism is obtained. The equivalence of the real- and reciprocal space formalisms is demonstrated by direct comparison in self-consistent density-functional calculations

Renormalization method and singularities in the theory of Langmuir turbulence

International Nuclear Information System (INIS)

Pelletier, G.

1977-01-01

The method of renormalization, using propagators and diagrams, is recalled with enough mathematical details to be read and used by a non-specialist. The Markovian models are discussed and applied to plasma turbulence. The physical meaning of the diagrams is exhibited. In addition to the usual resonance broadening, an improved renormalization is set out, including broadening of the nonlinear resonance with a beat wave by induced scattering. This improved renormalization is emphasized. In the case of Langmuir turbulence, it removes difficulties arising at the group velocity, and enhances large-scale induced-scattering diffusion. (author)

Dimension 7 operators in the b{yields}s transition

Energy Technology Data Exchange (ETDEWEB)

Chalons, G. [Karlsruhe Univ. (T.H.) (Germany). Inst. fuer Theoretische Teilchenphysik; Domingo, F. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2013-03-15

We extend the low-energy effective field theory relevant for b{yields}s transitions up to operators of mass-dimension 7 and compute the associated anomalous-dimension matrix. We then compare our findings to the known results for dimension 6 operators and derive a solution for the renormalization group equations involving operators of dimension 7. We finally apply our analysis to a particularly simple case where the Standard Model is extended by an electroweak-magnetic operator and consider limits on this scenario from the decays B{sub s}{yields}{mu}{sup +}{mu}{sup -} and B{yields}K{nu} anti {nu}.

Renormalized trajectory for non-linear sigma model and improved scaling behaviour

International Nuclear Information System (INIS)

Guha, A.; Okawa, M.; Zuber, J.B.

1984-01-01

We apply the block-spin renormalization group method to the O(N) Heisenberg spin model. Extending a previous work of Hirsch and Shenker, we find the renormalized trajectory for O(infinite) in two dimensions. Four finite N models, we choose a four-parameter action near the large-N renormalized trajectory and demonstrate a remarkable improvement in the approach to continuum limit by performing Monte Carlo simulation of O(3) and O(4) models. (orig.)

Considerations in development of expert systems for real-time space applications

Science.gov (United States)

Murugesan, S.

1988-01-01

Over the years, demand on space systems has increased tremendously and this trend will continue for the near future. Enhanced capabilities of space systems, however, can only be met with increased complexity and sophistication of onboard and ground systems. Artificial Intelligence and expert system techniques have great potential in space applications. Expert systems could facilitate autonomous decision making, improve in-orbit fault diagnosis and repair, enhance performance and reduce reliance on ground support. However, real-time expert systems, unlike conventional off-line consultative systems, have to satisfy certain special stringent requirements before they could be used for onboard space applications. Challenging and interesting new environments are faced while developing expert system space applications. This paper discusses the special characteristics, requirements and typical life cycle issues for onboard expert systems. Further, it also describes considerations in design, development, and implementation which are particularly important to real-time expert systems for space applications.

The fine-tuning problem in renormalized perturbation theory: Spontaneously-broken gauge models

International Nuclear Information System (INIS)

Foda, O.E.

1983-01-01

We study the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a model with spontaneously-broken gauge symmetries. We confirm previous results indicating that if the model is renormalized using BPHZ, then the tree-level hierarchy is not upset by the radiative corrections. Consequently, no fine-tuning of the initial parameters is required to maintain it, in contrast to the result obtained using Dimensional Renormalization. This verifies the conclusion that the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes. (orig.)

Modeling Growth and Yield of Schizolobium amazonicum under Different Spacings

Directory of Open Access Journals (Sweden)

Gilson Fernandes da Silva

2013-01-01

Full Text Available This study aimed to present an approach to model the growth and yield of the species Schizolobium amazonicum (Paricá based on a study of different spacings located in Pará, Brazil. Whole-stand models were employed, and two modeling strategies (Strategies A and B were tested. Moreover, the following three scenarios were evaluated to assess the accuracy of the model in estimating total and commercial volumes at five years of age: complete absence of data (S1; available information about the variables basal area, site index, dominant height, and number of trees at two years of age (S2; and this information available at five years of age (S3. The results indicated that the 3 × 2 spacing has a higher mortality rate than normal, and, in general, greater spacing corresponds to larger diameter and average height and smaller basal area and volume per hectare. In estimating the total and commercial volumes for the three scenarios tested, Strategy B seems to be the most appropriate method to estimate the growth and yield of Paricá plantations in the study region, particularly because Strategy A showed a significant bias in its estimates.

Off-shell renormalization in Higgs effective field theories

Science.gov (United States)

Binosi, Daniele; Quadri, Andrea

2018-04-01

The off-shell one-loop renormalization of a Higgs effective field theory possessing a scalar potential ˜ {({Φ}^{\\dagger}Φ -υ^2/2)}^N with N arbitrary is presented. This is achieved by renormalizing the theory once reformulated in terms of two auxiliary fields X 1,2, which, due to the invariance under an extended Becchi-Rouet-Stora-Tyutin symmetry, are tightly constrained by functional identities. The latter allow in turn the explicit derivation of the mapping onto the original theory, through which the (divergent) multi-Higgs amplitude are generated in a purely algebraic fashion. We show that, contrary to naive expectations based on the loss of power counting renormalizability, the Higgs field undergoes a linear Standard Model like redefinition, and evaluate the renormalization of the complete set of Higgs self-coupling in the N → ∞ case.

Some applications of renormalized RPA in bosonic field theories

International Nuclear Information System (INIS)

Hansen, H.; Chanfray, G.

2003-01-01

We present some applications of the renormalized RPA in bosonic field theories. We first present some developments for the explicit calculation of the total energy in Φ 4 theory and discuss its phase structure in 1 + 1 dimensions. We also demonstrate that the Goldstone theorem is satisfied in the O(N) model within the renormalized RPA. (authors)

The Physical Renormalization of Quantum Field Theories

International Nuclear Information System (INIS)

Binger, Michael William.; Stanford U., Phys. Dept.; SLAC

2007-01-01

The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, α(k 1 2 , k 2 2 , k 3 2 ), depends on three momentum scales and gives rise to an effective scale Q eff 2 (k 1 2 , k 2 2 , k 3 2 ) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi-scale analytic renormalization scheme based on gauge-invariant Green

Renormalization of the QEMD of a dyon field

International Nuclear Information System (INIS)

Panagiotakopoulos, C.

1983-01-01

A renormalized quantum electromagnetodynamics (QEMD) of a dyon field is defined. Finite and n-independent answers can be obtained in each order of the loop expansion for all processes. The electric and magnetic charges are not constrained with the Dirac condition and therefore perturbation theory can be made reliable. The renormalized theory is found to possess exact dual invariance. Comparisons with the general QEMD of electric and magnetic charges are made. (orig.)

Renormalization of the QEMD of a dyon field

International Nuclear Information System (INIS)

Panagiotakopoulos, C.

1982-05-01

A renormalized quantum electromagnetodynamics (QEMD) of a dyon field is defined. Finite and n independent answers can be obtained in each order of the loop expansion for all processes. The electric and magnetic charges are not constrained with the Dirac condition and therefore perturbation theory can be made reliable. The renormalized theory is found to possess exact dual invariance. Comparisons with the general QEMD of electric and magnetic charges are made. (author)

Non-perturbative versus perturbative renormalization of lattice operators

International Nuclear Information System (INIS)

Goeckeler, M.; Technische Hochschule Aachen; Horsley, R.; Ilgenfritz, E.M.; Oelrich, H.; Forschungszentrum Juelich GmbH; Schierholz, G.; Forschungszentrum Juelich GmbH; Perlt, H.; Schiller, A.; Rakow, P.

1995-09-01

Our objective is to compute the moments of the deep-inelastic structure functions of the nucleon on the lattice. A major source of uncertainty is the renormalization of the lattice operators that enter the calculation. In this talk we compare the renormalization constants of the most relevant twist-two bilinear quark operators which we have computed non-perturbatively and perturbatively to one loop order. Furthermore, we discuss the use of tadpole improved perturbation theory. (orig.)

Renormalization scheme-invariant perturbation theory

International Nuclear Information System (INIS)

Dhar, A.

1983-01-01

A complete solution to the problem of the renormalization scheme dependence of perturbative approximants to physical quantities is presented. An equation is derived which determines any physical quantity implicitly as a function of only scheme independent variables. (orig.)

Renormalization-group theory for the eddy viscosity in subgrid modeling

Science.gov (United States)

Zhou, YE; Vahala, George; Hossain, Murshed

1988-01-01

Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.

Renormalization of gauge theories without cohomology

International Nuclear Information System (INIS)

Anselmi, Damiano

2013-01-01

We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem. (orig.)

On truncations of the exact renormalization group

CERN Document Server

Morris, T R

1994-01-01

We investigate the Exact Renormalization Group (ERG) description of (Z_2 invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. Concentrating on the non-perturbative three dimensional Wilson fixed point, we then show that the sequence of truncations n=2,3,\\dots, obtained by expanding about the field \\varphi=0 and discarding all powers \\varphi^{2n+2} and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. No completely reliable method exists to reject the many spurious solutions that are also found. These properties are explained in terms of the analytic behaviour of the untruncated solutions -- which we describe in some detail.

Bose-Einstein condensed supermassive black holes: a case of renormalized quantum field theory in curved space-time

Czech Academy of Sciences Publication Activity Database

Nieuwenhuizen, T.M.; Špička, Václav

2010-01-01

Roč. 42, č. 3 (2010), s. 256-268 ISSN 1386-9477. [International Conference on Frontiers of Quantum and Mesoscopic Thermodynamics (FQMT '08). Praha, 28.07.2008-02.08.2008] Institutional research plan: CEZ:AV0Z10100521 Keywords : supermassive black hole * quantum held theory * Bose-Einstein condensation * renormalization Subject RIV: BE - Theoretical Physics Impact factor: 1.304, year: 2010

Turbulent mixing of a critical fluid: The non-perturbative renormalization

Directory of Open Access Journals (Sweden)

M. Hnatič

2018-01-01

Full Text Available Non-perturbative Renormalization Group (NPRG technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The compressible advecting flow is modeled by a random Gaussian velocity field with zero mean and correlation function 〈υjυi〉∼(Pji⊥+αPji∥/kd+ζ. Depending on the relations between the parameters ζ, α and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow, but there is a new nonequilibrium regime (universality class associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram (d, ζ of possible scaling regimes in the system. The physical point d=3, ζ=4/3 corresponding to three-dimensional fully developed Kolmogorov's turbulence, where critical fluctuations are irrelevant, is stable for α≲2.26. Otherwise, in the case of “strong compressibility” α≳2.26, the critical fluctuations of the order parameter become relevant for three-dimensional turbulence. Estimations of critical exponents for each scaling regime are presented.

Holographic renormalization group and cosmology in theories with quasilocalized gravity

International Nuclear Information System (INIS)

Csaki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John

2001-01-01

We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations

Effect of Plant and Row Spacing on the Yield and Oil Contents of ...

African Journals Online (AJOL)

Key words: Castor, Plant spacing, row spacing, seed yield. Introduction ... optimum plant population, fertilizer, quality seed, weeding practices, optimum plant ... 30 000 plants/ha for crops grown in the 750 to 900 mm rain fall is optimum. He.

Real-space visualization of remnant Mott gap and magnon excitations.

Science.gov (United States)

Wang, Y; Jia, C J; Moritz, B; Devereaux, T P

2014-04-18

We demonstrate the ability to visualize real-space dynamics of charge gap and magnon excitations in the Mott phase of the single-band Hubbard model and the remnants of these excitations with hole or electron doping. At short times, the character of magnetic and charge excitations is maintained even for large doping away from the Mott and antiferromagnetic phases. Doping influences both the real-space patterns and long timescales of these excitations with a clear carrier asymmetry attributable to particle-hole symmetry breaking in the underlying model. Further, a rapidly oscillating charge-density-wave-like pattern weakens, but persists as a visible demonstration of a subleading instability at half-filling which remains upon doping. The results offer an approach to analyzing the behavior of systems where momentum space is either inaccessible or poorly defined.

Irreversibility of world-sheet renormalization group flow

International Nuclear Information System (INIS)

Oliynyk, T.; Suneeta, V.; Woolgar, E.

2005-01-01

We demonstrate the irreversibility of a wide class of world-sheet renormalization group (RG) flows to first order in α ' in string theory. Our techniques draw on the mathematics of Ricci flows, adapted to asymptotically flat target manifolds. In the case of somewhere-negative scalar curvature (of the target space), we give a proof by constructing an entropy that increases monotonically along the flow, based on Perelman's Ricci flow entropy. One consequence is the absence of periodic solutions, and we are able to give a second, direct proof of this. If the scalar curvature is everywhere positive, we instead construct a regularized volume to provide an entropy for the flow. Our results are, in a sense, the analogue of Zamolodchikov's c-theorem for world-sheet RG flows on noncompact spacetimes (though our entropy is not the Zamolodchikov C-function)

Functional renormalization group approach to electronic structure calculations for systems without translational symmetry

Science.gov (United States)

Seiler, Christian; Evers, Ferdinand

2016-10-01

A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG flow is organized in the energy-domain rather than in k space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band structure, such as disordered metals or molecules. The energy-domain FRG (ɛ FRG) presented here accounts for Fermi-liquid corrections to quasiparticle energies and particle-hole excitations. It goes beyond the state of the art G W -BSE , because in ɛ FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the ɛ FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of ɛ FRG to the spinless disordered Hubbard model we calculate its phase boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S =1 /2 is also given.

Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies

Energy Technology Data Exchange (ETDEWEB)

Groh, Kai

2012-10-15

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement

Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies

International Nuclear Information System (INIS)

Groh, Kai

2012-10-01

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of

Extended BPH renormalization of cutoff scalar field theories

International Nuclear Information System (INIS)

Chalmers, G.

1996-01-01

We show through the use of diagrammatic techniques and a newly adapted BPH renormalization method that general momentum cutoff scalar field theories in four dimensions are perturbatively renormalizable. Weinberg close-quote s convergence theorem is used to show that operators in the Lagrangian with dimension greater than four, which are divided by powers of the cutoff, produce perturbatively only local divergences in the two-, three-, and four-point correlation functions. The naive use of the convergence theorem together with the BPH method is not appropriate for understanding the local divergences and renormalizability of these theories. We also show that the renormalized Green close-quote s functions are the same as in ordinary Φ 4 theory up to corrections suppressed by inverse powers of the cutoff. These conclusions are consistent with those of existing proofs based on the renormalization group. copyright 1996 The American Physical Society

Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?

Science.gov (United States)

Garkusha, A. V.; Kataev, A. L.; Molokoedov, V. S.

2018-02-01

The problem of scheme and gauge dependence of the factorization property of the renormalization group β-function in the SU( N c ) QCD generalized Crewther relation (GCR), which connects the flavor non-singlet contributions to the Adler and Bjorken polarized sum rule functions, is investigated at the O({a}_s^4) level of perturbation theory. It is known that in the gauge-invariant renormalization \\overline{MS} -scheme this property holds in the QCD GCR at least at this order. To study whether this factorization property is true in all gauge-invariant schemes, we consider the MS-like schemes in QCD and the QED-limit of the GCR in the \\overline{MS} -scheme and in two other gauge-independent subtraction schemes, namely in the momentum MOM and the on-shell OS schemes. In these schemes we confirm the existence of the β-function factorization in the QCD and QED variants of the GCR. The problem of the possible β-factorization in the gauge-dependent renormalization schemes in QCD is studied. To investigate this problem we consider the gauge non-invariant mMOM and MOMgggg-schemes. We demonstrate that in the mMOM scheme at the O({a}_s^3) level the β-factorization is valid for three values of the gauge parameter ξ only, namely for ξ = -3 , -1 and ξ = 0. In the O({a}_s^4) order of PT it remains valid only for case of the Landau gauge ξ = 0. The consideration of these two gauge-dependent schemes for the QCD GCR allows us to conclude that the factorization of RG β-function will always be implemented in any MOM-like renormalization schemes with linear covariant gauge at ξ = 0 and ξ = -3 at the O({a}_s^3) approximation. It is demonstrated that if factorization property for the MS-like schemes is true in all orders of PT, as theoretically indicated in the several works on the subject, then the factorization will also occur in the arbitrary MOM-like scheme in the Landau gauge in all orders of perturbation theory as well.

Exact solution for a quantum field with δ-like interaction: effective action and UV renormalization

International Nuclear Information System (INIS)

Solodukhin, Sergey N.

1999-01-01

A quantum field described by the field operator Δ a = Δ + aδ Σ involving a δ-like potential concentrated on a subspace Σ is considered. Mathematically, the treatment of the δ-potential is based on the theory of self-adjoint extension of the unperturbed operator Δ. We give the general expressions for the resolvent and the heat kernel of the perturbed operator Δ a . The main attention is paid to d = 2 δ-potential though d = 1 and d = 3 cases are considered in some detail. We calculate exactly the heat kernel, Green's functions and the effective action for the operator Δ a in diverse dimensions and for various spaces Σ. The renormalization phenomenon for the coupling constant a of d = 2 and d = 3 δ-potentials is observed. We find the non-perturbative behavior of the effective action with respect to the renormalized coupling a ren

A symmetrical treatment of bradyons and luxons by means of a non-real space

International Nuclear Information System (INIS)

Majernik, V.

1983-01-01

From the point of view of symmetry, it is interesting to note that there exist two kinds of physical particles - bradyons and luxons. In this connection the question arises whether it is not possible to treat luxons and bradyons in a symmetric way. The characteristic property of luxons is the fact that they move with the velocity of light. On the other hand, the characteristic property of bradyons is their ability to be localized. The bradyon-luxon symmetry would require such physical conditions in which luxons would behave as bradyons and bradyons as luxons. The author speculates that there exists a non-real space in addition to our real space in which bradyons would move with the velocity of light and luxons would be localized. This non-real, three-dimensional space (s-space), together with our three-dimensional real space (r-space), forms a suitable framework for the postulated bradyon-luxon symmetry. Within this framework he attempts to find the fundamental equations for bosons and fermions both in the s- and r-space, and to suggest a new hierarchy among the particles as well as a simple scheme of the fundamental physical interactions. (Auth.)

Renormalized Stress-Energy Tensor of an Evaporating Spinning Black Hole.

Science.gov (United States)

Levi, Adam; Eilon, Ehud; Ori, Amos; van de Meent, Maarten

2017-04-07

We provide the first calculation of the renormalized stress-energy tensor (RSET) of a quantum field in Kerr spacetime (describing a stationary spinning black hole). More specifically, we employ a recently developed mode-sum regularization method to compute the RSET of a minimally coupled massless scalar field in the Unruh vacuum state, the quantum state corresponding to an evaporating black hole. The computation is done here for the case a=0.7M, using two different variants of the method: t splitting and φ splitting, yielding good agreement between the two (in the domain where both are applicable). We briefly discuss possible implications of the results for computing semiclassical corrections to certain quantities, and also for simulating dynamical evaporation of a spinning black hole.

Cylinder renormalization for Siegel disks and a constructive Measurable Riemann Mapping Theorem

CERN Document Server

Gaydashev, D G

2006-01-01

The boundary of the Siegel disk of a quadratic polynomial with an irrationally indifferent fixed point with the golden mean rotation number has been observed to be self-similar. The geometry of this self-similarity is universal for a large class of holomorphic maps. A renormalization explanation of this universality has been proposed in the literature. However, one of the ingredients of this explanation, the hyperbolicity of renormalization, has not been proved yet. The present work considers a cylinder renormalization - a novel type of renormalization for holomorphic maps with a Siegel disk which is better suited for a hyperbolicity proof. A key element of a cylinder renormalization of a holomorphic map is a conformal isomorphism of a dynamical quotient of a subset of $\\field{C}$ to a bi-infinite cylinder $\\field{C} / \\field{Z}$. A construction of this conformal isomorphism is an implicit procedure which can be performed using the Measurable Riemann Mapping Theorem. We present a constructive proof of the Mea...

An Efficient Return Algorithm For Non-Associated Plasticity With Linear Yield Criteria In Principal Stress Space

DEFF Research Database (Denmark)

Clausen, Johan Christian; Damkilde, Lars; Andersen, Lars

2007-01-01

. The stress return and the formation of the constitutive matrix is carried out in principal stress space. Here the manipulations simplify and rely on geometrical arguments. The singularities arising at the intersection of yield planes are dealt with in a straightforward way also based on geometrical......An efficient return algorithm for stress update in numerical plasticity computations is presented. The yield criterion must be linear in principal stress space and can be composed of any number of yield planes. Each of these yield planes may have an associated or non-associated flow rule...

Renormalization group theory of phase transitions in square Ising systems

International Nuclear Information System (INIS)

Nienhuis, B.

