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20 pages, 602 KiB

Open AccessArticle

Quantum-Field Multiloop Calculations in Critical Dynamics

by Ella Ivanova, Georgii Kalagov, Marina Komarova and Mikhail Nalimov

Symmetry 2023, 15(5), 1026; https://doi.org/10.3390/sym15051026 - 06 May 2023

Viewed by 1064

The quantum-field renormalization group method is one of the most efficient and powerful tools for studying critical and scaling phenomena in interacting many-particle systems. The multiloop Feynman diagrams underpin the specific implementation of the renormalization group program. In recent years, multiloop computation has [...] Read more.

The quantum-field renormalization group method is one of the most efficient and powerful tools for studying critical and scaling phenomena in interacting many-particle systems. The multiloop Feynman diagrams underpin the specific implementation of the renormalization group program. In recent years, multiloop computation has had a significant breakthrough in both static and dynamic models of critical behavior. In the paper, we focus on the state-of-the-art computational techniques for critical dynamic diagrams and the results obtained with their help. The generic nature of the evaluated physical observables in a wide class of field models is manifested in the asymptotic character of perturbation expansions. Thus, the Borel resummation of series is required to process multiloop results. Such a procedure also enables one to take high-order contributions into consideration properly. The paper outlines the resummation framework in dynamic models and the circumstances in which it can be useful. An important resummation criterion is the properties of the higher-order asymptotics of the perturbation theory. In static theories, these properties are determined by the method of instanton analysis. A similar approach is applicable in critical dynamics models. We describe the calculation of these asymptotics in dynamical models and present the results of the corresponding resummation. Full article

(This article belongs to the Special Issue Review on Quantum Field Theory)

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Review

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40 pages, 509 KiB

Open AccessReview

Effective Quantum Field Theory Methods for Calculating Feynman Integrals

by Anatoly V. Kotikov

Symmetry 2024, 16(1), 52; https://doi.org/10.3390/sym16010052 - 29 Dec 2023

Viewed by 736

Abstract

A review of modern methods for effective calculations of Feynman integrals containing both massless propagators and propagators with masses is given. The effectiveness of these methods in various fields of their application is demonstrated by the examples under consideration. Full article

(This article belongs to the Special Issue Review on Quantum Field Theory)

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53 pages, 698 KiB

Open AccessFeature PaperReview

Critical Properties of Three-Dimensional Many-Flavor QEDs

by Simon Metayer and Sofian Teber

Symmetry 2023, 15(9), 1806; https://doi.org/10.3390/sym15091806 - 21 Sep 2023

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Abstract

We review several variants of three-dimensional quantum electrodynamics (QED

_{3}

) with

N_{f}

fermion (or boson) flavors, including fermionic (or spinorial) QED

_{3}

, bosonic (or scalar) QED

_{3}

,

N = 1

supersymmetric QED and also models of reduced QED (supersymmetric [...] Read more.

We review several variants of three-dimensional quantum electrodynamics (QED

_{3}

) with

N_{f}

fermion (or boson) flavors, including fermionic (or spinorial) QED

_{3}

, bosonic (or scalar) QED

_{3}

,

N = 1

supersymmetric QED and also models of reduced QED (supersymmetric or not). We begin with an introduction to these models and their flow to a stable infra-red fixed point in the large-

N_{f}

limit. We then present detailed state-of-the-art computations of the critical exponents of these models within the dimensional regularization (and reduction) scheme(s), at the next-to-leading order in the

1 / N_{f}

expansion and in an arbitrary covariant gauge. We finally discuss dynamical (matter) mass generation and the current status of our understanding of the phase structure of these models. Full article

(This article belongs to the Special Issue Review on Quantum Field Theory)

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40 pages, 607 KiB

Open AccessReview

Universality Classes of Percolation Processes: Renormalization Group Approach

by Michal Hnatič, Juha Honkonen, Tomáš Lučivjanský and Lukáš Mižišin

Symmetry 2023, 15(9), 1696; https://doi.org/10.3390/sym15091696 - 04 Sep 2023

Viewed by 1027

Abstract

Complex systems of classical physics in certain situations are characterized by intensive fluctuations of the quantities governing their dynamics. These include important phenomena such as (continuous) second-order phase transitions, fully developed turbulence, magnetic hydrodynamics, advective–diffusive processes, the kinetics of chemical reactions, percolation, and [...] Read more.

