Bold Feynman Diagrams and the Luttinger–Ward Formalism Via Gibbs Measures: Non-perturbative Analysis

AbstractWe prove a comprehensive version of the Ruelle–Perron–Frobenius Theorem with explicit estimates of the spectral radius of the Ruelle transfer operator and various other quantities related to spectral properties of this operator. The novelty here is that the Hölder constant of the function generating the operator appears only polynomially, not exponentially as in previously known estimates.

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Cwebs beyond three loops in multiparton amplitudes

Journal of High Energy Physics ◽

10.1007/jhep03(2021)188 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Neelima Agarwal ◽

Lorenzo Magnea ◽

Sourav Pal ◽

Anurag Tripathi

Keyword(s):

Gauge Theories ◽

Anomalous Dimension ◽

Wilson Line ◽

Building Blocks ◽

Feynman Diagrams ◽

Loop Order ◽

Abelian Gauge ◽

Sum Rule ◽

Combinatorial Properties ◽

Low Dimensional

Abstract Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.

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PHASE TRANSITIONS AND QUANTUM STABILIZATION IN QUANTUM ANHARMONIC CRYSTALS

Reviews in Mathematical Physics ◽

10.1142/s0129055x08003353 ◽

2008 ◽

Vol 20 (05) ◽

pp. 529-595 ◽

Cited By ~ 4

Author(s):

ALINA KARGOL ◽

YURI KONDRATIEV ◽

YURI KOZITSKY

Keyword(s):

Phase Transitions ◽

Gibbs Measures ◽

Quantum Effects ◽

Gibbs States ◽

Translation Invariance ◽

Unified Theory ◽

The Relationship ◽

Anharmonic Crystals

A unified theory of phase transitions and quantum effects in quantum anharmonic crystals is presented. In its framework, the relationship between these two phenomena is analyzed. The theory is based on the representation of the model Gibbs states in terms of path measures (Euclidean Gibbs measures). It covers the case of crystals without translation invariance, as well as the case of asymmetric anharmonic potentials. The results obtained are compared with those known in the literature.

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Uniqueness of Gibbs measures and absorption probabilities

Probability Theory and Applications ◽

10.1515/9783112314227-048 ◽

1987 ◽

pp. 359-360

Keyword(s):

Gibbs Measures ◽

Absorption Probabilities

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Stochastic computation of g − 2 in QED

Journal of High Energy Physics ◽

10.1007/jhep05(2021)119 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Ryuichiro Kitano ◽

Hiromasa Takaura ◽

Shoji Hashimoto

Keyword(s):

Perturbation Theory ◽

Numerical Computation ◽

Magnetic Moment ◽

Anomalous Magnetic Moment ◽

Stochastic Perturbation ◽

Higher Order ◽

Feynman Diagrams ◽

Perturbative Series ◽

Physical Quantities

Abstract We perform a numerical computation of the anomalous magnetic moment (g − 2) of the electron in QED by using the stochastic perturbation theory. Formulating QED on the lattice, we develop a method to calculate the coefficients of the perturbative series of g − 2 without the use of the Feynman diagrams. We demonstrate the feasibility of the method by performing a computation up to the α3 order and compare with the known results. This program provides us with a totally independent check of the results obtained by the Feynman diagrams and will be useful for the estimations of not-yet-calculated higher order values. This work provides an example of the application of the numerical stochastic perturbation theory to physical quantities, for which the external states have to be taken on-shell.

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ALMOST ADDITIVE THERMODYNAMIC FORMALISM: SOME RECENT DEVELOPMENTS

Reviews in Mathematical Physics ◽

10.1142/s0129055x10004168 ◽

2010 ◽

Vol 22 (10) ◽

pp. 1147-1179 ◽

Cited By ~ 12

Author(s):

LUIS BARREIRA

Keyword(s):

Variational Principle ◽

Existence And Uniqueness ◽

Gibbs Measures ◽

Thermodynamic Formalism ◽

Topological Pressure ◽

Present Stage ◽

The Past ◽

Recent Developments ◽

General Sequences ◽

Uniqueness Of Equilibrium

This is a survey on recent developments concerning a thermodynamic formalism for almost additive sequences of functions. While the nonadditive thermodynamic formalism applies to much more general sequences, at the present stage of the theory there are no general results concerning, for example, a variational principle for the topological pressure or the existence of equilibrium or Gibbs measures (at least without further restrictive assumptions). On the other hand, in the case of almost additive sequences, it is possible to establish a variational principle and to discuss the existence and uniqueness of equilibrium and Gibbs measures, among several other results. After presenting in a self-contained manner the foundations of the theory, the survey includes the description of three applications of the almost additive thermodynamic formalism: a multifractal analysis of Lyapunov exponents for a class of nonconformal repellers; a conditional variational principle for limits of almost additive sequences; and the study of dimension spectra that consider simultaneously limits into the future and into the past.

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