1978-01-01

Some renormalization group calculations are presented on a number of phase transitions in a square Ising model, both second and first order. Of these transitions critical exponents are calculated, the amplitudes of the power law divergences and the locus of the transition. In some cases attention is paid to the thermodynamic functions also far from the critical point. Universality and scaling are discussed and the renormalization group theory is reviewed. It is shown how a renormalization transformation, which relates two similar systems with different macroscopic dimensions, can be constructed, and how some critical properties of the system follow from this transformation. Several numerical and analytical applications are presented. (Auth.)

Renormalization of the g-boson effects for Os isotopes

International Nuclear Information System (INIS)

Zhang Zhanjun; Liu Yong; Sang Jianping

1996-01-01

A modified renormalization approach based on that proposed by Druce et al. is presented. The overall agreement between the spectra calculated here and the accurate spectra is significantly improved. We also use Druce's approach to generate the renormalized spectra. It is shown that in our microscopic study, both of the approaches are very useful to the determination of several free parameters of fermion residual interactions

Poissonian renormalizations, exponentials, and power laws.

Science.gov (United States)

Eliazar, Iddo

2013-05-01

This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.

Loop optimization for tensor network renormalization

Science.gov (United States)

Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.

One-loop renormalization of a gravity-scalar system

Energy Technology Data Exchange (ETDEWEB)

Park, I.Y. [Philander Smith College, Department of Applied Mathematics, Little Rock, AR (United States)

2017-05-15

Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the ''mass'' term. One-loop calculations lead to renormalization of the cosmological and Newton constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information. (orig.)

One-loop renormalization of a gravity-scalar system

International Nuclear Information System (INIS)

Park, I.Y.

2017-01-01

Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the ''mass'' term. One-loop calculations lead to renormalization of the cosmological and Newton constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information. (orig.)

One-loop renormalization of a gravity-scalar system

Science.gov (United States)

Park, I. Y.

2017-05-01

Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the "mass" term. One-loop calculations lead to renormalization of the cosmological and Newton constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information.

The ab-initio density matrix renormalization group in practice

Energy Technology Data Exchange (ETDEWEB)

Olivares-Amaya, Roberto; Hu, Weifeng; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic [Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States); Nakatani, Naoki [Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States); Catalysis Research Center, Hokkaido University, Kita 21 Nishi 10, Sapporo, Hokkaido 001-0021 (Japan)

2015-01-21

The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.

The ab-initio density matrix renormalization group in practice.

Science.gov (United States)

Olivares-Amaya, Roberto; Hu, Weifeng; Nakatani, Naoki; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic

2015-01-21

The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.

Strong renormalization scheme dependence in τ-lepton decay: Fact or fiction?

International Nuclear Information System (INIS)

Chyla, J.

1995-01-01

The question of the renormalization scheme dependence of the τ semileptonic decay rate is examined in response to a recent criticism. Particular attention is payed to a distinction between a consistent quantitative description of this dependence and the actual selection of a subset of ''acceptable'' renormalization schemes. It is pointed out that this criticism is valid only within a particular definition of the ''strength'' of the renormalization scheme dependence and should not discourage further attempts to use the semileptonic τ decay rate for quantitative tests of perturbative QCD

A Real-Time Apple Grading System Using Multicolor Space

OpenAIRE

Toylan, Hayrettin; Kuscu, Hilmi

2014-01-01

This study was focused on the multicolor space which provides a better specification of the color and size of the apple in an image. In the study, a real-time machine vision system classifying apples into four categories with respect to color and size was designed. In the analysis, different color spaces were used. As a result, 97% identification success for the red fields of the apple was obtained depending on the values of the parameter “a” of CIE L*a*b*color space. Similarly, 94% identific...

Renormalization and radiative corrections to masses in a general Yukawa model

Science.gov (United States)

Fox, M.; Grimus, W.; Löschner, M.

2018-01-01

We consider a model with arbitrary numbers of Majorana fermion fields and real scalar fields φa, general Yukawa couplings and a ℤ4 symmetry that forbids linear and trilinear terms in the scalar potential. Moreover, fermions become massive only after spontaneous symmetry breaking of the ℤ4 symmetry by vacuum expectation values (VEVs) of the φa. Introducing the shifted fields ha whose VEVs vanish, MS¯ renormalization of the parameters of the unbroken theory suffices to make the theory finite. However, in this way, beyond tree level it is necessary to perform finite shifts of the tree-level VEVs, induced by the finite parts of the tadpole diagrams, in order to ensure vanishing one-point functions of the ha. Moreover, adapting the renormalization scheme to a situation with many scalars and VEVs, we consider the physical fermion and scalar masses as derived quantities, i.e. as functions of the coupling constants and VEVs. Consequently, the masses have to be computed order by order in a perturbative expansion. In this scheme, we compute the self-energies of fermions and bosons and show how to obtain the respective one-loop contributions to the tree-level masses. Furthermore, we discuss the modification of our results in the case of Dirac fermions and investigate, by way of an example, the effects of a flavor symmetry group.

A note on nonperturbative renormalization of effective field theory

Energy Technology Data Exchange (ETDEWEB)

Yang Jifeng [Department of Physics, East China Normal University, Shanghai 200062 (China)

2009-08-28

Within the realm of contact potentials, the key structures intrinsic of nonperturbative renormalization of T-matrices are unraveled using rigorous solutions and an inverse form of the algebraic Lippmann-Schwinger equation. The intrinsic mismatches between effective field theory power counting and nonperturbative divergence structures are shown for the first time to preclude the conventional counterterm algorithm from working in the renormalization of EFT for NN scattering in nonperturbative regimes.

A note on nonperturbative renormalization of effective field theory

International Nuclear Information System (INIS)

Yang Jifeng

2009-01-01

Within the realm of contact potentials, the key structures intrinsic of nonperturbative renormalization of T-matrices are unraveled using rigorous solutions and an inverse form of the algebraic Lippmann-Schwinger equation. The intrinsic mismatches between effective field theory power counting and nonperturbative divergence structures are shown for the first time to preclude the conventional counterterm algorithm from working in the renormalization of EFT for NN scattering in nonperturbative regimes.

Exact renormalization group for gauge theories

International Nuclear Information System (INIS)

Balaban, T.; Imbrie, J.; Jaffe, A.

1984-01-01

Renormalization group ideas have been extremely important to progress in our understanding of gauge field theory. Particularly the idea of asymptotic freedom leads us to hope that nonabelian gauge theories exist in four dimensions and yet are capable of producing the physics we observe-quarks confined in meson and baryon states. For a thorough understanding of the ultraviolet behavior of gauge theories, we need to go beyond the approximation of the theory at some momentum scale by theories with one or a small number of coupling constants. In other words, we need a method of performing exact renormalization group transformations, keeping control of higher order effects, nonlocal effects, and large field effects that are usually ignored. Rigorous renormalization group methods have been described or proposed in the lectures of Gawedzki, Kupiainen, Mack, and Mitter. Earlier work of Glimm and Jaffe and Gallavotti et al. on the /phi/ model in three dimensions were quite important to later developments in this area. We present here a block spin procedure which works for gauge theories, at least in the superrenormalizable case. It should be enlightening for the reader to compare the various methods described in these proceedings-especially from the point of view of how each method is suited to the physics of the problem it is used to study

Complete one-loop renormalization of the Higgs-electroweak chiral Lagrangian

Science.gov (United States)

Buchalla, G.; Catà, O.; Celis, A.; Knecht, M.; Krause, C.

2018-03-01

Employing background-field method and super-heat-kernel expansion, we compute the complete one-loop renormalization of the electroweak chiral Lagrangian with a light Higgs boson. Earlier results from purely scalar fluctuations are confirmed as a special case. We also recover the one-loop renormalization of the conventional Standard Model in the appropriate limit.

Application of 't Hooft's renormalization scheme to two-loop calculations 230

International Nuclear Information System (INIS)

Vladimirov, A.A.

1975-01-01

The advantages of the Hooft scheme for asymptotic calculations in the renormalization group have been demonstrated. Two-loop calculations have been carried out in three renormalized models: in scalar electrodynamics, in a pseudoscalar Yukawa theory and in the Weiss-Zumino supersymmetrical model [ru

Exact renormalization group equations: an introductory review

Science.gov (United States)

Bagnuls, C.; Bervillier, C.

2001-07-01

We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.

Real time animation of space plasma phenomena

International Nuclear Information System (INIS)

Jordan, K.F.; Greenstadt, E.W.

1987-01-01

In pursuit of real time animation of computer simulated space plasma phenomena, the code was rewritten for the Massively Parallel Processor (MPP). The program creates a dynamic representation of the global bowshock which is based on actual spacecraft data and designed for three dimensional graphic output. This output consists of time slice sequences which make up the frames of the animation. With the MPP, 16384, 512 or 4 frames can be calculated simultaneously depending upon which characteristic is being computed. The run time was greatly reduced which promotes the rapid sequence of images and makes real time animation a foreseeable goal. The addition of more complex phenomenology in the constructed computer images is now possible and work proceeds to generate these images

Poissonian renormalizations, exponentials, and power laws

Science.gov (United States)

Eliazar, Iddo

2013-05-01

This paper presents a comprehensive “renormalization study” of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to “white noise” and to “1/f noise.” Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.

Real-space grid implementation of the projector augmented wave method

DEFF Research Database (Denmark)

Mortensen, Jens Jørgen; Hansen, Lars Bruno; Jacobsen, Karsten Wedel

2005-01-01

A grid-based real-space implementation of the projector augmented wave sPAWd method of Blöchl fPhys. Rev. B 50, 17953 s1994dg for density functional theory sDFTd calculations is presented. The use of uniform three-dimensional s3Dd real-space grids for representing wave functions, densities...... valence wave functions that can be represented on relatively coarse grids. We demonstrate the accuracy of the method by calculating the atomization energies of 20 small molecules, and the bulk modulus and lattice constants of bulk aluminum. We show that the approach in terms of computational efficiency...... is comparable to standard plane-wave methods, but the memory requirements are higher....

Near real-time geomagnetic data for space weather applications in the European sector

Science.gov (United States)

Johnsen, M. G.; Hansen, T. L.

2012-12-01

Tromsø Geophysical Observatory (TGO) is responsible for making and maintaining long time-series of geomagnetic measurements in Norway. TGO is currently operating 3 geomagnetic observatories and 11 variometer stations from southern Norway to Svalbard . Data from these 14 locations are acquired, processed and made available for the user community in near real-time. TGO is participating in several European Union (EU) and European Space Agency (ESA) space weather related projects where both near real-time data and derived products are provided. In addition the petroleum industry is benefiting from our real-time data services for directional drilling. Near real-time data from TGO is freely available for non-commercial purposes. TGO is exchanging data in near real-time with several institutions, enabling the presentation of near real-time geomagnetic data from more than 40 different locations in Fennoscandia and Greenland. The open exchange of non real-time geomagnetic data has been successfully going on for many years through services such as the world data center in Kyoto, SuperMAG, IMAGE and SPIDR. TGO's vision is to take this one step further and make the exchange of near real-time geomagnetic data equally available for the whole community. This presentation contains an overview of TGO, our activities and future aims. We will show how our near real-time data are presented. Our contribution to the space weather forecasting and nowcasting effort in the EU and ESA will be presented with emphasis on our real-time auroral activity index and brand new auroral activity monitor and electrojet tracker.

Asynchronous communication in real space process algebra

OpenAIRE

Baeten, JCM Jos; Bergstra, JA Jan

1990-01-01

A version of classical real space process algebra is given in which messages travel with constant speed through a three-dimensional medium. It follows that communication is asynchronous and has a broadcasting character. A state operator is used to describe asynchronous message transfer and a priority mechanism allows to express the broadcasting mechanism. As an application, a protocol is specified in which the receiver moves with respect to the sender.

Framing the Real: Lefèbvre and NeoRealist Cinematic Space as Practice

OpenAIRE

Brancaleone, David

2014-01-01

In 1945 Roberto Rossellini's Neo-realist Rome, Open City set in motion an approach to cinema and its representation of real life – and by extension real spaces – that was to have international significance in film theory and practice. However, the re-use of the real spaces of the city, and elsewhere, as film sets in Neo-realist film offered (and offers) more than an influential aesthetic and set of cinematic theories. Through Neo-realism, it can be argued that we gain access to a cinematic re...

Programmering af applikationer med dSPACE real-time værktøjer

DEFF Research Database (Denmark)

Voigt, Kristian

1998-01-01

real-time direkte på et virkeligt system. Reguleringen af systemet sker vha. et DSP- og I/O-kort. En model af systemet opbygges vha. Matlab/Simulink fra firmaet The Mathworks. Modellen oversættes til C-kode vha. Real-Time Workshop fra firmaet The Mathworks. For at gøre C-koden hardwarespecifik bruges...... software fra hardwareleverandøren - dSPACE. Firmaet dSPACE har desuden levereret software til at monitorere real-time værdier i systemet, og software til at ændre på parametre i modellen i real-time.I brugervejledningens Appendix F findes et eksempel, der gennemgår hele forløbet med opstart af programmer...

Renormalization group improved Yennie-Frautschi-Suura theory for Z0 physics

International Nuclear Information System (INIS)

Ward, B.F.L.

1987-06-01

Described is a recently developed renormalization group improved version of the program of Yennie, Frautschi and Suura for the exponentiation of infrared divergences in Abelian gauge theories. Particular attention is paid to the relevance of this renormalization group improved exponentiation to Z 0 physics at the SLC and LEP

Physical renormalization condition for de Sitter QED

Science.gov (United States)

Hayashinaka, Takahiro; Xue, She-Sheng

2018-05-01

We considered a new renormalization condition for the vacuum expectation values of the scalar and spinor currents induced by a homogeneous and constant electric field background in de Sitter spacetime. Following a semiclassical argument, the condition named maximal subtraction imposes the exponential suppression on the massive charged particle limit of the renormalized currents. The maximal subtraction changes the behaviors of the induced currents previously obtained by the conventional minimal subtraction scheme. The maximal subtraction is favored for a couple of physically decent predictions including the identical asymptotic behavior of the scalar and spinor currents, the removal of the IR hyperconductivity from the scalar current, and the finite current for the massless fermion.

Real-time 3-D space numerical shake prediction for earthquake early warning

Science.gov (United States)

Wang, Tianyun; Jin, Xing; Huang, Yandan; Wei, Yongxiang

2017-12-01

In earthquake early warning systems, real-time shake prediction through wave propagation simulation is a promising approach. Compared with traditional methods, it does not suffer from the inaccurate estimation of source parameters. For computation efficiency, wave direction is assumed to propagate on the 2-D surface of the earth in these methods. In fact, since the seismic wave propagates in the 3-D sphere of the earth, the 2-D space modeling of wave direction results in inaccurate wave estimation. In this paper, we propose a 3-D space numerical shake prediction method, which simulates the wave propagation in 3-D space using radiative transfer theory, and incorporate data assimilation technique to estimate the distribution of wave energy. 2011 Tohoku earthquake is studied as an example to show the validity of the proposed model. 2-D space model and 3-D space model are compared in this article, and the prediction results show that numerical shake prediction based on 3-D space model can estimate the real-time ground motion precisely, and overprediction is alleviated when using 3-D space model.

Developing Near Real-time Data-assimilative Models and Tools for the Space Environment, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — The IDA4D and AMIE data assimilation methods are currently of limited use for real-time space weather applications because either they don't run in real-time (IDA4D)...

Real-time monitoring of genetically modified Chlamydomonas reinhardtii during the Foton M3 space mission

Science.gov (United States)

Lambreva, M.; Rea, G.; Antonacci, A.; Serafini, A.; Damasso, M.; Pastorelli, S.; Margonelli, A.; Johanningmeier, U.; Bertalan, I.; Pezzotti, G.; Giardi, M. T.

2008-09-01

. We analysed the hourly changes and the daily light/dark trend in the maximum quantum yield of PSII photochemistry, Fv/Fm (Fig.2). Some physiological parameters that characterize the post-flight effect on algae viability and photosynthetic performance were also determined. The dose and particle flux during Foton-M3 flight were monitored in real time by the active spectrum-dosimeter Liulin- Photo, mounted on the top of Photo-II fluorimeter (Fig.2). Liulin-Photo measurements provided information on the amount of the energy released on the samples and the quality of the incident ionizing radiation [3]. The space flight results in relationship with the ground control simulation are discussed.

Quantum theory in real Hilbert space: How the complex Hilbert space structure emerges from Poincaré symmetry

Science.gov (United States)

Moretti, Valter; Oppio, Marco

As earlier conjectured by several authors and much later established by Solèr (relying on partial results by Piron, Maeda-Maeda and other authors), from the lattice theory point of view, Quantum Mechanics may be formulated in real, complex or quaternionic Hilbert spaces only. Stückelberg provided some physical, but not mathematically rigorous, reasons for ruling out the real Hilbert space formulation, assuming that any formulation should encompass a statement of Heisenberg principle. Focusing on this issue from another — in our opinion, deeper — viewpoint, we argue that there is a general fundamental reason why elementary quantum systems are not described in real Hilbert spaces. It is their basic symmetry group. In the first part of the paper, we consider an elementary relativistic system within Wigner’s approach defined as a locally-faithful irreducible strongly-continuous unitary representation of the Poincaré group in a real Hilbert space. We prove that, if the squared-mass operator is non-negative, the system admits a natural, Poincaré invariant and unique up to sign, complex structure which commutes with the whole algebra of observables generated by the representation itself. This complex structure leads to a physically equivalent reformulation of the theory in a complex Hilbert space. Within this complex formulation, differently from what happens in the real one, all selfadjoint operators represent observables in accordance with Solèr’s thesis, and the standard quantum version of Noether theorem may be formulated. In the second part of this work, we focus on the physical hypotheses adopted to define a quantum elementary relativistic system relaxing them on the one hand, and making our model physically more general on the other hand. We use a physically more accurate notion of irreducibility regarding the algebra of observables only, we describe the symmetries in terms of automorphisms of the restricted lattice of elementary propositions of the

Functional renormalization group approach to interacting three-dimensional Weyl semimetals

Science.gov (United States)

Sharma, Anand; Scammell, Arthur; Krieg, Jan; Kopietz, Peter

2018-03-01

We investigate the effect of long-range Coulomb interaction on the quasiparticle properties and the dielectric function of clean three-dimensional Weyl semimetals at zero temperature using a functional renormalization group (FRG) approach. The Coulomb interaction is represented via a bosonic Hubbard-Stratonovich field which couples to the fermionic density. We derive truncated FRG flow equations for the fermionic and bosonic self-energies and for the three-legged vertices with two fermionic and one bosonic external legs. We consider two different cutoff schemes—cutoff in fermionic or bosonic propagators—in order to calculate the renormalized quasiparticle velocity and the dielectric function for an arbitrary number of Weyl nodes and the interaction strength. If we approximate the dielectric function by its static limit, our results for the velocity and the dielectric function are in good agreement with that of A. A. Abrikosov and S. D. Beneslavskiĭ [Sov. Phys. JETP 32, 699 (1971)] exhibiting slowly varying logarithmic momentum dependence for small momenta. We extend their result for an arbitrary number of Weyl nodes and finite frequency by evaluating the renormalized velocity in the presence of dynamic screening and calculate the wave function renormalization.

DeWitt-Schwinger renormalization and vacuum polarization in d dimensions

International Nuclear Information System (INIS)

Thompson, R. T.; Lemos, Jose P. S.

2009-01-01

Calculation of the vacuum polarization, 2 (x)>, and expectation value of the stress tensor, μν (x)>, has seen a recent resurgence, notably for black hole spacetimes. To date, most calculations of this type have been done only in four dimensions. Extending these calculations to d dimensions includes d-dimensional renormalization. Typically, the renormalizing terms are found from Christensen's covariant point splitting method for the DeWitt-Schwinger expansion. However, some manipulation is required to put the correct terms into a form that is compatible with problems of the vacuum polarization type. Here, after a review of the current state of affairs for 2 (x)> and μν (x)> calculations and a thorough introduction to the method of calculating 2 (x)>, a compact expression for the DeWitt-Schwinger renormalization terms suitable for use in even-dimensional spacetimes is derived. This formula should be useful for calculations of 2 (x)> and μν (x)> in even dimensions, and the renormalization terms are shown explicitly for four and six dimensions. Furthermore, use of the finite terms of the DeWitt-Schwinger expansion as an approximation to 2 (x)> for certain spacetimes is discussed, with application to four and five dimensions.