Complex systems of classical physics in certain situations are characterized by intensive fluctuations of the quantities governing their dynamics. These include important phenomena such as (continuous) second-order phase transitions, fully developed turbulence, magnetic hydrodynamics, advective–diffusive processes, the kinetics of chemical reactions, percolation, and processes in financial markets. The theoretical goal of the study of such systems is to determine and predict the temporal and spatial dependence of statistical correlations of fluctuating variables. Modern methods of quantum field theory, originally developed in high-energy physics to describe the properties of elementary particles, allow for quantitative analysis of such correlations. Peculiarities of quantum field theory in solving two paradigmatic statistical problems related to percolation are reviewed, and new results on calculating representative universal parameters such as critical exponents that describe asymptotic behavior are presented. Full article

(This article belongs to the Special Issue Review on Quantum Field Theory)

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30 pages, 543 KiB

Open AccessReview

Field-Theoretic Renormalization Group in Models of Growth Processes, Surface Roughening and Non-Linear Diffusion in Random Environment: Mobilis in Mobili

by Nikolay V. Antonov, Nikolay M. Gulitskiy, Polina I. Kakin, Nikita M. Lebedev and Maria M. Tumakova

Symmetry 2023, 15(8), 1556; https://doi.org/10.3390/sym15081556 - 08 Aug 2023

Viewed by 765

Abstract

This paper is concerned with intriguing possibilities for non-conventional critical behavior that arise when a nearly critical strongly non-equilibrium system is subjected to chaotic or turbulent motion of the environment. We briefly explain the connection between the critical behavior theory and the quantum [...] Read more.

This paper is concerned with intriguing possibilities for non-conventional critical behavior that arise when a nearly critical strongly non-equilibrium system is subjected to chaotic or turbulent motion of the environment. We briefly explain the connection between the critical behavior theory and the quantum field theory that allows the application of the powerful methods of the latter to the study of stochastic systems. Then, we use the results of our recent research to illustrate several interesting effects of turbulent environment on the non-equilibrium critical behavior. Specifically, we couple the Kazantsev–Kraichnan “rapid-change” velocity ensemble that describes the environment to the three different stochastic models: the Kardar–Parisi–Zhang equation with time-independent random noise for randomly growing surface, the Hwa–Kardar model of a “running sandpile” and the generalized Pavlik model of non-linear diffusion with infinite number of coupling constants. Using field-theoretic renormalization group analysis, we show that the effect can be quite significant leading to the emergence of induced non-linearity or making the original anisotropic scaling appear only through certain “dimensional transmutation”. Full article

(This article belongs to the Special Issue Review on Quantum Field Theory)

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51 pages, 1692 KiB

Open AccessFeature PaperReview

B Meson Decays in the Covariant Confined Quark Model

by Stanislav Dubnička, Anna Z. Dubničková, Mikhail A. Ivanov and Andrej Liptaj

Symmetry 2023, 15(8), 1542; https://doi.org/10.3390/sym15081542 - 04 Aug 2023

Cited by 1 | Viewed by 827

Abstract

The aim of this text is to present the covariant confined quark model (CCQM) and review its applications in the decays of B mesons. We do so in the context of existing experimental measurements and theoretical results of other authors, which we also [...] Read more.