A shape dynamical approach to holographic renormalization

Energy Technology Data Exchange (ETDEWEB)

Gomes, Henrique [University of California at Davis, Davis, CA (United States); Gryb, Sean [Utrecht University, Institute for Theoretical Physics, Utrecht (Netherlands); Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics, Nijmegen (Netherlands); Koslowski, Tim [University of New Brunswick, Fredericton, NB (Canada); Mercati, Flavio; Smolin, Lee [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)

2015-01-01

We provide a bottom-up argument to derive some known results from holographic renormalization using the classical bulk-bulk equivalence of General Relativity and Shape Dynamics, a theory with spatial conformal (Weyl) invariance. The purpose of this paper is twofold: (1) to advertise the simple classical mechanism, trading off gauge symmetries, that underlies the bulk-bulk equivalence of General Relativity and Shape Dynamics to readers interested in dualities of the type of AdS/conformal field theory (CFT); and (2) to highlight that this mechanism can be used to explain certain results of holographic renormalization, providing an alternative to the AdS/CFT conjecture for these cases. To make contact with the usual semiclassical AdS/CFT correspondence, we provide, in addition, a heuristic argument that makes it plausible that the classical equivalence between General Relativity and Shape Dynamics turns into a duality between radial evolution in gravity and the renormalization group flow of a CFT. We believe that Shape Dynamics provides a new perspective on gravity by giving conformal structure a primary role within the theory. It is hoped that this work provides the first steps toward understanding what this new perspective may be able to teach us about holographic dualities. (orig.)

Renormalized second post-Newtonian spin contributions to the accumulated orbital phase for LISA sources

International Nuclear Information System (INIS)

Gergely, Laszlo Arpad; Mikoczi, Balazs

2009-01-01

We give here a new third post-Newtonian (3PN) spin-spin contribution (in the PN parameter ε) to the accumulated orbital phase of a compact binary, arising from the spin-orbit precessional motion of the spins. In the equal mass case, this contribution vanishes, but Laser Interferometer Space Antenna (LISA) sources of merging supermassive binary black holes have typically a mass ratio of 1:10. For such nonequal masses, this 3PN correction is periodic in time, with a period approximately ε -1 times larger than the period of gravitational waves. We derive a renormalized and simpler expression of the spin-spin coefficient at 2PN, as an average over the time scale of this period of the combined 2PN and 3PN contribution. We also find that for LISA sources the quadrupole-monopole contribution to the phase dominates over the spin-spin contribution, while the self-spin contribution is negligible even for the dominant spin. Finally, we define a renormalized total spin coefficient σ to be employed in the search for gravitational waves emitted by LISA sources.

Renormalization group treatment of nonrenormalizable interactions

International Nuclear Information System (INIS)

Kazakov, D I; Vartanov, G S

2006-01-01

The structure of the UV divergences in higher dimensional nonrenormalizable theories is analysed. Based on renormalization operation and renormalization group theory it is shown that even in this case the leading divergences (asymptotics) are governed by the one-loop diagrams the number of which, however, is infinite. An explicit expression for the one-loop counter term in an arbitrary D-dimensional quantum field theory without derivatives is suggested. This allows one to sum up the leading asymptotics which are independent of the arbitrariness in subtraction of higher order operators. Diagrammatic calculations in a number of scalar models in higher loops are performed to be in agreement with the above statements. These results do not support the idea of the naive power-law running of couplings in nonrenormalizable theories and fail (with one exception) to reveal any simple closed formula for the leading terms

Real-space description of semiconducting band gaps in substitutional systems

International Nuclear Information System (INIS)

Magri, R.; Zunger, A.

1991-01-01

The goal of ''band-gap engineering'' in substitutional lattices is to identify atomic configurations that would give rise to a desired value of the band gap. Yet, current theoretical approaches to the problems, based largely on compilations of band structures for various latice configurations, have not yielded simple rules relating structural motifs to band gaps. We show that the band gap of substitutional AlAs/GaAs lattices can be usefully expanded in terms of a hierarchy of contributions from real-space ''atomic figures'' (pairs, triplets, quadruplets) detemined from first-principles band-structure calculations. Pair figures (up to fourth neighbors) and three-body figures are dominant. In analogy with similar cluster expansions of the total energy, this permits a systematic search among all lattice configurations for those having ''special'' band gaps. This approach enables the design of substitutional systems with certain band-gap properties by assembling atomic figures. As an illustration, we predict that the [0 bar 12]-oriented (AlAs) 1 /(GaAs) 4 /(AlAs) 1 /(GaAs) 2 superlattice has the largest band gap among all Al 0.25 Ga 0.75 As lattices with a maximum of ten cations per unit cell

Rota-Baxter algebras and the Hopf algebra of renormalization

Energy Technology Data Exchange (ETDEWEB)

Ebrahimi-Fard, K.

2006-06-15

Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

Complex-mass shell renormalization of the higher-derivative electrodynamics

Energy Technology Data Exchange (ETDEWEB)

Turcati, Rodrigo [SISSA, Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy); Universidade Federal do Espirito Santo, Departamento de Fisica e Quimica, Vitoria, ES (Brazil); Laboratorio de Fisica Experimental (LAFEX), Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro (Brazil); Neves, Mario Junior [Universidade Federal Rural do Rio de Janeiro, Departamento de Fisica, Rio de Janeiro (Brazil)

2016-08-15

We consider a higher-derivative extension of QED modified by the addition of a gauge-invariant dimension-6 kinetic operator in the U(1) gauge sector. The Feynman diagrams at one-loop level are then computed. The modification in the spin-1 sector leads the electron self-energy and vertex corrections diagrams finite in the ultraviolet regime. Indeed, no regularization prescription is used to calculate these diagrams because the modified propagator always occurs coupled to conserved currents. Moreover, besides the usual massless pole in the spin-1 sector, there is the emergence of a massive one, which becomes complex when computing the radiative corrections at one-loop order. This imaginary part defines the finite decay width of the massive mode. To check consistency, we also derive the decay length using the electron-positron elastic scattering and show that both results are equivalent. Because the presence of this unstable mode, the standard renormalization procedures cannot be used and is necessary adopt an appropriate framework to perform the perturbative renormalization. For this purpose, we apply the complex-mass shell scheme (CMS) to renormalize the aforementioned model. As an application of the formalism developed, we estimate a quantum bound on the massive parameter using the measurement of the electron anomalous magnetic moment and compute the Uehling potential. At the end, the renormalization group is analyzed. (orig.)

Rota-Baxter algebras and the Hopf algebra of renormalization

International Nuclear Information System (INIS)

Ebrahimi-Fard, K.

2006-06-01

Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

Products of composite operators in the exact renormalization group formalism

Science.gov (United States)

Pagani, C.; Sonoda, H.

2018-02-01

We discuss a general method of constructing the products of composite operators using the exact renormalization group formalism. Considering mainly the Wilson action at a generic fixed point of the renormalization group, we give an argument for the validity of short-distance expansions of operator products. We show how to compute the expansion coefficients by solving differential equations, and test our method with some simple examples.

Renormalization in the stochastic quantization of field theories

International Nuclear Information System (INIS)

Brunelli, J.C.

1991-01-01

In the stochastic quantization scheme of Parisi and Wu the renormalization of the stochastic theory of some models in field theory is studied. Following the path integral approach for stochastic process the 1/N expansion of the non linear sigma model is performed and, using a Ward identity obtained, from a BRS symmetry of the effective action of this formulation. It is shown the renormalizability of the model. Using the Langevin approach for stochastic process the renormalizability of the massive Thirring model is studied showing perturbatively the vanishing of the renormalization group's beta functions at finite fictitious time. (author)

Fermionic functional integrals and the renormalization group

CERN Document Server

Feldman, Joel; Trubowitz, Eugene

2002-01-01

This book, written by well-known experts in the field, offers a concise summary of one of the latest and most significant developments in the theoretical analysis of quantum field theory. The renormalization group is the name given to a technique for analyzing the qualitative behavior of a class of physical systems by iterating a map on the vector space of interactions for the class. In a typical nonrigorous application of this technique, one assumes, based on one's physical intuition, that only a certain finite dimensional subspace (usually of dimension three or less) is important. The material in this book concerns a technique for justifying this approximation in a broad class of fermionic models used in condensed matter and high energy physics. This volume is based on the Aisenstadt Lectures given by Joel Feldman at the Centre de Recherches Mathematiques (Montreal, Canada). It is suitable for graduate students and research mathematicians interested in mathematical physics. Included are many problems and so...

Self-consistent DFT +U method for real-space time-dependent density functional theory calculations

Science.gov (United States)

Tancogne-Dejean, Nicolas; Oliveira, Micael J. T.; Rubio, Angel

2017-12-01

We implemented various DFT+U schemes, including the Agapito, Curtarolo, and Buongiorno Nardelli functional (ACBN0) self-consistent density-functional version of the DFT +U method [Phys. Rev. X 5, 011006 (2015), 10.1103/PhysRevX.5.011006] within the massively parallel real-space time-dependent density functional theory (TDDFT) code octopus. We further extended the method to the case of the calculation of response functions with real-time TDDFT+U and to the description of noncollinear spin systems. The implementation is tested by investigating the ground-state and optical properties of various transition-metal oxides, bulk topological insulators, and molecules. Our results are found to be in good agreement with previously published results for both the electronic band structure and structural properties. The self-consistent calculated values of U and J are also in good agreement with the values commonly used in the literature. We found that the time-dependent extension of the self-consistent DFT+U method yields improved optical properties when compared to the empirical TDDFT+U scheme. This work thus opens a different theoretical framework to address the nonequilibrium properties of correlated systems.

Biorthogonal moment expansions in coupled-cluster theory: Review of key concepts and merging the renormalized and active-space coupled-cluster methods

International Nuclear Information System (INIS)

Shen Jun; Piecuch, Piotr

2012-01-01

Graphical abstract: The key ideas behind biorthogonal moment expansions in coupled-cluster theory are discussed. Methods that enable merging active-space and renormalized coupled-cluster approaches are proposed and tested. Abstract: After reviewing recent progress in the area of the development of coupled-cluster (CC) methods for quasi-degenerate electronic states that are characterized by stronger non-dynamical correlation effects, including new generations of single- and multi-reference approaches that can handle bond breaking and excited states dominated by many-electron transitions, and after discussing the key elements of the left-eigenstate completely renormalized (CR) CC and equation-of-motion (EOM) CC methods, and the underlying biorthogonal method of moments of CC (MMCC) equations [P. Piecuch, M. Włoch, J. Chem. Phys. 123 (2005) 224105; P. Piecuch, M. Włoch, J.R. Gour, A. Kinal, Chem. Phys. Lett. 418 (2006) 467; M. Włoch, M.D. Lodriguito, P. Piecuch, J.R. Gour, Mol. Phys. 104 (2006) 2149], it is argued that it is beneficial to merge the CR-CC/EOMCC and active-space CC/EOMCC [P. Piecuch, Mol. Phys. 108 (2010) 2987, and references therein] theories into a single formalism. In order to accomplish this goal, the biorthogonal MMCC theory, which provides compact many-body expansions for the differences between the full configuration interaction and CC or, in the case of excited states, EOMCC energies, obtained using conventional truncation schemes in the cluster operator T and excitation operator R μ , is generalized, so that one can correct the CC/EOMCC energies obtained with arbitrary truncations in T and R μ for the selected many-electron correlation effects of interest. The resulting moment expansions, defining the new, Flexible MMCC (Flex-MMCC) formalism, and the ensuing CC(P; Q) hierarchy, proposed in the present work, enable one to correct energies obtained in the active-space CC and EOMCC calculations, in which one selects higher many

The renormalization group: scale transformations and changes of scheme

International Nuclear Information System (INIS)

Roditi, I.

1983-01-01

Starting from a study of perturbation theory, the renormalization group is expressed, not only for changes of scale but also within the original view of Stueckelberg and Peterman, for changes of renormalization scheme. The consequences that follow from using that group are investigated. Following a more general point of view a method to obtain an improvement of the perturbative results for physical quantities is proposed. The results obtained with this method are compared with those of other existing methods. (L.C.) [pt

Real-time estimation of free spaces in regulated on-street parking spaces using artificial neural networks

Energy Technology Data Exchange (ETDEWEB)

Magaña Suarez, M.

2016-07-01

In this paper we will develop a methodology for estimating the percentage of free parking spaces available in the area of the city where a user is interested through a real-time query in a mobile app. The smartphone screen will provide a colour-coded map of the requested area that indicates the saturation state of the parking spaces. (Author)

The energy-momentum operator in curved space-time

International Nuclear Information System (INIS)

Brown, M.R.; Ottewill, A.C.

1983-01-01

It is argued that the only meaningful geometrical measure of the energy-momentum of states of matter described by a free quantum field theory in a general curved space-time is that provided by a normal ordered energy-momentum operator. The finite expectation values of this operator are contrasted with the conventional renormalized expectation values and it is further argued that the use of renormalization theory is inappropriate in this context. (author)

Non-perturbative renormalization of static-light four-fermion operators in quenched lattice QCD

Energy Technology Data Exchange (ETDEWEB)

Palombi, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Papinutto, M.; Pena, C. [CERN, Geneva (Switzerland). Physics Dept., Theory Div.; Wittig, H. [Mainz Univ. (Germany). Inst. fuer Kernphysik

2007-06-15

We perform a non-perturbative study of the scale-dependent renormalization factors of a multiplicatively renormalizable basis of {delta}B=2 parity-odd four-fermion operators in quenched lattice QCD. Heavy quarks are treated in the static approximation with various lattice discretizations of the static action. Light quarks are described by nonperturbatively O(a) improved Wilson-type fermions. The renormalization group running is computed for a family of Schroedinger functional (SF) schemes through finite volume techniques in the continuum limit. We compute non-perturbatively the relation between the renormalization group invariant operators and their counterparts renormalized in the SF at a low energy scale. Furthermore, we provide non-perturbative estimates for the matching between the lattice regularized theory and all the SF schemes considered. (orig.)

Renormalization group and mayer expansions

International Nuclear Information System (INIS)

Mack, G.

1984-01-01

Mayer expansions promise to become a powerful tool in exact renormalization group calculations. Iterated Mayer expansions were sucessfully used in the rigorous analysis of 3-dimensional U (1) lattice gauge theory by Gopfert and the author, and it is hoped that they will also be useful in the 2-dimensional nonlinear σ-model, and elsewhere

Renormalization group evolution of Dirac neutrino masses

International Nuclear Information System (INIS)

Lindner, Manfred; Ratz, Michael; Schmidt, Michael Andreas

2005-01-01

There are good reasons why neutrinos could be Majorana particles, but there exist also a number of very good reasons why neutrinos could have Dirac masses. The latter option deserves more attention and we derive therefore analytic expressions describing the renormalization group evolution of mixing angles and of the CP phase for Dirac neutrinos. Radiative corrections to leptonic mixings are in this case enhanced compared to the quark mixings because the hierarchy of neutrino masses is milder and because the mixing angles are larger. The renormalization group effects are compared to the precision of current and future neutrino experiments. We find that, in the MSSM framework, radiative corrections of the mixing angles are for large tan β comparable to the precision of future experiments

Mass renormalization in sine-Gordon model

International Nuclear Information System (INIS)

Xu Bowei; Zhang Yumei

1991-09-01

With a general gaussian wave functional, we investigate the mass renormalization in the sine-Gordon model. At the phase transition point, the sine-Gordon system tends to a system of massless free bosons which possesses conformal symmetry. (author). 8 refs, 1 fig

Effect of plant spacing on weed suppression and yield of fluted ...

African Journals Online (AJOL)

The field study was conducted to evaluate the effect of plant spacing on weed suppression yield and economic benefit of fluted pumpkin (Telfeiria occidentalis Hook F). The experiment was carried out at the Department of Crop and Soil Science Demonstration Plot, Faculty of Agriculture, University of Port Harcourt, Nigeria ...

Renormalization of three-quark operators for baryon distribution amplitudes

Energy Technology Data Exchange (ETDEWEB)

Gruber, Michael

2017-07-01

In this thesis we design and study three-quark operators that are essential for the calculation of baryon distribution amplitudes. These nonperturbative objects grant insight into the internal structure of hadrons, but their renormalization patterns are nontrivial and need to be treated with care. With the application to lattice simulations in mind we discuss two renormalization schemes, MS and RI{sup '}/SMOM, and connect them by calculating conversion factors. Armed with this knowledge we are able to extract phenomenologically relevant results from an accompanying lattice analysis.

Renormalization of three-quark operators for baryon distribution amplitudes

International Nuclear Information System (INIS)

Gruber, Michael

2017-01-01

In this thesis we design and study three-quark operators that are essential for the calculation of baryon distribution amplitudes. These nonperturbative objects grant insight into the internal structure of hadrons, but their renormalization patterns are nontrivial and need to be treated with care. With the application to lattice simulations in mind we discuss two renormalization schemes, MS and RI ' /SMOM, and connect them by calculating conversion factors. Armed with this knowledge we are able to extract phenomenologically relevant results from an accompanying lattice analysis.

On the renormalization of string functionals

International Nuclear Information System (INIS)

Dietz, K.; Filk, T.

1982-09-01

We investigate analytic renormalization procedures for functional integrals, corresponding to field theories defined on compact manifolds, which arise e.g. from string functionals of the Nambu-Schild-Eguchi type. Although these models belong to the nonrenormalizable class of quantum field theories, we prove finiteness for a rectangular string shape up to three loop level, for circular boundary up to two loop order, and for a variety of graphs in higher order, thus indicating that the result might hold in general. From the explicit calculation of the two loop approximation we extract the first model dependent corrections to the qanti q - potential or the Casimir effect. The importance of dilation transformations for the properties of the renormalization procedure are investigated. We prove that under certain conditions, forced by symmetry properties, the association of finite values to divergent series is unique, independent of the regularization procedure. (orig.)

Renormalization group and Mayer expansions

International Nuclear Information System (INIS)

Mack, G.

1984-02-01

Mayer expansions promise to become a powerful tool in exact renormalization group calculations. Iterated Mayer expansions were sucessfully used in the rigorous analysis of 3-dimensional U(1) lattice gauge theory by Goepfert and the author, and it is hoped that they will also be useful in the 2-dimensional nonlinear sigma-model, and elsewhere. (orig.)

Superfield perturbation theory and renormalization

International Nuclear Information System (INIS)

Delbourgo, R.

1975-01-01

The perturbation theory graphs and divergences in super-symmetric Lagrangian models are studied by using superfield techniques. In super PHI 3 -theory very little effort is needed to arrive at the single infinite (wave function) renormalization counterterm, while in PHI 4 -theory the method indicates the counter-Lagrangians needed at the one-loop level and possibly beyond

The renormalization group of relativistic quantum field theory as a set of generalized, spontaneously broken, symmetry transformations

International Nuclear Information System (INIS)

Maris, Th.A.J.

1976-01-01

The renormalization group theory has a natural place in a general framework of symmetries in quantum field theories. Seen in this way, a 'renormalization group' is a one-parametric subset of the direct product of dilatation and renormalization groups. This subset of spontaneously broken symmetry transformations connects the inequivalent solutions generated by a parameter-dependent regularization procedure, as occurs in renormalized perturbation theory. By considering the global, rather than the infinitesimal, transformations, an expression for general vertices is directly obtained, which is the formal solution of exact renormalization group equations [pt

Systematic renormalization of the effective theory of Large Scale Structure

International Nuclear Information System (INIS)

Abolhasani, Ali Akbar; Mirbabayi, Mehrdad; Pajer, Enrico

2016-01-01

A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and predictive. Here we introduce a systematic renormalization procedure, which neatly associates counterterms to the UV-sensitive diagrams order by order, as it is commonly done in quantum field theory. As a concrete example, we renormalize the one-loop power spectrum and bispectrum of both density and velocity. In addition, we present a series of results that are valid to all orders in perturbation theory. First, we show that while systematic renormalization requires temporally non-local counterterms, in practice one can use an equivalent basis made of local operators. We give an explicit prescription to generate all counterterms allowed by the symmetries. Second, we present a formal proof of the well-known general argument that the contribution of short distance perturbations to large scale density contrast δ and momentum density π(k) scale as k 2 and k, respectively. Third, we demonstrate that the common practice of introducing counterterms only in the Euler equation when one is interested in correlators of δ is indeed valid to all orders.

Fine-grained entanglement loss along renormalization-group flows

International Nuclear Information System (INIS)

Latorre, J.I.; Rico, E.; Luetken, C.A.; Vidal, G.

2005-01-01

We explore entanglement loss along renormalization group trajectories as a basic quantum information property underlying their irreversibility. This analysis is carried out for the quantum Ising chain as a transverse magnetic field is changed. We consider the ground-state entanglement between a large block of spins and the rest of the chain. Entanglement loss is seen to follow from a rigid reordering, satisfying the majorization relation, of the eigenvalues of the reduced density matrix for the spin block. More generally, our results indicate that it may be possible to prove the irreversibility along renormalization group trajectories from the properties of the vacuum only, without need to study the whole Hamiltonian

Bulk renormalization and particle spectrum in codimension-two brane worlds

International Nuclear Information System (INIS)

Salvio, Alberto

2013-01-01

We study the Casimir energy due to bulk loops of matter fields in codimension-two brane worlds and discuss how effective field theory methods allow us to use this result to renormalize the bulk and brane operators. In the calculation we explicitly sum over the Kaluza-Klein (KK) states with a new convenient method, which is based on a combined use of zeta function and dimensional regularization. Among the general class of models we consider we include a supersymmetric example, 6D gauged chiral supergravity. Although much of our discussion is more general, we treat in some detail a class of compactifications, where the extra dimensions parametrize a rugby ball shaped space with size stabilized by a bulk magnetic flux. The rugby ball geometry requires two branes, which can host the Standard Model fields and carry both tension and magnetic flux (of the bulk gauge field), the leading terms in a derivative expansion. The brane properties have an impact on the KK spectrum and therefore on the Casimir energy as well as on the renormalization of the brane operators. A very interesting feature is that when the two branes carry exactly the same amount of flux, one half of the bulk supersymmetries survives after the compactification, even if the brane tensions are large. We also discuss the implications of these calculations for the natural value of the cosmological constant when the bulk has two large extra dimensions and the bulk supersymmetry is partially preserved (or completely broken).

A real-space stochastic density matrix approach for density functional electronic structure.

Science.gov (United States)

Beck, Thomas L

2015-12-21

The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.

Renormalization in Large Momentum Effective Theory of Parton Physics.

Science.gov (United States)

Ji, Xiangdong; Zhang, Jian-Hui; Zhao, Yong

2018-03-16

In the large-momentum effective field theory approach to parton physics, the matrix elements of nonlocal operators of quark and gluon fields, linked by straight Wilson lines in a spatial direction, are calculated in lattice quantum chromodynamics as a function of hadron momentum. Using the heavy-quark effective theory formalism, we show a multiplicative renormalization of these operators at all orders in perturbation theory, both in dimensional and lattice regularizations. The result provides a theoretical basis for extracting parton properties through properly renormalized observables in Monte Carlo simulations.

Density matrix renormalization group for a highly degenerate quantum system: Sliding environment block approach

Science.gov (United States)

Schmitteckert, Peter

2018-04-01

We present an infinite lattice density matrix renormalization group sweeping procedure which can be used as a replacement for the standard infinite lattice blocking schemes. Although the scheme is generally applicable to any system, its main advantages are the correct representation of commensurability issues and the treatment of degenerate systems. As an example we apply the method to a spin chain featuring a highly degenerate ground-state space where the new sweeping scheme provides an increase in performance as well as accuracy by many orders of magnitude compared to a recently published work.

Flying through code/space: the real virtuality of air travel

OpenAIRE

Martin Dodge; Rob Kitchin

2004-01-01

Commercial air travel is a key global industry facilitating the complex daily movements of planes, people, goods, and services across the world. In this paper we analyse contemporary air travel through the conceptualisation of a culture of real virtuality.We contend that air travel now consists of passage through 'code/space'. Such code/space includes travel websites, check-in, security check- points, flight decks, air-traffic control, immigration, and customs checkpoints, which t...

Some aspects of quantum field theory in non-Minkowskian space-times

International Nuclear Information System (INIS)

Toms, D.J.

1980-01-01

Several aspects of quantum field theory in space-times which are different from Minkowski space-time, either because of the presence of a non-zero curvature or as a consequence of the topology of the manifold, are discussed. The Casimir effect is a quantum field theory in a space-time which has a different topology. A short review of some of its popular derivations is presented with comments. Renormalization of interacting scalar field theories in a flat space-time with a non-Minkowskian topology is considered. The presence of a non-trivial topology can lead to additional non-local divergent terms in the Schwinger-Dyson equations for a general scalar field theory; however, the theory may be renormalized with the same choice of counterterms as in Minkowski space-time. Propagators can develop poles corresponding to the generation of a topological mass. Zeta-function regularization is shown to fit naturally into the functional approach to the effective potential. This formalism is used to calculate the effective potential for some scalar field theories in non-Minkowskian space-times. Topological mass generation is discussed, and it is shown how radiative corrections can lead to spontaneous symmetry breaking. One- and two-loop contributions to the vacuum energy density are obtained for both massless and massive fields. In the massive case the role of renormalization in removing non-local divergences is discussed

Probing renormalization group flows using entanglement entropy

International Nuclear Information System (INIS)

Liu, Hong; Mezei, Márk

2014-01-01

In this paper we continue the study of renormalized entanglement entropy introduced in http://dx.doi.org/10.1007/JHEP04(2013)162. In particular, we investigate its behavior near an IR fixed point using holographic duality. We develop techniques which, for any static holographic geometry, enable us to extract the large radius expansion of the entanglement entropy for a spherical region. We show that for both a sphere and a strip, the approach of the renormalized entanglement entropy to the IR fixed point value contains a contribution that depends on the whole RG trajectory. Such a contribution is dominant, when the leading irrelevant operator is sufficiently irrelevant. For a spherical region such terms can be anticipated from a geometric expansion, while for a strip whether these terms have geometric origins remains to be seen

Renormalization group flow of the Higgs potential.

Science.gov (United States)

Gies, Holger; Sondenheimer, René

2018-03-06

We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows one to describe the effective potential as a function of both scalar field amplitude and renormalization group scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps in clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability.This article is part of the Theo Murphy meeting issue 'Higgs cosmology'. © 2018 The Author(s).

Temperature dependent quasiparticle renormalization in nickel metal

Energy Technology Data Exchange (ETDEWEB)

Ovsyannikov, Ruslan; Sanchez-Barriga, Jaime; Fink, Joerg; Duerr, Hermann A. [Helmholtz Zentrum Berlin (Germany). BESSY II

2009-07-01

One of the fundamental consequences of electron correlation effects is that the bare particles in solids become 'dressed', i.e. they acquire an increased effective mass and a lifetime. We studied the spin dependent quasiparticle band structure of Ni(111) with high resolution angle resolved photoemission spectroscopy. At low temperatures (50 K) a renormalization of quasiparticle energy and lifetime indicative of electron-phonon coupling is observed in agreement with literature. With increasing temperature we observe a decreasing quasiparticle lifetime at the Fermi level for all probed minority spin bands as expected from electron phonon coupling. Surprisingly the majority spin states behave differently. We actually observe a slightly increased lifetime at room temperature. The corresponding increase in Fermi velocity points to a temperature dependent reduction of the majority spin quasiparticle renormalization.

Two-loop renormalization of quantum gravity simplified

Science.gov (United States)

Bern, Zvi; Chi, Huan-Hang; Dixon, Lance; Edison, Alex

2017-02-01

The coefficient of the dimensionally regularized two-loop R3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when nondynamical three-forms are added to the theory, or when a pseudoscalar is replaced by the antisymmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences for renormalized scattering processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple. We explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.

B-physics from non-perturbatively renormalized HQET in two-flavour lattice QCD

Energy Technology Data Exchange (ETDEWEB)

Bernardoni, Fabio; Simma, Hubert [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Blossier, Benoit; Gerardin, Antoine [Paris-11 Univ., 91 - Orsay (France). Lab. de Physique Theorique; CNRS, Orsay (France); Bulava, John [CERN, Geneva (Switzerland). Physics Department; Della Morte, Michele; Hippel, Georg M. von [Mainz Univ. (Germany). Inst. fuer Kernphysik; Fritzsch, Patrick [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Garron, Nicolas [Trinity College, Dublin (Ireland). School of Mathematics; Heitger, Jochen [Muenster Univ. (Germany). Inst. fuer Theoretische Physik 1; Collaboration: ALPHA Collaboration

2012-10-15

We report on the ALPHA Collaboration's lattice B-physics programme based on N{sub f}=2 O(a) improved Wilson fermions and HQET, including all NLO effects in the inverse heavy quark mass, as well as non-perturbative renormalization and matching, to fix the parameters of the effective theory. Our simulations in large physical volume cover 3 lattice spacings a {approx} (0.08-0.05) fm and pion masses down to 190 MeV to control continuum and chiral extrapolations. We present the status of results for the b-quark mass and the B{sub (s)}-meson decay constants, f{sub B} and f{sub B{sub s}}.

Comparative interpretations of renormalization inversion technique for reconstructing unknown emissions from measured atmospheric concentrations

Science.gov (United States)

Singh, Sarvesh Kumar; Kumar, Pramod; Rani, Raj; Turbelin, Grégory

2017-04-01

The study highlights a theoretical comparison and various interpretations of a recent inversion technique, called renormalization, developed for the reconstruction of unknown tracer emissions from their measured concentrations. The comparative interpretations are presented in relation to the other inversion techniques based on principle of regularization, Bayesian, minimum norm, maximum entropy on mean, and model resolution optimization. It is shown that the renormalization technique can be interpreted in a similar manner to other techniques, with a practical choice of a priori information and error statistics, while eliminating the need of additional constraints. The study shows that the proposed weight matrix and weighted Gram matrix offer a suitable deterministic choice to the background error and measurement covariance matrices, respectively, in the absence of statistical knowledge about background and measurement errors. The technique is advantageous since it (i) utilizes weights representing a priori information apparent to the monitoring network, (ii) avoids dependence on background source estimates, (iii) improves on alternative choices for the error statistics, (iv) overcomes the colocalization problem in a natural manner, and (v) provides an optimally resolved source reconstruction. A comparative illustration of source retrieval is made by using the real measurements from a continuous point release conducted in Fusion Field Trials, Dugway Proving Ground, Utah.

Renormalized powers of quantum white noise

International Nuclear Information System (INIS)

Accardi, L.; Boukas, A.

2009-01-01

Giving meaning to the powers of the creation and annihilation densities (quantum white noise) is an old and important problem in quantum field theory. In this paper we present an account of some new ideas that have recently emerged in the attempt to solve this problem. We emphasize the connection between the Lie algebra of the renormalized higher powers of quantum white noise (RHPWN), which can be interpreted as a suitably deformed (due to renormalization) current algebra over the 1-mode full oscillator algebra, and the current algebra over the centerless Virasoro (or Witt)-Zamolodchikov-ω ∞ Lie algebras of conformal field theory. Through a suitable definition of the action on the vacuum vector we describe how to obtain a Fock representation of all these algebras. We prove that the restriction of the vacuum to the abelian subalgebra generated by the field operators gives an infinitely divisible process whose marginal distribution is the beta (or continuous binomial). (authors)

Beam-helicity associated electroproduction of real photons ep {yields} e{gamma}{pi}N in the {Delta}-resonance region

Energy Technology Data Exchange (ETDEWEB)

Airapetian, A. [Giessen Univ. (Germany). 2. Physikalisches Inst.; Michigan Univ., Ann Arbor, MI (United States). Randall Laboratory of Physics; Akopov, N. [Yerevan Physics Institute (Argentina); Aschenauer, E.C. [DESY Zeuthen (Germany)] [and others; Collaboration: HERMES Collaboration

2013-10-15

The beam-helicity asymmetry in associated electroproduction of real photons, ep {yields} e{gamma}{pi}N, in the {Delta}(1232)-resonance region is measured using the longitudinally polarized HERA positron beam and an unpolarized hydrogen target. Azimuthal Fourier amplitudes of this asymmetry are extracted separately for two channels, ep {yields} e{gamma}{pi}{sup 0}p and ep {yields} e{gamma}{pi}{sup +}n, from a data set collected with a recoil detector. All asymmetry amplitudes are found to be consistent with zero.

Research on Control Method Based on Real-Time Operational Reliability Evaluation for Space Manipulator

Directory of Open Access Journals (Sweden)

Yifan Wang

2014-05-01

Full Text Available A control method based on real-time operational reliability evaluation for space manipulator is presented for improving the success rate of a manipulator during the execution of a task. In this paper, a method for quantitative analysis of operational reliability is given when manipulator is executing a specified task; then a control model which could control the quantitative operational reliability is built. First, the control process is described by using a state space equation. Second, process parameters are estimated in real time using Bayesian method. Third, the expression of the system's real-time operational reliability is deduced based on the state space equation and process parameters which are estimated using Bayesian method. Finally, a control variable regulation strategy which considers the cost of control is given based on the Theory of Statistical Process Control. It is shown via simulations that this method effectively improves the operational reliability of space manipulator control system.

Numerical renormalization group studies of the partially brogen SU(3) Kondo model

International Nuclear Information System (INIS)

Fuh Chuo, Evaristus

2013-04-01

The two-channel Kondo (2CK) effect with its exotic ground state properties has remained difficult to realize in physical systems. At low energies, a quantum impurity with orbital degree of freedom, like a proton bound in an interstitial lattice space, comprises a 3-level system with a unique ground state and (at least) doubly degenerate rotational excitations with excitation energy Δ 0 . When immersed in a metal, electronic angular momentum scattering induces transitions between any two of these levels (couplings J), while the electron spin is conserved. We show by extensive numerical renormalization group (NRG) calculations that without fi ne-tuning of parameters this system exhibits a 2CK fixed point, due to Kondo correlations in the excited-state doublet whose degeneracy is stabilized by the host lattice parity, while the channel symmetry (electron spin) is guaranteed by time reversal symmetry. We find a pronounced plateau in the entropy at S(T K 0 )=k B ln 2 between the high-T value, S(T>>Δ 0 )=k B ln 3, and the 2CK ground state value, S(0)=k B ln √(2). This indicates a downward renormalization of the doublet below the non-interacting ground state, thus realizing the 2CK fixed point, in agreement with earlier conjectures. We mapped out the phase diagram of the model in the J-Δ 0 plane. The Kondo temperature T K shows non-monotonic J-dependence, characteristic for 2CK systems. Beside the two-channel Kondo effect of the model, we also study the single-channel version, which is realized by applying a strong magnetic fi eld to the conduction band electrons so that their degeneracy is lifted and consequently having only one kind of electrons scattering off the impurity. This single-channel case is easier to analyze since the Hilbert space is not as large as that of the 2CK. We equally find a downward renormalization of the excited state energy by the Kondo correlations in the SU(2) doublet. In a wide range of parameter values this stabilizes the single

Can renormalization group flow end in a Big Mess?

International Nuclear Information System (INIS)

Morozov, Alexei; Niemi, Antti J.

2003-01-01

The field theoretical renormalization group equations have many common features with the equations of dynamical systems. In particular, the manner how Callan-Symanzik equation ensures the independence of a theory from its subtraction point is reminiscent of self-similarity in autonomous flows towards attractors. Motivated by such analogies we propose that besides isolated fixed points, the couplings in a renormalizable field theory may also flow towards more general, even fractal attractors. This could lead to Big Mess scenarios in applications to multiphase systems, from spin-glasses and neural networks to fundamental string (M?) theory. We consider various general aspects of such chaotic flows. We argue that they pose no obvious contradictions with the known properties of effective actions, the existence of dissipative Lyapunov functions, and even the strong version of the c-theorem. We also explain the difficulties encountered when constructing effective actions with chaotic renormalization group flows and observe that they have many common virtues with realistic field theory effective actions. We conclude that if chaotic renormalization group flows are to be excluded, conceptually novel no-go theorems must be developed

Thermal effects in quantized fields in the example of the Gross-Neveu model

International Nuclear Information System (INIS)

Englert, B.G.

1981-01-01

The Gross-Nerau model is applied to discuss thermal effects in quantized fields in an exemplary way. For this the effective potential for arbitrary temperature is calculated in one-loop approximation, i.e. in lowest order of the 1/N-expansion. It is proved to be convenient to regulate the model dimensionally and to renormalize by subtraction in the momentum dimensionally and to renormalize by subtraction in the momentum space. From the effective potential the temperature dependence of the fermion mass generated by dynamical symmetry breaking is obtained. This result can be reproduced by a manifestly selfconsistent calculation which leads in a natural way to the tadpole equation. The calculation of temperature dependent elastic scattering cross sections rounds the one-loop calculations of and gives hints, in which direction the experimental search for thermal effects could possible be successful. Furthermore the tadpole equation is evaluation in two-loop approximation. Thereby it is shown that only a self-consistent renormalization yields evaluable results while in a perturbative renormalization the dimensional transmutation cannot be performed. Indeed no real improvements of the one-loop results are obtained which is due to the fact that not all contributions of the next 1/N-order are taken into account. (orig.) [de

Renormalization of Magnetic Excitations in Praseodymium

DEFF Research Database (Denmark)

Lindgård, Per-Anker

1975-01-01

The magnetic exciton renormalization and soft-mode behaviour as the temperature approaches zero of the singlet-doublet magnet (dhcp)pr are accounted for by a selfconsistent rpa theory with no adjustable parameters. The crystal-field splitting between the ground state and the doublet is d=3.74 mev...

The large-Nc renormalization group

International Nuclear Information System (INIS)

Dorey, N.

1995-01-01

In this talk, we review how effective theories of mesons and baryons become exactly soluble in the large-N c , limit. We start with a generic hadron Lagrangian constrained only by certain well-known large-N c , selection rules. The bare vertices of the theory are dressed by an infinite class of UV divergent Feynman diagrams at leading order in 1/N c . We show how all these leading-order dia, grams can be summed exactly using semiclassical techniques. The saddle-point field configuration is reminiscent of the chiral bag: hedgehog pions outside a sphere of radius Λ -1 (Λ being the UV cutoff of the effective theory) matched onto nucleon degrees of freedom for r ≤ Λ -1 . The effect of this pion cloud is to renormalize the bare nucleon mass, nucleon-Δ hyperfine mass splitting, and Yukawa couplings of the theory. The corresponding large-N c , renormalization group equations for these parameters are presented, and solved explicitly in a series of simple models. We explain under what conditions the Skyrmion emerges as a UV fixed-point of the RG flow as Λ → ∞

Strong-Weak CP Hierarchy from Non-Renormalization Theorems

Energy Technology Data Exchange (ETDEWEB)

Hiller, Gudrun

2002-01-28

We point out that the hierarchy between the measured values of the CKM phase and the strong CP phase has a natural origin in supersymmetry with spontaneous CP violation and low energy supersymmetry breaking. The underlying reason is simple and elegant: in supersymmetry the strong CP phase is protected by an exact non-renormalization theorem while the CKM phase is not. We present explicit examples of models which exploit this fact and discuss corrections to the non-renormalization theorem in the presence of supersymmetry breaking. This framework for solving the strong CP problem has generic predictions for the superpartner spectrum, for CP and flavor violation, and predicts a preferred range of values for electric dipole moments.

Renormalization-group study of the four-body problem

International Nuclear Information System (INIS)

Schmidt, Richard; Moroz, Sergej

2010-01-01

We perform a renormalization-group analysis of the nonrelativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the region where the scattering length is infinite and all energies are close to the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of others that the four-body problem is universal, now also from a renormalization-group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound-state spectrum and comment on the influence of effective range corrections.

Running with rugby balls: bulk renormalization of codimension-2 branes

Science.gov (United States)

Williams, M.; Burgess, C. P.; van Nierop, L.; Salvio, A.

2013-01-01

We compute how one-loop bulk effects renormalize both bulk and brane effective interactions for geometries sourced by codimension-two branes. We do so by explicitly integrating out spin-zero, -half and -one particles in 6-dimensional Einstein-Maxwell-Scalar theories compactified to 4 dimensions on a flux-stabilized 2D geometry. (Our methods apply equally well for D dimensions compactified to D - 2 dimensions, although our explicit formulae do not capture all divergences when D > 6.) The renormalization of bulk interactions are independent of the boundary conditions assumed at the brane locations, and reproduce standard heat-kernel calculations. Boundary conditions at any particular brane do affect how bulk loops renormalize this brane's effective action, but not the renormalization of other distant branes. Although we explicitly compute our loops using a rugby ball geometry, because we follow only UV effects our results apply more generally to any geometry containing codimension-two sources with conical singularities. Our results have a variety of uses, including calculating the UV sensitivity of one-loop vacuum energy seen by observers localized on the brane. We show how these one-loop effects combine in a surprising way with bulk back-reaction to give the complete low-energy effective cosmological constant, and comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.

Structural impact on the eigenenergy renormalization for carbon and silicon allotropes and boron nitride polymorphs

Science.gov (United States)

Tutchton, Roxanne; Marchbanks, Christopher; Wu, Zhigang

2018-05-01

The phonon-induced renormalization of electronic band structures is investigated through first-principles calculations based on the density functional perturbation theory for nine materials with various crystal symmetries. Our results demonstrate that the magnitude of the zero-point renormalization (ZPR) of the electronic band structure is dependent on both crystal structure and material composition. We have performed analysis of the electron-phonon-coupling-induced renormalization for two silicon (Si) allotropes, three carbon (C) allotropes, and four boron nitride (BN) polymorphs. Phonon dispersions of each material were computed, and our analysis indicates that materials with optical phonons at higher maximum frequencies, such as graphite and hexagonal BN, have larger absolute ZPRs, with the exception of graphene, which has a considerably smaller ZPR despite having phonon frequencies in the same range as graphite. Depending on the structure and material, renormalizations can be comparable to the GW many-body corrections to Kohn-Sham eigenenergies and, thus, need to be considered in electronic structure calculations. The temperature dependence of the renormalizations is also considered, and in all materials, the eigenenergy renormalization at the band gap and around the Fermi level increases with increasing temperature.

On the hierarchical lattices approximation of Bravais lattices: Specific heat and correlation length

International Nuclear Information System (INIS)

Tsallis, C.

1984-01-01

Certain types of real-space renormalization groups (which essentially approximate Bravais lattices through hierarchical ones) do not preserve standard thermodynamic convexity properties. It is pointed out that this serious defect is not intrinsic to any real-space renormalization. It can be avoided if form-invariance (under uniform translation of the energy scale) of the equation connecting the Bravais lattice (which is intended to study) to the hierarchical one (which approximates it) is demanded. In addition to that expressions for the critical exponentes ν and α corresponding to hierarchical lattices are analysed; these are consistent with Melrose recent analysis of the fractal intrinsic dimensionality. (Author) [pt

Quantum renormalization group approach to geometric phases in spin chains

International Nuclear Information System (INIS)

Jafari, R.

2013-01-01

A relation between geometric phases and criticality of spin chains are studied using the quantum renormalization-group approach. I have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. The renormalization scheme demonstrates how the first derivative of the geometric phase with respect to the field strength diverges at the critical point and maximum value of the first derivative, and its position, scales with the exponent of the system size

Sorting Real Numbers in $O(n\\sqrt{\\log n})$ Time and Linear Space

OpenAIRE

Han, Yijie

2017-01-01

We present an $O(n\\sqrt{\\log n})$ time and linear space algorithm for sorting real numbers. This breaks the long time illusion that real numbers have to be sorted by comparison sorting and take $\\Omega (n\\log n)$ time to be sorted.

QCD: Renormalization for the practitioner

International Nuclear Information System (INIS)

Pascual, P.; Tarrach, R.

1984-01-01

These notes correspond to a GIFT (Grupo Interuniversitario de Fisica Teorica) course which was given by us in autumn 1983 at the University of Barcelona. Their main subject is renormalization in perturbative QCD and only the last chapter goes beyond perturbation theory. They are essentially self contained and their aim is to teach the student the techniques of perturbative QCD and the QCD sum rules. (orig./HSI)

New renormalization group approach to multiscale problems

Energy Technology Data Exchange (ETDEWEB)

Einhorn, M B; Jones, D R.T.

1984-02-27

A new renormalization group is presented which exploits invariance with respect to more than one scale. The method is illustrated by a simple model, and future applications to fields such as critical phenomena and supersymmetry are speculated upon.

Renormalization Group Invariance of the Pole Mass in the Multi-Higgs System

Science.gov (United States)

Kim, Chungku

2018-06-01

We have investigated the renormalization group running of the pole mass in the multi-Higgs theory in two different types of gauge fixing conditions. The pole mass, when expressed in terms of the Lagrangian parameters, turns out to be invariant under the renormalization group with the beta and gamma functions of the symmetric phase.

The pairing theory of polarons in real- and impulse spaces

International Nuclear Information System (INIS)

Dzhumanov, S.; Abboudy, S.; Baratov, A.A.

1995-07-01

A consistent pairing theory of carriers in real- and impulse spaces is developed. The pairing of different free (F), delocalized (D) and self-trapped (S) carriers in real-space, leading to the formation of various bipolaronic states are considered within the continuum model and adiabatic approximation taking into account the combined effect of the short- and long-range components of electron-lattice interaction with and without electron correlation. The formation possibility of D- and S-bipolarons as a function of ε ∞ /ε 0 are shown. The pairing scenarios of carriers in k-space leading to the formation of different bipolarons (including also Cooper pairs dynamic bipolarons) are considered within the generalized BCS-like model taking into account the combined phonon and polaron-bag mediated processes. It is shown that the pure BCS pairing picture is the particular case of the general BCS-like one. The possible relevance of the obtained results to high-T c superconductors is discussed in details in the framework of a novel two-stage Fermi-Bose-liquid scenarios of superconductivity which is caused by single particle and pair condensation of an attracting bipolarons. (author). 51 refs, 6 figs

Real-space imaging of fractional quantum Hall liquids

Science.gov (United States)

Hayakawa, Junichiro; Muraki, Koji; Yusa, Go

2013-01-01

Electrons in semiconductors usually behave like a gas--as independent particles. However, when confined to two dimensions under a perpendicular magnetic field at low temperatures, they condense into an incompressible quantum liquid. This phenomenon, known as the fractional quantum Hall (FQH) effect, is a quantum-mechanical manifestation of the macroscopic behaviour of correlated electrons that arises when the Landau-level filling factor is a rational fraction. However, the diverse microscopic interactions responsible for its emergence have been hidden by its universality and macroscopic nature. Here, we report real-space imaging of FQH liquids, achieved with polarization-sensitive scanning optical microscopy using trions (charged excitons) as a local probe for electron spin polarization. When the FQH ground state is spin-polarized, the triplet/singlet intensity map exhibits a spatial pattern that mirrors the intrinsic disorder potential, which is interpreted as a mapping of compressible and incompressible electron liquids. In contrast, when FQH ground states with different spin polarization coexist, domain structures with spontaneous quasi-long-range order emerge, which can be reproduced remarkably well from the disorder patterns using a two-dimensional random-field Ising model. Our results constitute the first reported real-space observation of quantum liquids in a class of broken symmetry state known as the quantum Hall ferromagnet.

Renormalization group and the superconducting susceptibility of a Fermi liquid

International Nuclear Information System (INIS)

Parameswaran, S. A.; Sondhi, S. L.; Shankar, R.

2010-01-01

A free Fermi gas has, famously, a superconducting susceptibility that diverges logarithmically at zero temperature. In this paper we ask whether this is still true for a Fermi liquid and find that the answer is that it does not. From the perspective of the renormalization group for interacting fermions, the question arises because a repulsive interaction in the Cooper channel is a marginally irrelevant operator at the Fermi liquid fixed point and thus is also expected to infect various physical quantities with logarithms. Somewhat surprisingly, at least from the renormalization group viewpoint, the result for the superconducting susceptibility is that two logarithms are not better than one. In the course of this investigation we derive a Callan-Symanzik equation for the repulsive Fermi liquid using the momentum-shell renormalization group, and use it to compute the long-wavelength behavior of the superconducting correlation function in the emergent low-energy theory. We expect this technique to be of broader interest.

Re-Normalization Method of Doppler Lidar Signal for Error Reduction

Energy Technology Data Exchange (ETDEWEB)

Park, Nakgyu; Baik, Sunghoon; Park, Seungkyu; Kim, Donglyul [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Kim, Dukhyeon [Hanbat National Univ., Daejeon (Korea, Republic of)

2014-05-15

In this paper, we presented a re-normalization method for the fluctuations of Doppler signals from the various noises mainly due to the frequency locking error for a Doppler lidar system. For the Doppler lidar system, we used an injection-seeded pulsed Nd:YAG laser as the transmitter and an iodine filter as the Doppler frequency discriminator. For the Doppler frequency shift measurement, the transmission ratio using the injection-seeded laser is locked to stabilize the frequency. If the frequency locking system is not perfect, the Doppler signal has some error due to the frequency locking error. The re-normalization process of the Doppler signals was performed to reduce this error using an additional laser beam to an Iodine cell. We confirmed that the renormalized Doppler signal shows the stable experimental data much more than that of the averaged Doppler signal using our calibration method, the reduced standard deviation was 4.838 Χ 10{sup -3}.

Renormalized perturbation theory: Vlasov-Poisson System, weak turbulence limit and gyrokinetics

International Nuclear Information System (INIS)

Zhang, Y.Z.; Mahajan, S.M.

1987-10-01

The Self-consistency of the renormalized perturbation theory is demonstrated by applying it to the Vlasov-Poisson System and showing that the theory has the correct weak turbulence limit. Energy conservation is proved to arbitrary high order for the electrostatic drift waves. The theory is applied to derive renormalized equations for a low-β gyrokinetic system. Comparison of our theory with other current theories is presented. 22 refs

Quark-mixing renormalization effects on the W-boson partial decay widths

International Nuclear Information System (INIS)

Almasy, A.A.; Kniehl, B.A.; Sirlin, A.

2008-10-01

We briefly review existing proposals for the renormalization of the Cabibbo- Kobayashi-Maskawa matrix and study their numerical effects on the W-boson partial decay widths. The differences between the decay widths predicted by the various renormalization schemes are generally negligible, while their deviations from the MS results are very small, except for W + → u anti b and W + →c anti b, where they reach approximately 4%. (orig.)

A brief comparison between grid based real space algorithms and spectrum algorithms for electronic structure calculations

International Nuclear Information System (INIS)

Wang, Lin-Wang

2006-01-01

Quantum mechanical ab initio calculation constitutes the biggest portion of the computer time in material science and chemical science simulations. As a computer center like NERSC, to better serve these communities, it will be very useful to have a prediction for the future trends of ab initio calculations in these areas. Such prediction can help us to decide what future computer architecture can be most useful for these communities, and what should be emphasized on in future supercomputer procurement. As the size of the computer and the size of the simulated physical systems increase, there is a renewed interest in using the real space grid method in electronic structure calculations. This is fueled by two factors. First, it is generally assumed that the real space grid method is more suitable for parallel computation for its limited communication requirement, compared with spectrum method where a global FFT is required. Second, as the size N of the calculated system increases together with the computer power, O(N) scaling approaches become more favorable than the traditional direct O(N 3 ) scaling methods. These O(N) methods are usually based on localized orbital in real space, which can be described more naturally by the real space basis. In this report, the author compares the real space methods versus the traditional plane wave (PW) spectrum methods, for their technical pros and cons, and the possible of future trends. For the real space method, the author focuses on the regular grid finite different (FD) method and the finite element (FE) method. These are the methods used mostly in material science simulation. As for chemical science, the predominant methods are still Gaussian basis method, and sometime the atomic orbital basis method. These two basis sets are localized in real space, and there is no indication that their roles in quantum chemical simulation will change anytime soon. The author focuses on the density functional theory (DFT), which is the

All-order renormalization of propagator matrix for Majorana fermions with inter-generation mixing

International Nuclear Information System (INIS)

Kniehl, Bernd A.

2014-04-01

We consider a mixed system of unstable Majorana fermions in a general parity-nonconserving theory and renormalize its propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. In contrast to the case of unstable Dirac fermions, the WFR matrices of the in and out states are uniquely fixed, while they again bifurcate in the sense that they are no longer related by pseudo-Hermitian conjugation. We present closed analytic expressions for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions, as well as their expansions through two loops. In the case of stable Majorana fermions, the well-known one-loop results are recovered.

Mass yields of secondary organic aerosols from the oxidation of α-pinene and real plant emissions

Directory of Open Access Journals (Sweden)

J. N. Smith

2011-02-01

Full Text Available Biogenic volatile organic compounds (VOCs are a significant source of global secondary organic aerosol (SOA; however, quantifying their aerosol forming potential remains a challenge. This study presents smog chamber laboratory work, focusing on SOA formation via oxidation of the emissions of two dominant tree species from boreal forest area, Scots pine (Pinus sylvestris L. and Norway spruce (Picea abies, by hydroxyl radical (OH and ozone (O3. Oxidation of α-pinene was also studied as a reference system. Tetramethylethylene (TME and 2-butanol were added to control OH and O3 levels, thereby allowing SOA formation events to be categorized as resulting from either OH-dominated or O3-initiated chemistry. SOA mass yields from α-pinene are consistent with previous studies while the yields from the real plant emissions are generally lower than that from α-pinene, varying from 1.9% at an aerosol mass loading of 0.69 μg m−3 to 17.7% at 26.0 μg m−3. Mass yields from oxidation of real plant emissions are subject to the interactive effects of the molecular structures of plant emissions and their reaction chemistry with OH and O3, which lead to variations in condensable product volatility. SOA formation can be reproduced with a two-product gas-phase partitioning absorption model in spite of differences in the source of oxidant species and product volatility in the real plant emission experiments. Condensable products from OH-dominated chemistry showed a higher volatility than those from O3-initiated systems during aerosol growth stage. Particulate phase products became less volatile via aging process which continued after input gas-phase oxidants had been completely consumed.

Influence of Poultry Manure Rates and Spacing on Growth, Yield, Nutrient Concentration , Uptake and Proximate Composition of Onion (Allium cepa L.

Directory of Open Access Journals (Sweden)

Ehizogie Joyce FALODUN

2018-03-01

Full Text Available Plant spacing determines to a greater extent crop performance in terms of growth and yield. The production of crop with organic fertilizer also plays a vital role in organic agriculture. Field studies were conducted to evaluate the effects of spacing and poultry manure on the growth, yield and quality of onion. Three spacing regimes were carried out consisting of (15cm x 15 cm , 20 cm x 20 cm and 25 cm x 25 cm and four levels of poultry manure at ( 0, 5, 10 and 15 t /ha . The effects of spacing and poultry manure were evaluated for 2 years based on plant growth, yield, nutrient concentration, uptake and proximate composition of onion plant. Leaf thickness, bulb and shoot fresh weights were significantly increased by the wider spacing of 20 cm x 20 cm and 25 cm x 25 cm, compared with the narrower spacing of 15cm x 15 cm in both seasons. However, highest total dry yield (1.82 and 1.58 t /ha, shoot yield (2.31 and 1.32 t /ha and total fresh yield (13.69 and 12.55 t/ha were obtained with the spacing of 20cm x 20 cm in both years. Similarly, application of poultry manure increased leaf thickness, bulb and shoot fresh weights and yields compared with the control. Generally, using 10 t/ha poultry manure has a superior effect on proximate composition and most of growth parameters and yield components achieved the highest nutrient concentrations and uptake on most of the macro and micronutrients in leaves and bulbs as compared with the control in both years.

Buckling of thermally fluctuating spherical shells: Parameter renormalization and thermally activated barrier crossing

Science.gov (United States)

Baumgarten, Lorenz; Kierfeld, Jan

2018-05-01

We study the influence of thermal fluctuations on the buckling behavior of thin elastic capsules with spherical rest shape. Above a critical uniform pressure, an elastic capsule becomes mechanically unstable and spontaneously buckles into a shape with an axisymmetric dimple. Thermal fluctuations affect the buckling instability by two mechanisms. On the one hand, thermal fluctuations can renormalize the capsule's elastic properties and its pressure because of anharmonic couplings between normal displacement modes of different wavelengths. This effectively lowers its critical buckling pressure [Košmrlj and Nelson, Phys. Rev. X 7, 011002 (2017), 10.1103/PhysRevX.7.011002]. On the other hand, buckled shapes are energetically favorable already at pressures below the classical buckling pressure. At these pressures, however, buckling requires to overcome an energy barrier, which only vanishes at the critical buckling pressure. In the presence of thermal fluctuations, the capsule can spontaneously overcome an energy barrier of the order of the thermal energy by thermal activation already at pressures below the critical buckling pressure. We revisit parameter renormalization by thermal fluctuations and formulate a buckling criterion based on scale-dependent renormalized parameters to obtain a temperature-dependent critical buckling pressure. Then we quantify the pressure-dependent energy barrier for buckling below the critical buckling pressure using numerical energy minimization and analytical arguments. This allows us to obtain the temperature-dependent critical pressure for buckling by thermal activation over this energy barrier. Remarkably, both parameter renormalization and thermal activation lead to the same parameter dependence of the critical buckling pressure on temperature, capsule radius and thickness, and Young's modulus. Finally, we study the combined effect of parameter renormalization and thermal activation by using renormalized parameters for the energy

Functional renormalization group study of fluctuation effects in fermionic superfluids

Energy Technology Data Exchange (ETDEWEB)

Eberlein, Andreas

2013-03-22

This thesis is concerned with ground state properties of two-dimensional fermionic superfluids. In such systems, fluctuation effects are particularly strong and lead for example to a renormalization of the order parameter and to infrared singularities. In the first part of this thesis, the fermionic two-particle vertex is analysed and the fermionic renormalization group is used to derive flow equations for a decomposition of the vertex in charge, magnetic and pairing channels. In the second part, the channel-decomposition scheme is applied to various model systems. In the superfluid state, the fermionic two-particle vertex develops rich and singular dependences on momentum and frequency. After simplifying its structure by exploiting symmetries, a parametrization of the vertex in terms of boson-exchange interactions in the particle-hole and particle-particle channels is formulated, which provides an efficient description of the singular momentum and frequency dependences. Based on this decomposition of the vertex, flow equations for the effective interactions are derived on one- and two-loop level, extending existing channel-decomposition schemes to (i) the description of symmetry breaking in the Cooper channel and (ii) the inclusion of those two-loop renormalization contributions to the vertex that are neglected in the Katanin scheme. In the second part, the superfluid ground state of various model systems is studied using the channel-decomposition scheme for the vertex and the flow equations. A reduced model with interactions in the pairing and forward scattering channels is solved exactly, yielding insights into the singularity structure of the vertex. For the attractive Hubbard model at weak coupling, the momentum and frequency dependence of the two-particle vertex and the frequency dependence of the self-energy are determined on one- and two-loop level. Results for the suppression of the superfluid gap by fluctuations are in good agreement with the literature

PyR@TE. Renormalization group equations for general gauge theories

Science.gov (United States)

Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.

2014-03-01

Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer

A Real-Time Apple Grading System Using Multicolor Space

Directory of Open Access Journals (Sweden)

Hayrettin Toylan

2014-01-01

Full Text Available This study was focused on the multicolor space which provides a better specification of the color and size of the apple in an image. In the study, a real-time machine vision system classifying apples into four categories with respect to color and size was designed. In the analysis, different color spaces were used. As a result, 97% identification success for the red fields of the apple was obtained depending on the values of the parameter “a” of CIE L*a*b*color space. Similarly, 94% identification success for the yellow fields was obtained depending on the values of the parameter y of CIE XYZ color space. With the designed system, three kinds of apples (Golden, Starking, and Jonagold were investigated by classifying them into four groups with respect to two parameters, color and size. Finally, 99% success rate was achieved in the analyses conducted for 595 apples.

On the renormalization of operator products: the scalar gluonic case

International Nuclear Information System (INIS)

Zoller, Max F.

2016-01-01

In this paper we study the renormalization of the product of two operators O 1 =−(1/4)G μν G μν in QCD. An insertion of two such operators O 1 (x)O 1 (0) into a Greens function produces divergent contact terms for x→0. In the course of the computation of the operator product expansion (OPE) of the correlator of two such operators i∫ d 4 x e iqx T{ O 1 (x)O 1 (0)} to three-loop order http://dx.doi.org/10.1007/JHEP12(2012)119; http://dx.doi.org/10.1007/JHEP10(2014)169 we discovered that divergent contact terms remain not only in the leading Wilson coefficient C 0 , which is just the VEV of the correlator, but also in the Wilson coefficient C 1 in front of O 1 . As this correlator plays an important role for example in QCD sum rules a full understanding of its renormalization is desireable. This work explains how the divergences encountered in higher orders of an OPE of this correlator should be absorbed in counterterms and derives an additive renormalization constant for C 1 from first principles and to all orders in perturnbation theory. The method to derive the renormalization of this operator product is an extension of the ideas of V. Spiridonov, Anomalous dimension of g μν 2 and β-function, Preprint IYAI-P-0378 (1984). and can be generalized to other cases.

RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN SOLVER

International Nuclear Information System (INIS)

Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.

2010-01-01

We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.

Finite size scaling and phenomenological renormalization

International Nuclear Information System (INIS)

Derrida, B.; Seze, L. de; Vannimenus, J.

1981-05-01

The basic equations of the phenomenological renormalization method are recalled. A simple derivation using finite-size scaling is presented. The convergence of the method is studied analytically for the Ising model. Using this method we give predictions for the 2d bond percolation. Finally we discuss how the method can be applied to random systems

Metric and topology on a non-standard real line and non-standard space-time

International Nuclear Information System (INIS)

Tahir Shah, K.

1981-04-01

We study metric and topological properties of extended real line R* and compare it with the non-standard model of real line *R. We show that some properties, like triangular inequality, cannot be carried over R* from R. This confirms F. Wattenberg's result for measure theory on Dedekind completion of *R. Based on conclusions from these results we propose a non-standard model of space-time. This space-time is without undefined objects like singularities. (author)

Renormalization of the fragmentation equation: Exact self-similar solutions and turbulent cascades

Science.gov (United States)

Saveliev, V. L.; Gorokhovski, M. A.

2012-12-01

Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E1539-375510.1103/PhysRevE.65.051205 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.

Renormalization group approaches to low-dimensional systems. Scrutinization of the spin-functional RG for the 2D XXZ model and real-time RG study of a generic 2-level quantum dot in the Coulomb blockade regime in nonequilibrium

Energy Technology Data Exchange (ETDEWEB)

Goettel, Stefan

2015-05-22

In this thesis, we study two recently developed methods to tackle low-dimensional correlated quantum systems. In the first part, we benchmark the extension of the functional renormalization group to spin-systems. We apply it to the two-dimensional XXZ model and reproduce the prediction for the phase transition from planar to axial ordering at the isotropic point. The interpretation of the critical scale (where the flow of the susceptibility diverges) as the critical temperature of the system can be questioned, since it yields only good results in the Ising limit. Especially near the isotropic point, this interpretation becomes unsatisfactory as the Mermin-Wagner theorem is violated. We discuss several problems of the method and conclude that it should only be used to explore phase diagrams. In the second part, we extend previous works to two-level quantum dots in the Coulomb blockade regime with special hopping matrices in nonequilibrium, e.g., the Kondo model, to the generic form, including ferromagnetic leads, spin-orbit interactions etc. The dot and the transport observables are determined completely by the hybridization matrix, leading to one of our major results that all these models can be mapped to the Anderson impurity model with ferromagnetic leads. We investigate this model with a well-controlled real-time renormalization group approach and justify the results of a poor man's scaling analysis. By using a singular value decomposition of the tunneling matrix we can rotate the model to the anisotropic Kondo model in the high-energy regime to solve the flow equations analytically. With this, we calculate the stationary dot magnetization and the current. The minimum of the magnetization is found to be an ellipsoid as function of the magnetic field, where the stretching factor determines the distance to the scaling limit. Afterwards, we consider the special case of two external reservoirs and the system being in the scaling limit and discuss the golden

Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms

Science.gov (United States)

Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.

2016-07-01

Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

Using NASA Data in the Classroom: Promoting STEM Learning in Formal Education using Real Space Science Data

Science.gov (United States)

Lawton, B.; Hemenway, M. K.; Mendez, B.; Odenwald, S.

2013-04-01

Among NASA's major education goals is the training of students in the Science, Technology, Engineering, and Math (STEM) disciplines. The use of real data, from some of the most sophisticated observatories in the world, provides formal educators the opportunity to teach their students real-world applications of the STEM subjects. Combining real space science data with lessons aimed at meeting state and national education standards provides a memorable educational experience that students can build upon throughout their academic careers. Many of our colleagues have adopted the use of real data in their education and public outreach (EPO) programs. There are challenges in creating resources using real data for classroom use that include, but are not limited to, accessibility to computers/Internet and proper instruction. Understanding and sharing these difficulties and best practices with the larger EPO community is critical to the development of future resources. In this session, we highlight three examples of how NASA data is being utilized in the classroom: the Galaxies and Cosmos Explorer Tool (GCET) that utilizes real Hubble Space Telescope data; the computer image-analysis resources utilized by the NASA WISE infrared mission; and the space science derived math applications from SpaceMath@NASA featuring the Chandra and Kepler space telescopes. Challenges and successes are highlighted for these projects. We also facilitate small-group discussions that focus on additional benefits and challenges of using real data in the formal education environment. The report-outs from those discussions are given here.

Renormalization-group decimation technique for spectra, wave-functions and density of states

International Nuclear Information System (INIS)

Wiecko, C.; Roman, E.

1983-09-01

The Renormalization Group decimation technique is very useful for problems described by 1-d nearest neighbour tight-binding model with or without translational invariance. We show how spectra, wave-functions and density of states can be calculated with little numerical work from the renormalized coefficients upon iteration. The results of this new procedure are verified using the model of Soukoulis and Economou. (author)

Renormalization Group scale-setting in astrophysical systems

Science.gov (United States)

Domazet, Silvije; Štefančić, Hrvoje

2011-09-01

A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the Renormalization Group running scale are discussed. The procedure is elaborated for several highly symmetric systems with matter in the form of an ideal fluid and for two models of running of the Newton coupling and the cosmological term. For a static spherically symmetric system with the matter obeying the polytropic equation of state the running scale-setting is performed analytically. The obtained result for the running scale matches the Ansatz introduced in a recent paper by Rodrigues, Letelier and Shapiro which provides an excellent explanation of rotation curves for a number of galaxies. A systematic explanation of the galaxy rotation curves using the scale-setting procedure introduced in this Letter is identified as an important future goal.

Renormalization Group scale-setting in astrophysical systems

International Nuclear Information System (INIS)

Domazet, Silvije; Stefancic, Hrvoje

2011-01-01

A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the Renormalization Group running scale are discussed. The procedure is elaborated for several highly symmetric systems with matter in the form of an ideal fluid and for two models of running of the Newton coupling and the cosmological term. For a static spherically symmetric system with the matter obeying the polytropic equation of state the running scale-setting is performed analytically. The obtained result for the running scale matches the Ansatz introduced in a recent paper by Rodrigues, Letelier and Shapiro which provides an excellent explanation of rotation curves for a number of galaxies. A systematic explanation of the galaxy rotation curves using the scale-setting procedure introduced in this Letter is identified as an important future goal.

Perturbative renormalization of composite operators via flow equations. Pt. 1

Energy Technology Data Exchange (ETDEWEB)

Keller, G. (Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (Germany). Werner-Heisenberg-Inst. fuer Physik); Kopper, C. (Goettingen Univ. (Germany). Inst. fuer Theoretische Physik)

1992-09-01

We apply the general framework of the continuous renormalization group, whose significance for perturbative quantum field theories was recognized by Polchinski, to investigate by new and mathematically simple methods the perturbative renormalization of composite operators. In this paper we demonstrate the perturbative renormalizability of the Green functions of the Euclidean massive {Phi}{sub 4}{sup 4} theory with one insertion of a (possibly oversubtracted, in the BPHZ language) composite operator. Moreover we show that our method admits an easy proof of the Zimmermann identities and of the Lowenstein rule. (orig.).

Perturbative renormalization of composite operators via flow equations. Pt. 1

International Nuclear Information System (INIS)

Keller, G.; Kopper, C.

1992-01-01

We apply the general framework of the continuous renormalization group, whose significance for perturbative quantum field theories was recognized by Polchinski, to investigate by new and mathematically simple methods the perturbative renormalization of composite operators. In this paper we demonstrate the perturbative renormalizability of the Green functions of the Euclidean massive Φ 4 4 theory with one insertion of a (possibly oversubtracted, in the BPHZ language) composite operator. Moreover we show that our method admits an easy proof of the Zimmermann identities and of the Lowenstein rule. (orig.)

Justification of the zeta-function renormalization in rigid string model

International Nuclear Information System (INIS)

Nesterenko, V.V.; Pirozhenko, I.G.

1997-01-01

A consistent procedure for regularization of divergences and for the subsequent renormalization of the string tension is proposed in the framework of the one-loop calculation of the interquark potential generated by the Polyakov-Kleinert string. In this way, a justification of the formal treatment of divergences by analytic continuation of the Riemann and Epstein-Hurwitz zeta-functions is given. A spectral representation for the renormalized string energy at zero temperature is derived, which enables one to find the Casimir energy in this string model at nonzero temperature very easy

Hopf-algebraic renormalization of QED in the linear covariant gauge

Energy Technology Data Exchange (ETDEWEB)

Kißler, Henry, E-mail: kissler@physik.hu-berlin.de

2016-09-15

In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.

Quantum field theory in curved space-time

International Nuclear Information System (INIS)

Najmi, A.-H.

1982-09-01

The problem of constructing states for quantum field theories in nonstationary background space-times is set out. A formalism in which the problem of constructing states can be attacked more easily than at present is presented. The ansatz of energy-minimization as a means of constructing states is formulated in this formalism and its general solution for the free scalar field is found. It has been known, in specific cases, that such states suffer from the problem of unitary inequivalence (the pathology). An example in Minowski space-time is presented in which global operators, such as the particle-number operator, do not exist but all physical observables, such as the renormalized energy density are finite. This model has two Fock-sectors as its space of physical states. A simple extension of this model, i.e. enlarging the Fock-space of states is found not to remedy the pathology: in a Robertson-Walker space-time the quantum field acquires an infinite amount of renormalized energy density to the future of the hypersurface on which the energy density is minimized. Finally, the solution of the ansatz of energy minimization for the free, massive Hermitian fermion field is presented. (author)

Vacuum polarization and renormalized charge in ν-dimensions

International Nuclear Information System (INIS)

Marinho Junior, R.M.; Lucinda, J.

1984-01-01

The expression for the vacuum polarization is obtained for any momentum transfer in ν dimensions. Using the Wilson loop for QED, the renormalized electric charge in ν dimensions is calculated. (Author) [pt

Renormalization group equations and the Lifshitz point in noncommutative Landau-Ginsburg theory

International Nuclear Information System (INIS)

Chen, G.-H.; Wu, Y.-S.

2002-01-01

A one-loop renormalization group (RG) analysis is performed for noncommutative Landau-Ginsburg theory in an arbitrary dimension. We adopt a modern version of the Wilsonian RG approach, in which a shell integration in momentum space bypasses the potential IR singularities due to UV-IR mixing. The momentum-dependent trigonometric factors in interaction vertices, characteristic of noncommutative geometry, are marginal under RG transformations, and their marginality is preserved at one loop. A negative Θ-dependent anomalous dimension is discovered as a novel effect of the UV-IR mixing. We also found a noncommutative Wilson-Fisher (NCWF) fixed point in less than four dimensions. At large noncommutativity, a momentum space instability is induced by quantum fluctuations, and a consequential first-order phase transition is identified together with a Lifshitz point in the phase diagram. In the vicinity of the Lifshitz point, we introduce two critical exponents ν m and β k , whose values are determined to be 1/4 and 1/2, respectively, at mean-field level

Some Double Sequence Spaces of Fuzzy Real Numbers of Paranormed Type

Directory of Open Access Journals (Sweden)

Bipul Sarma

2013-01-01

Full Text Available We study different properties of convergent, null, and bounded double sequence spaces of fuzzy real numbers like completeness, solidness, sequence algebra, symmetricity, convergence-free, and so forth. We prove some inclusion results too.

Real Time Space Weather Support for Chandra X-Ray Observatory Operations

Science.gov (United States)

O'Dell, Stephen L.; Minow, Joseph I.; Miller, J. Scott; Wolk, Scott J.; Aldcroft, Thomas L.; Spitzbart, Bradley D.; Swartz. Douglas A.

2012-01-01

NASA launched the Chandra X-ray Observatory in July 1999. Soon after first light in August 1999, however, degradation in the energy resolution and charge transfer efficiency of the Advanced CCD Imaging Spectrometer (ACIS) x-ray detectors was observed. The source of the degradation was quickly identified as radiation damage in the charge-transfer channel of the front-illuminated CCDs, by weakly penetrating ( soft , 100 500 keV) protons as Chandra passed through the Earth s radiation belts and ring currents. As soft protons were not considered a risk to spacecraft health before launch, the only on-board radiation monitoring system is the Electron, Proton, and Helium Instrument (EPHIN) which was included on Chandra with the primary purpose of monitoring energetic solar particle events. Further damage to the ACIS detector has been successfully mitigated through a combination of careful mission planning, autonomous on-board radiation protection, and manual intervention based upon real-time monitoring of the soft-proton environment. The AE-8 and AP-8 trapped radiation models and Chandra Radiation Models are used to schedule science operations in regions of low proton flux. EPHIN has been used as the primary autonomous in-situ radiation trigger; but, it is not sensitive to the soft protons that damage the front-illuminated CCDs. Monitoring of near-real-time space weather data sources provides critical information on the proton environment outside the Earth s magnetosphere due to solar proton events and other phenomena. The operations team uses data from the Geostationary Operational Environmental Satellites (GOES) to provide near-real-time monitoring of the proton environment; however, these data do not give a representative measure of the soft-proton (real-time data provided by NOAA s Space Weather Prediction Center. This presentation describes the radiation mitigation strategies to minimize the proton damage in the ACIS CCD detectors and the importance of real-time data

Renormalization Group Functional Equations

CERN Document Server

Curtright, Thomas L

2011-01-01

Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories. With minimal assumptions, the methods produce continuous flows from step-scaling {\\sigma} functions, and lead to exact functional relations for the local flow {\\beta} functions, whose solutions may have novel, exotic features, including multiple branches. As a result, fixed points of {\\sigma} are sometimes not true fixed points under continuous changes in scale, and zeroes of {\\beta} do not necessarily signal fixed points of the flow, but instead may only indicate turning points of the trajectories.

Functional-derivative study of the Hubbard model. III. Fully renormalized Green's function

International Nuclear Information System (INIS)

Arai, T.; Cohen, M.H.

1980-01-01

The functional-derivative method of calculating the Green's function developed earlier for the Hubbard model is generalized and used to obtain a fully renormalized solution. Higher-order functional derivatives operating on the basic Green's functions, G and GAMMA, are all evaluated explicitly, thus making the solution applicable to the narrow-band region as well as the wide-band region. Correction terms Phi generated from functional derivatives of equal-time Green's functions of the type delta/sup n/ /deltaepsilon/sup n/, etc., with n > or = 2. It is found that the Phi's are, in fact, renormalization factors involved in the self-energy Σ and that the structure of the Phi's resembles that of Σ and contains the same renormalization factors Phi. The renormalization factors Phi are shown to satisfy a set of equations and can be evaluated self-consistently. In the presence of the Phi's, all difficulties found in the previous results (papers I and II) are removed, and the energy spectrum ω can now be evaluated for all occupations n. The Schwinger relation is the only basic relation used in generating this fully self-consistent Green's function, and the Baym-Kadanoff continuity condition is automatically satisfied

Generalized Callan-Symanzik equations and the Renormalization Group

International Nuclear Information System (INIS)

MacDowell, S.W.

1975-01-01

A set of generalized Callan-Symanzik equations derived by Symanzik, relating Green's functions with arbitrary number of mass insertions, is shown be equivalent to the new Renormalization Group equation proposed by S. Weinberg

Exact renormalization group as a scheme for calculations

International Nuclear Information System (INIS)

Mack, G.

1985-10-01

In this lecture I report on recent work to use exact renormalization group methods to construct a scheme for calculations in quantum field theory and classical statistical mechanics on the continuum. (orig./HSI)

Frontiers and critical expoents in percolation and Ising and Potts ferromagnets: renormalization group and others techniques

International Nuclear Information System (INIS)

Magalhaes, A.C.N. de.

1982-01-01

By using real space renormalization group methods, bond percolation on d-dimensional hypercubic (d = 2, 3, 4), first - and second - neighbour isotropic square, anisotropic square and 'inhomogeneous' 4-8 lattices is studied. Through some extrapolation methods, critical points and/or frontiers are obtained (as well as the critical exponent ν sub(p) in the isotropic cases) for these lattices that, or agree well with other available results, or are new as far as it is know (first - and second - neighbour isotropic square and 'inhomogeneous' 4-8 lattices). A conjecture concerning approximate (eventually exact) critical points and, in certain situations, critical frontiers of q-state Potts ferromagnets on d-dimensional lattices (d > 1) is formulated. This conjecture is verified within good accuracy for all the lattices whose critical points are known, and it allows the prediction of a great number of new results, some of them it is believed to be exact. Within a real space renomalization group framework, accurate approximations for the critical frontiers associated with the quenched bond-diluted first-neighbour spin-1/2 Ising ferromagnet on triangular and honeycomb lattices are calculated. The best numerical proposals lead, in both pure bond percolation (p = p sub(c)) and pure Ising (p = 1) limits, to the exact critical points and (dt 0 /dp) sub(p = p sub(c)) (where t 0 identical to tanh J/K sub(B) T), and to a 0.15% (0.96%) error in (dt 0 /dp) sub(p = 1) for the triangular (honeycomb) lattice; for p sub(c) 0 (for fixed p) of 0.27% (0.14%) is estimated for the triangular (honeycomb) lattice. It is exhibited, for many star-triangle graph pairs with any number of terminals and different sizes, that the exact q = 1, 2, 3, 4 critical points of Potts ferromagnets can aZZ of them, be obtained from any one of such graph pairs. (Author) [pt

Development of a global toroidal gyrokinetic Vlasov code with new real space field solver

International Nuclear Information System (INIS)

Obrejan, Kevin; Imadera, Kenji; Li, Ji-Quan; Kishimoto, Yasuaki

2015-01-01

This work introduces a new full-f toroidal gyrokinetic (GK) Vlasov simulation code that uses a real space field solver. This solver enables us to compute the gyro-averaging operators in real space to allow proper treatment of finite Larmor radius (FLR) effects without requiring any particular hypothesis and in any magnetic field configuration (X-point, D-shaped etc). The code was well verified through benchmark tests such as toroidal Ion Temperature Gradient (ITG) instability and collisionless damping of zonal flow. (author)

Renormalization group and critical phenomena

International Nuclear Information System (INIS)

Ji Qing

2004-01-01

The basic clue and the main steps of renormalization group method used for the description of critical phenomena is introduced. It is pointed out that this method really reflects the most important physical features of critical phenomena, i.e. self-similarity, and set up a practical solving method from it. This way of setting up a theory according to the features of the physical system is really a good lesson for today's physicists. (author)

A non-renormalization theorem for conformal anomalies

International Nuclear Information System (INIS)

Petkou, Anastasios; Skenderis, Kostas

1999-01-01

We provide a non-renormalization theorem for the coefficients of the conformal anomaly associated with operators with vanishing anomalous dimensions. Such operators include conserved currents and chiral operators in superconformal field theories. We illustrate the theorem by computing the conformal anomaly of 2-point functions both by a computation in the conformal field theory and via the AdS/CFT correspondence. Our results imply that 2- and 3-point functions of chiral primary operators in N=4 SU(N) SYM will not renormalize provided that a 'generalized Adler-Bardeen theorem' holds. We further show that recent arguments connecting the non-renormalizability of the above-mentioned correlation functions to a bonus U(1) Y symmetry are incomplete due to possible U(1) Y violating contact terms. The tree level contribution to the contact terms may be set to zero by considering appropriately normalized operators. Non-renormalizability of the above-mentioned correlation functions, however, will follow only if these contact terms saturate by free fields

Numerical renormalization group studies of the partially brogen SU(3) Kondo model

Energy Technology Data Exchange (ETDEWEB)

Fuh Chuo, Evaristus

2013-04-15

The two-channel Kondo (2CK) effect with its exotic ground state properties has remained difficult to realize in physical systems. At low energies, a quantum impurity with orbital degree of freedom, like a proton bound in an interstitial lattice space, comprises a 3-level system with a unique ground state and (at least) doubly degenerate rotational excitations with excitation energy {Delta}{sub 0}. When immersed in a metal, electronic angular momentum scattering induces transitions between any two of these levels (couplings J), while the electron spin is conserved. We show by extensive numerical renormalization group (NRG) calculations that without fi ne-tuning of parameters this system exhibits a 2CK fixed point, due to Kondo correlations in the excited-state doublet whose degeneracy is stabilized by the host lattice parity, while the channel symmetry (electron spin) is guaranteed by time reversal symmetry. We find a pronounced plateau in the entropy at S(T{sub K}>{Delta}{sub 0})=k{sub B} ln 3, and the 2CK ground state value, S(0)=k{sub B} ln {radical}(2). This indicates a downward renormalization of the doublet below the non-interacting ground state, thus realizing the 2CK fixed point, in agreement with earlier conjectures. We mapped out the phase diagram of the model in the J-{Delta}{sub 0} plane. The Kondo temperature T{sub K} shows non-monotonic J-dependence, characteristic for 2CK systems. Beside the two-channel Kondo effect of the model, we also study the single-channel version, which is realized by applying a strong magnetic fi eld to the conduction band electrons so that their degeneracy is lifted and consequently having only one kind of electrons scattering off the impurity. This single-channel case is easier to analyze since the Hilbert space is not as large as that of the 2CK. We equally find a downward renormalization of the excited state energy by the Kondo correlations in the SU(2) doublet

Genetic algorithms for adaptive real-time control in space systems

Science.gov (United States)

Vanderzijp, J.; Choudry, A.

1988-01-01

Genetic Algorithms that are used for learning as one way to control the combinational explosion associated with the generation of new rules are discussed. The Genetic Algorithm approach tends to work best when it can be applied to a domain independent knowledge representation. Applications to real time control in space systems are discussed.

Functional renormalization group approach to the two dimensional Bose gas

Energy Technology Data Exchange (ETDEWEB)

Sinner, A; Kopietz, P [Institut fuer Theoretische Physik, Universitaet Frankfurt, Max-von-Laue Strasse 1, 60438 Frankfurt (Germany); Hasselmann, N [International Center for Condensed Matter Physics, Universidade de BrasIlia, Caixa Postal 04667, 70910-900 BrasIlia, DF (Brazil)], E-mail: hasselma@itp.uni-frankfurt.de, E-mail: sinner@itp.uni-frankfurt.de

2009-02-01

We investigate the small frequency and momentum structure of the weakly interacting Bose gas in two dimensions using a functional renormalization group approach. The flow equations are derived within a derivative approximation of the effective action up to second order in spatial and temporal variables and investigated numerically. The truncation we employ is based on the perturbative structure of the theory and is well described as a renormalization group enhanced perturbation theory. It allows to calculate corrections to the Bogoliubov spectrum and to investigate the damping of quasiparticles. Our approach allows to circumvent the divergences which plague the usual perturbative approach.

Closed-form irreducible differential formulations of the Wilson renormalization group

International Nuclear Information System (INIS)

Vvedensky, D.D.; Chang, T.S.; Nicoll, J.F.

1983-01-01

We present a detailed derivation of the one-particle--irreducible (1PI) differential renormalization-group generators originally developed by Nicoll and Chang and by Chang, Nicoll, and Young. We illustrate the machinery of the irreducible formulation by calculating to order epsilon 2 the characteristic time exponent z for the time-dependent Ginsburg-Landau model in the cases of conserved and nonconserved order parameter. We then calculate both z and eta to order epsilon 2 by applying to the 1PI generator an extension of the operator expansion technique developed by Wegner for the Wilson smooth-cutoff renormalization-group generator

Renormalization group approach to a p-wave superconducting model

International Nuclear Information System (INIS)

Continentino, Mucio A.; Deus, Fernanda; Caldas, Heron

2014-01-01

We present in this work an exact renormalization group (RG) treatment of a one-dimensional p-wave superconductor. The model proposed by Kitaev consists of a chain of spinless fermions with a p-wave gap. It is a paradigmatic model of great actual interest since it presents a weak pairing superconducting phase that has Majorana fermions at the ends of the chain. Those are predicted to be useful for quantum computation. The RG allows to obtain the phase diagram of the model and to study the quantum phase transition from the weak to the strong pairing phase. It yields the attractors of these phases and the critical exponents of the weak to strong pairing transition. We show that the weak pairing phase of the model is governed by a chaotic attractor being non-trivial from both its topological and RG properties. In the strong pairing phase the RG flow is towards a conventional strong coupling fixed point. Finally, we propose an alternative way for obtaining p-wave superconductivity in a one-dimensional system without spin–orbit interaction.

A rigorous treatment of the lattice renormalization problem of f$_{B}$

CERN Document Server

Boucaud, P; Micheli, J; Pène, O; Rossi, G C; Boucaud, Ph.

1993-01-01

The $B$-meson decay constant can be measured on the lattice using a $1/m_b$ expansion. To relate the physical quantity to Monte Carlo data one has to know the renormalization coefficient, $Z$, between the lattice operators and their continuum counterparts. We come back to this computation to resolve discrepancies found in previous calculations. We define and discuss in detail the renormalization procedure that allows the (perturbative) computation of $Z$. Comparing the one-loop calculations in the effective Lagrangian approach with the direct two-loop calculation of the two-point $B$-meson correlator in the limit of large $b$-quark mass, we prove that the two schemes give consistent results to order $\\alpha_s$. We show that there is, however, a renormalization prescription ambiguity that can have sizeable numerical consequences. This ambiguity can be resolved in the framework of an $O(a)$ improved calculation, and we describe the correct prescription in that case. Finally we give the numerical values of $Z$ t...

Renormalization schemes for the Two-Higgs-Doublet Model and applications to h → WW/ZZ → 4 fermions

DEFF Research Database (Denmark)

Altenkamp, Lukas; Dittmaier, Stefan; Rzehak, Heidi

2017-01-01

We perform the renormalization of different types of Two-Higgs-Doublet Models for the calculation of observables at next-to-leading order. In detail, we suggest four different renormalization schemes based on on-shell renormalization conditions as far as possible and on M S ¯ prescriptions for th...

Renormalization-group theory of spinodal decomposition

International Nuclear Information System (INIS)

Mazenko, G.F.; Valls, O.T.; Zhang, F.C.

1985-01-01

Renormalization-group (RG) methods developed previously for the study of the growth of order in unstable systems are extended to treat the spinodal decomposition of the two-dimensional spin-exchange kinetic Ising model. The conservation of the order parameter and fixed-length sum rule are properly preserved in the theory. Various correlation functions in both coordinate and momentum space are calculated as functions of time. The scaling function for the structure factor is extracted. We compare our results with direct Monte Carlo (MC) simulations and find them in good agreement. The time rescaling parameter entering the RG analysis is temperature dependent, as was determined in previous work through a RG analysis of MC simulations. The results exhibit a long-time logarithmic growth law for the typical domain size, both analytically and numerically. In the time region where MC simulations have previously been performed, the logarithmic growth law can be fitted to a power law with an effective exponent. This exponent is found to be in excellent agreement with the result of MC simulations. The logarithmic growth law agrees with a physical model of interfacial motion which involves an interplay between the local curvature and an activated jump across the interface

Breaking generalized covariance, classical renormalization, and boundary conditions from superpotentials

International Nuclear Information System (INIS)

Livshits, Gideon I.

2014-01-01

Superpotentials offer a direct means of calculating conserved charges associated with the asymptotic symmetries of space-time. Yet superpotentials have been plagued with inconsistencies, resulting in nonphysical or incongruent values for the mass, angular momentum, and energy loss due to radiation. The approach of Regge and Teitelboim, aimed at a clear Hamiltonian formulation with a boundary, and its extension to the Lagrangian formulation by Julia and Silva have resolved these issues, and have resulted in a consistent, well-defined and unique variational equation for the superpotential, thereby placing it on a firm footing. A hallmark solution of this equation is the KBL superpotential obtained from the first-order Lovelock Lagrangian. Nevertheless, here we show that these formulations are still insufficient for Lovelock Lagrangians of higher orders. We present a paradox, whereby the choice of fields affects the superpotential for equivalent on-shell dynamics. We offer two solutions to this paradox: either the original Lagrangian must be effectively renormalized, or that boundary conditions must be imposed, so that space-time be asymptotically maximally symmetric. Non-metricity is central to this paradox, and we show how quadratic non-metricity in the bulk of space-time contributes to the conserved charges on the boundary, where it vanishes identically. This is a realization of the gravitational Higgs mechanism, proposed by Percacci, where the non-metricity is the analogue of the Goldstone boson

Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: theory and application to the study of chromium dimer.

Science.gov (United States)

Kurashige, Yuki; Yanai, Takeshi

2011-09-07

We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian. © 2011 American Institute of Physics

Nucleation of the lamellar phase from the disordered phase of the renormalized Landau-Brazovskii model

Science.gov (United States)

Carilli, Michael F.; Delaney, Kris T.; Fredrickson, Glenn H.

2018-02-01

Using the zero-temperature string method, we investigate nucleation of a stable lamellar phase from a metastable disordered phase of the renormalized Landau-Brazovskii model at parameters explicitly connected to those of an experimentally accessible diblock copolymer melt. We find anisotropic critical nuclei in qualitative agreement with previous experimental and analytic predictions; we also find good quantitative agreement with the predictions of a single-mode analysis. We conduct a thorough search for critical nuclei containing various predicted and experimentally observed defect structures. The predictions of the renormalized model are assessed by simulating the bare Landau-Brazovskii model with fluctuations. We find that the renormalized model makes reasonable predictions for several important quantities, including the order-disorder transition (ODT). However, the critical nucleus size depends sharply on proximity to the ODT, so even small errors in the ODT predicted by the renormalized model lead to large errors in the predicted critical nucleus size. We conclude that the renormalized model is a poor tool to study nucleation in the fluctuating Landau-Brazovskii model, and recommend that future studies work with the fluctuating bare model directly, using well-chosen collective variables to investigate kinetic pathways in the disorder → lamellar transition.

Scaling laws, renormalization group flow and the continuum limit in non-compact lattice QED

International Nuclear Information System (INIS)

Goeckeler, M.; Horsley, R.; Rakow, P.; Schierholz, G.; Sommer, R.

1992-01-01

We investigate the ultra-violet behavior of non-compact lattice QED with light staggered fermions. The main question is whether QED is a non-trivial theory in the continuum limit, and if not, what is its range of validity as a low-energy theory. Perhaps the limited range of validity could offer an explanation of why the fine-structure constant is so small. Non-compact QED undergoes a second-order chiral phase transition at strong coupling, at which the continuum limit can be taken. We examine the phase diagram and the critical behavior of the theory in detail. Moreover, we address the question as to whether QED confines in the chirally broken phase. This is done by investigating the potential between static external charges. We then compute the renormalized charge and derive the Callan-Symanzik β-function in the critical region. No ultra-violet stable zero is found. Instead, we find that the evolution of charge is well described by renormalized perturbation theory, and that the renormalized charge vanishes at the critical point. The consequence is that QED can only be regarded as a cut-off theory. We evaluate the maximum value of the cut-off as a function of the renormalized charge. Next, we compute the masses of fermion-antifermion composite states. The scaling behavior of these masses is well described by an effective action with mean-field critical exponents plus logarithmic corrections. This indicates that also the matter sector of the theory is non-interacting. Finally, we investigate and compare the renormalization group flow of different quantities. Altogether, we find that QED is a valid theory only for samll renormalized charges. (orig.)

Quantum corrections in thermal states of fermions on anti-de Sitter space-time

Science.gov (United States)

Ambruş, Victor E.; Winstanley, Elizabeth

2017-12-01

We study the energy density and pressure of a relativistic thermal gas of massless fermions on four-dimensional Minkowski and anti-de Sitter space-times using relativistic kinetic theory. The corresponding quantum field theory quantities are given by components of the renormalized expectation value of the stress-energy tensor operator acting on a thermal state. On Minkowski space-time, the renormalized vacuum expectation value of the stress-energy tensor is by definition zero, while on anti-de Sitter space-time the vacuum contribution to this expectation value is in general nonzero. We compare the properties of the vacuum and thermal expectation values of the energy density and pressure for massless fermions and discuss the circumstances in which the thermal contribution dominates over the vacuum one.

Inter and intra row spacing effects on growth, seed yield and oil contents of white mustard (sinapis alba l.) under rainfed conditions

International Nuclear Information System (INIS)

Arif, M.; Shehzad, M.A.

2012-01-01

A field experiment was conducted to evaluate the effect of different plant densities on growth and yield of white mustard during Rabi 2008-09 under rain fed conditions. Three plant spacing (5, 10 and 15 cm) and three row spacing (10, 20 and 30 cm) were applied during the course of study. Results indicated that plant density has significant effects on growth, seed yield and oil contents of white mustard. Number of pods per plant (2002), number of seeds per pod (4.67), 1000 seed weight (5.02 g), oil contents (32.21 %) and fatty acids except linoleic acid significantly increased by increasing plant spacing due to less competition among plants for moisture, light and nutrients. The maximum plant height (148.9 cm) was with 10 X 20 cm spacing. Maximum seed yield (2046 kg ha/sup -1/) was recorded for row spacing 15 cm where plants were spaced 10 cm within rows. At higher plant density, the overall seed yield of white mustard increased with increasing number of pods per plant. Thus, it is concluded that white mustard should be grown at 150 cm grids for higher yield output. (author)

Effect of inter-row spacing and plant stand per hill on the yield of ...

African Journals Online (AJOL)

Yield was used to determined the best inter-row spacing and plant stand per bill ... high yieldlng cowpea Vigna unguicuJata lines at Serere Agricultural and Animal P.roduction .... constitute a rich source of adaptation to local conditions.

Neutral currents and electromagnetic renormalization of the vector part of neutrino weak interaction

International Nuclear Information System (INIS)

Folomeshkin, V.N.

1976-01-01

The nature and properties of neutral currents in neutrino processes at high energies are theoretically investigated. Electronagmetic renormalization of diagonal ((νsub(e)e(νsub(e)e) and (νsub(μ)μ)(νsub(μ)μ)) and nondiagonal ((νsub(e)μ)(νsub(e)μ)) interactions is discussed in terms of the universal fourfermion interaction model. It is shown that electromagnetic renormalization of neutrino vector interaction caused an effective appearance of vector neutral currents with photon isotopic structure. The value for the interaction constant is unambigously defined by the ratio of the total cross-section for electron-positron annihilation into muonic pairs. Interaction (renormalization) constants for neutral currents are pointed out to be always smaller than interaction constants for charge currents

Real-space local polynomial basis for solid-state electronic-structure calculations: A finite-element approach

International Nuclear Information System (INIS)

Pask, J.E.; Klein, B.M.; Fong, C.Y.; Sterne, P.A.

1999-01-01

We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the method is completely general and its convergence can be controlled systematically. Because the basis functions are strictly local in real space, the method allows for variable resolution in real space; produces sparse, structured matrices, enabling the effective use of iterative solution methods; and is well suited to parallel implementation. The method thus combines the significant advantages of both real-space-grid and basis-oriented approaches and so promises to be particularly well suited for large, accurate ab initio calculations. We develop the theory of our approach in detail, discuss advantages and disadvantages, and report initial results, including electronic band structures and details of the convergence of the method. copyright 1999 The American Physical Society

Renormalization group evolution of the universal theories EFT

International Nuclear Information System (INIS)

Wells, James D.; Zhang, Zhengkang

2016-01-01

The conventional oblique parameters analyses of precision electroweak data can be consistently cast in the modern framework of the Standard Model effective field theory (SMEFT) when restrictions are imposed on the SMEFT parameter space so that it describes universal theories. However, the usefulness of such analyses is challenged by the fact that universal theories at the scale of new physics, where they are matched onto the SMEFT, can flow to nonuniversal theories with renormalization group (RG) evolution down to the electroweak scale, where precision observables are measured. The departure from universal theories at the electroweak scale is not arbitrary, but dictated by the universal parameters at the matching scale. But to define oblique parameters, and more generally universal parameters at the electroweak scale that directly map onto observables, additional prescriptions are needed for the treatment of RG-induced nonuniversal effects. We perform a RG analysis of the SMEFT description of universal theories, and discuss the impact of RG on simplified, universal-theories-motivated approaches to fitting precision electroweak and Higgs data.

A real space calculation of absolutely unstable modes for two-plasmon decay in inhomogeneous plasma

International Nuclear Information System (INIS)

Powers, L.V.; Berger, R.L.

1986-01-01

Growth rates for absolute modes of two-plasmon decay are obtained by solving for eigenmodes of the coupled mode equations for obliquely scattered Langmuir waves in real space. This analysis establishes a connection both to previous analysis in Fourier transform space and to other parametric instabilities, the analysis of which is commonly done in real space. The essential feature of the instability which admits absolute modes in an inhomogeneous plasma is the strong spatial dependence of the coupling coefficients. Landau damping limits the perpendicular wavenumbers of the most unstable modes and raises the instability thresholds for background plasma temperatures above 1 keV. (author)

E-cigarette marketing and older smokers: road to renormalization.

Science.gov (United States)

Cataldo, Janine K; Petersen, Anne Berit; Hunter, Mary; Wang, Julie; Sheon, Nicolas

2015-05-01

To describe older smokers' perceptions of risks and use of e-cigarettes, and their responses to marketing and knowledge of, and opinions about, regulation of e-cigarettes. Eight 90-minute focus groups with 8 to 9 participants met in urban and suburban California to discuss topics related to cigarettes and alternative tobacco products. Older adults are using e-cigarettes for cessation and as a way to circumvent no-smoking policies; they have false perceptions about the effectiveness and safety of e-cigarettes. They perceive e-cigarette marketing as a way to renormalize smoking. To stem the current epidemic of nicotine addiction, the FDA must take immediate action because e-cigarette advertising promotes dual use and may contribute to the renormalization of smoking.

Renormalization (and power counting) of effective field theories for the nuclear force

International Nuclear Information System (INIS)

Timoteo, Varese S.; Szpigel, Sergio; Duraes, Francisco O.

2011-01-01

The most common scheme used to regularize the Lippman-Schwinger (LS) equation is to introduce a sharp or smooth regularizing function that suppresses the contributions from the potential matrix elements for momenta larger than a given cutoff scale, which separates high-energy/short-distance scales and low-energy/long-distance scales, thus eliminating the ultraviolet divergences in the momentum integrals. Then, one needs determine the strengths of the contact interactions, the so called low-energy constants (LEC), by fitting a set of low-energy scattering data. Once the LECs are fixed for a given cutoff, the LS equation can be solved to evaluate other observables. Such a procedure, motivated by Wilsons renormalization group, relies on the fundamental premise of EFT that physics at low-energy/long-distance scales is insensitive with respect to the details of the dynamics at high-energy/short-distance scales, i.e. the relevant high-energy/short- distance effects for describing the low-energy observables can be captured in the cutoff-dependent LECs. The NN interaction can be considered properly renormalized when the calculated observables are independent of the cutoff scale within the range of validity of the ChEFT or involves a small residual cutoff dependence due to the truncation of the chiral expansion. In the language of Wilsons renormalization group, this means that the LECs must run with the cutoff scale in such a way that the scattering amplitude becomes renormalization group invariant (RGI). Here we consider pionless EFT up to NNLO and chiral EFT up to NNLO and use a subtractive renormalization scheme to describe the NN scattering channels with. We fix the strength of the contact interactions at a reference scale, chosen to be the one the provides the best fit, and then evolve the driving terms with a non-relativistic Callan-Symanzik equation to slide the renormalization scale. By computing phase shift relative differences, we show that the method is RGI. We

Renormalization group treatment for spin waves in the randomly disordered Heisenberg chain

International Nuclear Information System (INIS)

Chaves, C.M.; Koiller, B.

1983-03-01

Local densities of states in the randomly disordered binary quantum Heisenberg chain using a generalization of a recently developed approach based on renormalization group ideas are calculated. It envolves decimating alternate apins along the chain in such a way as to obtain recursion relations to describe the renormalized set of Green's function equations of motion. The densities of states are richly structured, indicating that the method takes into account compositional fluctuations of arbitrary range. (Author) [pt

Noncommutative quantum field theory: attempts on renormalization

International Nuclear Information System (INIS)

Popp, L.

2002-05-01

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

Real-Time Mapping Spectroscopy on the Ground, in the Air, and in Space

Science.gov (United States)

Thompson, D. R.; Allwood, A.; Chien, S.; Green, R. O.; Wettergreen, D. S.

2016-12-01

Real-time data interpretation can benefit both remote in situ exploration and remote sensing. Basic analyses at the sensor can monitor instrument performance and reveal invisible science phenomena in real time. This promotes situational awareness for remote robotic explorers or campaign decision makers, enabling adaptive data collection, reduced downlink requirements, and coordinated multi-instrument observations. Fast analysis is ideal for mapping spectrometers providing unambiguous, quantitative geophysical measurements. This presentation surveys recent computational advances in real-time spectroscopic analysis for Earth science and planetary exploration. Spectral analysis at the sensor enables new operations concepts that significantly improve science yield. Applications include real-time detection of fugitive greenhouse emissions by airborne monitoring, real-time cloud screening and mineralogical mapping by orbital spectrometers, and adaptive measurement by the PIXL instrument on the Mars 2020 rover. Copyright 2016 California Institute of Technology. All Rights Reserved. We acknowledge support of the US Government, NASA, the Earth Science Division and Terrestrial Ecology program.

One-loop renormalization of Lee-Wick gauge theory

International Nuclear Information System (INIS)

Grinstein, Benjamin; O'Connell, Donal

2008-01-01

We examine the renormalization of Lee-Wick gauge theory to one-loop order. We show that only knowledge of the wave function renormalization is necessary to determine the running couplings, anomalous dimensions, and vector boson masses. In particular, the logarithmic running of the Lee-Wick vector boson mass is exactly related to the running of the coupling. In the case of an asymptotically free theory, the vector boson mass runs to infinity in the ultraviolet. Thus, the UV fixed point of the pure gauge theory is an ordinary quantum field theory. We find that the coupling runs more quickly in Lee-Wick gauge theory than in ordinary gauge theory, so the Lee-Wick standard model does not naturally unify at any scale. Finally, we present results on the beta function of more general theories containing dimension six operators which differ from previous results in the literature.

Renormalization and asymptotic freedom in quantum gravity

International Nuclear Information System (INIS)

Tomboulis, E.T.

1984-01-01

The article reviews some recent attempts to construct satisfactory theories of quantum gravity within the framework of local, continuum field theory. Quantum gravity; the renormalization group and its fixed points; fixed points and dimensional continuation in gravity; and quantum gravity at d=4-the 1/N expansion-asymptotic freedom; are all discussed. (U.K.)

Physical renormalization schemes and asymptotic safety in quantum gravity

Science.gov (United States)

Falls, Kevin

2017-12-01

The methods of the renormalization group and the ɛ -expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical renormalization schemes are exploited where the renormalization group flow equations take a form which is independent of the parameterisation of the physical degrees of freedom (i.e. the gauge fixing condition and the choice of field variables). Instead the flow equation depends on the anomalous dimensions of reference observables. In the presence of spacetime boundaries we find that the required balance between the Einstein-Hilbert action and Gibbons-Hawking-York boundary term is preserved by the beta functions. Exploiting the ɛ -expansion near two dimensions we consider Einstein gravity coupled to matter. Scheme independence is generically obscured by the loop-expansion due to breaking of two-dimensional Weyl invariance. In schemes which preserve two-dimensional Weyl invariance we avoid the loop expansion and find a unique ultraviolet (UV) fixed point. At this fixed point the anomalous dimensions are large and one must resum all loop orders to obtain the critical exponents. Performing the resummation a set of universal scaling dimensions are found. These scaling dimensions show that only a finite number of matter interactions are relevant. This is a strong indication that quantum gravity is renormalizable.

Optimal renormalization scales and commensurate scale relations

International Nuclear Information System (INIS)

Brodsky, S.J.; Lu, H.J.

1996-01-01

Commensurate scale relations relate observables to observables and thus are independent of theoretical conventions, such as the choice of intermediate renormalization scheme. The physical quantities are related at commensurate scales which satisfy a transitivity rule which ensures that predictions are independent of the choice of an intermediate renormalization scheme. QCD can thus be tested in a new and precise way by checking that the observables track both in their relative normalization and in their commensurate scale dependence. For example, the radiative corrections to the Bjorken sum rule at a given momentum transfer Q can be predicted from measurements of the e+e - annihilation cross section at a corresponding commensurate energy scale √s ∝ Q, thus generalizing Crewther's relation to non-conformal QCD. The coefficients that appear in this perturbative expansion take the form of a simple geometric series and thus have no renormalon divergent behavior. The authors also discuss scale-fixed relations between the threshold corrections to the heavy quark production cross section in e+e - annihilation and the heavy quark coupling α V which is measurable in lattice gauge theory

Real Time Space Weather Support for Chandra X-ray Observatory Operations

Science.gov (United States)

O'Dell, S. L.; Miller, S.; Minow, J. I.; Wolk, S.; Aldcroft, T. L.; Spitzbart, B. D.; Swartz, D. A.

2012-12-01

NASA launched the Chandra X-ray Observatory in July 1999. Soon after first light in August 1999, however, degradation in the energy resolution and charge transfer efficiency of the Advanced CCD Imaging Spectrometer (ACIS) x-ray detectors was observed. The source of the degradation was quickly identified as radiation damage in the charge-transfer channel of the front-illuminated CCDs, by weakly penetrating ("soft", 100-500 keV) protons as Chandra passed through the Earth's radiation belts and ring currents. As soft protons were not considered a risk to spacecraft health before launch, the only on-board radiation monitoring system is the Electron, Proton, and Helium Instrument (EPHIN) which was included on Chandra with the primary purpose of monitoring energetic solar particle events. Further damage to the ACIS detector has been successfully mitigated through a combination of careful mission planning, autonomous on-board radiation protection, and manual intervention based upon real-time monitoring of the soft-proton environment. The AE-8 and AP-8 trapped radiation models and Chandra Radiation Models are used to schedule science operations in regions of low proton flux. EPHIN has been used as the primary autonomous in-situ radiation trigger; but, it is not sensitive to the soft protons that damage the front-illuminated CCDs. Monitoring of near-real-time space weather data sources provides critical information on the proton environment outside the Earth's magnetosphere due to solar proton events and other phenomena. The operations team uses data from the Geostationary Operational Environmental Satellites (GOES) to provide near-real-time monitoring of the proton environment; however, these data do not give a representative measure of the soft-proton (real-time data provided by NOAA's Space Weather Prediction Center. This presentation will discuss radiation mitigation against proton damage, including models and real-time data sources used to protect the ACIS detector

Renormalization analysis of catalytic Wright-Fisher diffusions

Czech Academy of Sciences Publication Activity Database

Swart, Jan M.; Fleischmann, K.

2006-01-01

Roč. 2006, č. 11 (2006), s. 585-654 ISSN 1083-6489 R&D Projects: GA ČR GA201/06/1323 Institutional research plan: CEZ:AV0Z10750506 Keywords : renormalization * catalytic Wright-Fisher diffusion * embedded particle system * extinction * unbounded growth * interacting diffusions * universality Subject RIV: BA - General Mathematics Impact factor: 0.676, year: 2006

Renormalization group approach to causal bulk viscous cosmological models

International Nuclear Information System (INIS)

Belinchon, J A; Harko, T; Mak, M K

2002-01-01

The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the scaling properties of the gravitational field equations, the causal evolution equation of the bulk viscous pressure and the equations of state. The requirement of scale invariance imposes strong constraints on the temporal evolution of the bulk viscosity coefficient, temperature and relaxation time, thus leading to the possibility of obtaining the bulk viscosity coefficient-energy density dependence. For a cosmological model with bulk viscosity coefficient proportional to the Hubble parameter, we perform the analysis of the renormalization group flow around the scale-invariant fixed point, thereby obtaining the long-time behaviour of the scale factor

E-cigarette Marketing and Older Smokers: Road to Renormalization

Science.gov (United States)

Cataldo, Janine K.; Petersen, Anne Berit; Hunter, Mary; Wang, Julie; Sheon, Nicolas

2015-01-01

Objectives To describe older smokers’ perceptions of risks and use of e-cigarettes, and their responses to marketing and knowledge of, and opinions about, regulation of e-cigarettes. Methods Eight 90-minute focus groups with 8 to 9 participants met in urban and suburban California to discuss topics related to cigarettes and alternative tobacco products. Results Older adults are using e-cigarettes for cessation and as a way to circumvent no-smoking policies; they have false perceptions about the effectiveness and safety of e-cigarettes. They perceive e-cigarette marketing as a way to renormalize smoking. Conclusions To stem the current epidemic of nicotine addiction, the FDA must take immediate action because e-cigarette advertising promotes dual use and may contribute to the renormalization of smoking. PMID:25741681

Smoothness in Banach spaces. Selected problems

Czech Academy of Sciences Publication Activity Database

Fabian, Marián; Montesinos, V.; Zizler, Václav

2006-01-01

Roč. 100, č. 2 (2006), s. 101-125 ISSN 1578-7303 R&D Projects: GA ČR(CZ) GA201/04/0090; GA AV ČR(CZ) IAA100190610 Institutional research plan: CEZ:AV0Z10190503 Keywords : smooth norm * renorming * weakly compactly generated space Subject RIV: BA - General Mathematics

Renormalization group aspects of 3-dimensional Pure U(1) lattice gauge theory

International Nuclear Information System (INIS)

Gopfert, M.; Mack, G.

1983-01-01

A few surprises in a recent study of the 3-dimensional pure U(1) lattice gauge theory model, from the point of view of the renormalization group theory, are discussed. Since the gauge group U(1) of this model is abelian, the model is subject to KramersWannier duality transformation. One obtains a ferromagnet with a global symmetry group Z. The duality transformation shows that the surface tension alpha of the model equals the strong tension of the U(1) gauge model. A theorem to represent the true asymptotic behaviour of alpha is derived. A second theorem considers the correlation functions. Discrepiancies between the theorems result in a solution that ''is regarded as a catastrophe'' in renormalization group theory. A lesson is drawn: To choose a good block spin in a renormalization group procedure, know what the low lying excitations of the theory are, to avoid integrating some of them by mischief

Radiatively induced symmetry breaking and the conformally coupled magnetic monopole in AdS space

Science.gov (United States)

Edery, Ariel; Graham, Noah

2013-11-01

We implement quantum corrections for a magnetic monopole in a classically conformally invariant theory containing gravity. This yields the trace (conformal) anomaly and introduces a length scale in a natural fashion via the process of renormalization. We evaluate the one-loop effective potential and extract the vacuum expectation value (VEV) from it; spontaneous symmetry breaking is radiatively induced. The VEV is set at the renormalization scale M and we exchange the dimensionless scalar coupling constant for the dimensionful VEV via dimensional transmutation. The asymptotic (background) spacetime is anti-de Sitter (AdS) and its Ricci scalar is determined entirely by the VEV. We obtain analytical asymptotic solutions to the coupled set of equations governing gravitational, gauge and scalar fields that yield the magnetic monopole in an AdS spacetime.

RI/MOM and RI/SMOM renormalization of overlap quark bilinears on domain wall fermion configurations

Science.gov (United States)

Bi, Yujiang; Cai, Hao; Chen, Ying; Gong, Ming; Liu, Keh-Fei; Liu, Zhaofeng; Yang, Yi-Bo; χ QCD Collaboration

2018-05-01

Renormalization constants (RCs) of overlap quark bilinear operators on 2 +1 -flavor domain wall fermion configurations are calculated by using the RI/MOM and RI/SMOM schemes. The scale independent RC for the axial vector current is computed by using a Ward identity. Then the RCs for the quark field and the vector, tensor, scalar, and pseudoscalar operators are calculated in both the RI/MOM and RI/SMOM schemes. The RCs are converted to the MS ¯ scheme and we compare the numerical results from using the two intermediate schemes. The lattice size is 4 83×96 and the inverse spacing 1 /a =1.730 (4 ) GeV .

Instanton tunneling for de Sitter space with real projective spatial sections

Energy Technology Data Exchange (ETDEWEB)

Ong, Yen Chin [Center for Astronomy and Astrophysics, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China); Yeom, Dong-han, E-mail: ongyenchin@sjtu.edu.cn, E-mail: innocent.yeom@gmail.com [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China)

2017-04-01

The physics of tunneling from one spacetime to another is often understood in terms of instantons. For some instantons, it was recently shown in the literature that there are two complementary ''interpretations'' for their analytic continuations. Dubbed ''something-to-something'' and ''nothing-to-something'' interpretations, respectively, the former involves situation in which the initial and final hypersurfaces are connected by a Euclidean manifold, whereas the initial and final hypersurfaces in the latter case are not connected in such a way. We consider a de Sitter space with real projective space RP{sup 3} spatial sections, as was originally understood by de Sitter himself. This original version of de Sitter space has several advantages over the usual de Sitter space with S{sup 3} spatial sections. In particular, the interpretation of the de Sitter entropy as entanglement entropy is much more natural. We discuss the subtleties involved in the tunneling of such a de Sitter space.

Real analysis measure theory, integration, and Hilbert spaces

CERN Document Server

Stein, Elias M

2005-01-01

Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After

Amount of gauge transformations in neutral-vector field theory. [Renormalization, free Lagrangian density

Energy Technology Data Exchange (ETDEWEB)

Kubo, R; Yokoyama, K

1974-11-01

The purpose of this work is to study the structure of c-number gauge transformation in connection with renormalization problem. In the wide theory of neutral vector fields, there is the gauge structure described essentially by free Lagrangian density. The c-number gauge transformation makes the Lagrangian invariant correspondingly to the usual case of quantum electrodynamics. The c-number transformation can be used to derive relationships among all relevant renormalization constants in the case of interacting fields. In the presence of interaction, total Lagrangian density L is written as L=L/sub 0/+L/sub 1/+L/sub 2/, where L/sub 1/ is given from matter-field Lagrangian density, and L/sub 2/ denotes necessary additional counter terms. In order to conserve the gauge structure, the form of L is invariant under the gauge transformation. Since L matter is self-adjoining, L/sub 1/ remains invariant by itself under the transformation. The form of L/sub 2/ is finally given from the observation that L/sub 3/ cannot contain wave-function renormalization constants. Since L/sub 2/ is invariant under q-number gauge transformation, this transformation in unrenormalized form makes the present L form-invariant. Therefore, together with the above results, auxiliary fields produce the q-number gauge transformation for renormalized fields.

On Rationality of Moduli Spaces of Vector Bundles on Real ...

Indian Academy of Sciences (India)

Let be a real form of a Hirzebruch surface. Let M H ( r , c 1 , c 2 ) be the moduli space of vector bundles on . Under some numerical conditions on r , c 1 and c 2 , we identify those M H ( r , c 1 , c 2 ) that are rational. Author Affiliations. Indranil Biswas1 Ronnie Sebastian2. School of Mathematics, Tata Institute of ...

Virtual environment navigation with look-around mode to explore new real spaces by people who are blind.

Science.gov (United States)

Lahav, Orly; Gedalevitz, Hadas; Battersby, Steven; Brown, David; Evett, Lindsay; Merritt, Patrick

2018-05-01

This paper examines the ability of people who are blind to construct a mental map and perform orientation tasks in real space by using Nintendo Wii technologies to explore virtual environments. The participant explores new spaces through haptic and auditory feedback triggered by pointing or walking in the virtual environments and later constructs a mental map, which can be used to navigate in real space. The study included 10 participants who were congenitally or adventitiously blind, divided into experimental and control groups. The research was implemented by using virtual environments exploration and orientation tasks in real spaces, using both qualitative and quantitative methods in its methodology. The results show that the mode of exploration afforded to the experimental group is radically new in orientation and mobility training; as a result 60% of the experimental participants constructed mental maps that were based on map model, compared with only 30% of the control group participants. Using technology that enabled them to explore and to collect spatial information in a way that does not exist in real space influenced the ability of the experimental group to construct a mental map based on the map model. Implications for rehabilitation The virtual cane system for the first time enables people who are blind to explore and collect spatial information via the look-around mode in addition to the walk-around mode. People who are blind prefer to use look-around mode to explore new spaces, as opposed to the walking mode. Although the look-around mode requires users to establish a complex collecting and processing procedure for the spatial data, people who are blind using this mode are able to construct a mental map as a map model. For people who are blind (as for the sighted) construction of a mental map based on map model offers more flexibility in choosing a walking path in a real space, accounting for changes that occur in the space.

Renormalization of Extended QCD2

International Nuclear Information System (INIS)

Fukaya, Hidenori; Yamamura, Ryo

2015-01-01

Extended QCD (XQCD), proposed by Kaplan [D. B. Kaplan, arXiv:1306.5818], is an interesting reformulation of QCD with additional bosonic auxiliary fields. While its partition function is kept exactly the same as that of original QCD, XQCD naturally contains properties of low-energy hadronic models. We analyze the renormalization group flow of 2D (X)QCD, which is solvable in the limit of a large number of colors N c , to understand what kind of roles the auxiliary degrees of freedom play and how the hadronic picture emerges in the low-energy region

Renormalization of weak noises of arbitrary shape for one-dimensional critical dynamical systems Announcement of results and numerical explorations

CERN Document Server

Diaz-Espinosa, O

2006-01-01

We study the effect of noise on one--dimensional critical dynamical systems (that is, maps with a renormalization theory). We consider in detail two examples of such dynamical systems: unimodal maps of the interval at the accumulation of period--doubling and smooth homeomorphisms of the circle with a critical point and with golden mean rotation number. We show that, if we scale the space and the time, several properties of the noise (the cumulants or Wick--ordered moments) satisfy some scaling relations. A consequence of the scaling relations is that a version of the central limit theorem holds. Irrespective of the shape of the initial noise, if the bare noise is weak enough, the effective noise becomes close to Gaussian in several senses that we can make precise. We notice that the conclusions are false for maps with positive Lyapunov exponents. The method of analysis is close in spirit to the study of scaling limits in renormalization theory. We also perform several numerical experiments that confirm the ri...

The O(N) model at nonzero temperature: renormalization of the gap equations in Hartree and large-N approximations

International Nuclear Information System (INIS)

Lenaghan, J.T.; Rischke, D.H.

2000-01-01

The temperature dependence of the sigma meson and pion masses is studied in the framework of the O(N ) model. The Cornwall-Jackiw-Tomboulis formalism is applied to derive gap equations for the masses in the Hartree and large-N approximations. Renormalization of the gap equations is carried out within the cut-off and counter-term renormalization schemes. A consistent renormalization of the gap equations within the cut-off scheme is found to be possible only in the large-N approximation and for a finite value of the cut-off. On the other hand, the counter-term scheme allows for a consistent renormalization of both the large-N and Hartree approximations. In these approximations, the meson masses at a given nonzero temperature depend in general on the choice of the cut-off or renormalization scale. As an application, we also discuss the in-medium on-shell decay widths for sigma mesons and pions at rest. (author)

Symmetries for Light-Front Quantization of Yukawa Model with Renormalization

Science.gov (United States)

Żochowski, Jan; Przeszowski, Jerzy A.

2017-12-01

In this work we discuss the Yukawa model with the extra term of self-interacting scalar field in D=1+3 dimensions. We present the method of derivation the light-front commutators and anti-commutators from the Heisenberg equations induced by the kinematical generating operator of the translation P+. Mentioned Heisenberg equations are the starting point for obtaining this algebra of the (anti-) commutators. Some discrepancies between existing and proposed method of quantization are revealed. The Lorentz and the CPT symmetry, together with some features of the quantum theory were applied to obtain the two-point Wightman function for the free fermions. Moreover, these Wightman functions were computed especially without referring to the Fock expansion. The Gaussian effective potential for the Yukawa model was found in the terms of the Wightman functions. It was regularized by the space-like point-splitting method. The coupling constants within the model were redefined. The optimum mass parameters remained regularization independent. Finally, the Gaussian effective potential was renormalized.

Six-dimensional real and reciprocal space small-angle X-ray scattering tomography.

Science.gov (United States)

Schaff, Florian; Bech, Martin; Zaslansky, Paul; Jud, Christoph; Liebi, Marianne; Guizar-Sicairos, Manuel; Pfeiffer, Franz

2015-11-19

When used in combination with raster scanning, small-angle X-ray scattering (SAXS) has proven to be a valuable imaging technique of the nanoscale, for example of bone, teeth and brain matter. Although two-dimensional projection imaging has been used to characterize various materials successfully, its three-dimensional extension, SAXS computed tomography, poses substantial challenges, which have yet to be overcome. Previous work using SAXS computed tomography was unable to preserve oriented SAXS signals during reconstruction. Here we present a solution to this problem and obtain a complete SAXS computed tomography, which preserves oriented scattering information. By introducing virtual tomography axes, we take advantage of the two-dimensional SAXS information recorded on an area detector and use it to reconstruct the full three-dimensional scattering distribution in reciprocal space for each voxel of the three-dimensional object in real space. The presented method could be of interest for a combined six-dimensional real and reciprocal space characterization of mesoscopic materials with hierarchically structured features with length scales ranging from a few nanometres to a few millimetres--for example, biomaterials such as bone or teeth, or functional materials such as fuel-cell or battery components.

Real-space and real-time dynamics of CRISPR-Cas9 visualized by high-speed atomic force microscopy.

Science.gov (United States)

Shibata, Mikihiro; Nishimasu, Hiroshi; Kodera, Noriyuki; Hirano, Seiichi; Ando, Toshio; Uchihashi, Takayuki; Nureki, Osamu

2017-11-10

The CRISPR-associated endonuclease Cas9 binds to a guide RNA and cleaves double-stranded DNA with a sequence complementary to the RNA guide. The Cas9-RNA system has been harnessed for numerous applications, such as genome editing. Here we use high-speed atomic force microscopy (HS-AFM) to visualize the real-space and real-time dynamics of CRISPR-Cas9 in action. HS-AFM movies indicate that, whereas apo-Cas9 adopts unexpected flexible conformations, Cas9-RNA forms a stable bilobed structure and interrogates target sites on the DNA by three-dimensional diffusion. These movies also provide real-time visualization of the Cas9-mediated DNA cleavage process. Notably, the Cas9 HNH nuclease domain fluctuates upon DNA binding, and subsequently adopts an active conformation, where the HNH active site is docked at the cleavage site in the target DNA. Collectively, our HS-AFM data extend our understanding of the action mechanism of CRISPR-Cas9.

What have we learned from quantum field theory in curved space-time

International Nuclear Information System (INIS)

Fulling, S.A.

1984-01-01

The paper reviews the quantum field theory in curved space-time. Field quantization in gravitational backgrounds; particle creation by black holes; Hawking radiation; quantum field theory in curved space-time; covariant renormalization of the stress-energy-momentum tensor; quantum field theory and quantum gravity; are all discussed. (U.K.)

Reconstruction of real-space linear matter power spectrum from multipoles of BOSS DR12 results

Science.gov (United States)

Lee, Seokcheon

2018-02-01

Recently, the power spectrum (PS) multipoles using the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 (DR12) sample are analyzed [1]. The based model for the analysis is the so-called TNS quasi-linear model and the analysis provides the multipoles up to the hexadecapole [2]. Thus, one might be able to recover the real-space linear matter PS by using the combinations of multipoles to investigate the cosmology [3]. We provide the analytic form of the ratio of quadrupole (hexadecapole) to monopole moments of the quasi-linear PS including the Fingers-of-God (FoG) effect to recover the real-space PS in the linear regime. One expects that observed values of the ratios of multipoles should be consistent with those of the linear theory at large scales. Thus, we compare the ratios of multipoles of the linear theory, including the FoG effect with the measured values. From these, we recover the linear matter power spectra in real-space. These recovered power spectra are consistent with the linear matter power spectra.

Massive quantum field theory in two-dimensional Robertson-Walker space-time

International Nuclear Information System (INIS)

Bunch, T.S.; Christensen, S.M.; Fulling, S.A.

1978-01-01

The stress tensor of a massive scalar field, as an integral over normal modes (which are not mere plane waves), is regularized by covariant point separation. When the expectation value in a Parker-Fulling adiabatic vacuum state is expanded in the limit of small curvature-to-mass ratios, the series coincides in each order with the Schwinger-DeWitt-Christensen proper-time expansion. The renormalization ansatz suggested by these expansions (which applies to arbitrary curvature-to-mass ratios and arbitrary quantum state) can be implemented at the integrand level for practical computations. The renormalized tensor (1) passes in the massless limit, for appropriate choice of state, to the known vacuum stress of a massless field, (2) agrees with the explicit results of Bernard and Duncan for a special model, and (3) has a nonzero vacuum expectation value in the two-dimensional ''Milne universe'' (flat space in hyperbolic coordinates). Following Wald, we prove that the renormalized tensor is conserved and point out that there is no arbitrariness in the renormalization procedure. The general approach of this paper is applicable to four-dimensional models