The aim of this text is to present the covariant confined quark model (CCQM) and review its applications in the decays of B mesons. We do so in the context of existing experimental measurements and theoretical results of other authors, which we also review. The physics principles are, in detail, exposed for the CCQM; the other results (theoretical and experimental) are surveyed in an enumerative way with comments. We proceed by considering, successively, three categories of decay processes: leptonic, semileptonic and non-leptonic. Full article

(This article belongs to the Special Issue Review on Quantum Field Theory)

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27 pages, 961 KiB

Open AccessReview

Perturbative Asymptotic Safety and Its Phenomenological Applications

by Alexander Bednyakov and Alfiia Mukhaeva

Symmetry 2023, 15(8), 1497; https://doi.org/10.3390/sym15081497 - 28 Jul 2023

Cited by 3 | Viewed by 688

Abstract

Asymptotic safety is a remarkable example when fruitful ideas borrowed from statistical physics proliferate to high-energy physics. The concept of asymptotic safety is tightly connected to fixed points (FPs) of the renormalization-group (RG) flow, and generalize well-known asymptotic freedom to a scale-invariant ultraviolet [...] Read more.

Asymptotic safety is a remarkable example when fruitful ideas borrowed from statistical physics proliferate to high-energy physics. The concept of asymptotic safety is tightly connected to fixed points (FPs) of the renormalization-group (RG) flow, and generalize well-known asymptotic freedom to a scale-invariant ultraviolet completion with non-vanishing interactions. In this review, we discuss the key ideas behind asymptotic safety, a mechanism for achieving it, and the conditions it imposes on general gauge–Yukawa field theories. We also pay special attention to possible phenomenological applications and provide an overview of standard model (SM) extensions potentially exhibiting asymptotic safety. Full article

(This article belongs to the Special Issue Review on Quantum Field Theory)

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24 pages, 907 KiB

Open AccessReview

Phase Diagram of Dense Two-Color QCD at Low Temperatures

by Victor V. Braguta

Symmetry 2023, 15(7), 1466; https://doi.org/10.3390/sym15071466 - 24 Jul 2023

Cited by 1 | Viewed by 908

Abstract

This review is devoted to the modern understanding of the two-color QCD phase diagram at finite baryon density and low temperatures. First, we consider the theoretical picture of this phase diagram. It is believed that at low baryon density, two-color QCD can be [...] Read more.

This review is devoted to the modern understanding of the two-color QCD phase diagram at finite baryon density and low temperatures. First, we consider the theoretical picture of this phase diagram. It is believed that at low baryon density, two-color QCD can be described by chiral perturbation theory (ChPT), which predicts a second-order phase transition with Bose-Einstein condensation of diquarks at

μ = m_{π} / 2

. At larger baryon chemical potentials, the interactions between baryons become important, and ChPT is not applicable anymore. At sufficiently large baryon chemical potential, the Fermi sphere composed of quarks is formed, and diquarks are condensed on the surface of this sphere. In this region, two-color baryon matter reveals properties similar to those of the Quarkyonic phase. Particular attention in this review is paid to lattice studies of dense two-color QCD phase diagram. In the low-density region, the results of lattice studies are in agreement with ChPT predictions. At sufficiently large baryon densities, lattice studies observe a Fermi sphere composed of quarks and condensation of diquarks on its surface. Thus, available lattice studies support most of the theoretical predictions. Finally, we discuss the status of the deconfinement in cold dense two-color matter, which was observed in lattice simulation with staggered fermions. Full article

(This article belongs to the Special Issue Review on Quantum Field Theory)

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41 pages, 1172 KiB

Open AccessFeature PaperReview

On Instabilities Caused by Magnetic Background Fields

by Michael Bordag

Symmetry 2023, 15(6), 1137; https://doi.org/10.3390/sym15061137 - 23 May 2023

Cited by 1 | Viewed by 815

Abstract

We review instabilities that appear from the coupling of spin-one fields to a magnetic background in a non-Abelian theory. Such coupling results, due to asymptotic freedom in a negative quantum, contribute to the effective potential. In QCD, the Savvidy vacuum results. However, due [...] Read more.

We review instabilities that appear from the coupling of spin-one fields to a magnetic background in a non-Abelian theory. Such coupling results, due to asymptotic freedom in a negative quantum, contribute to the effective potential. In QCD, the Savvidy vacuum results. However, due to the tachyonic mode, such a state is not stable, and the question about the true ground state of QCD is still open. In the electroweak model, the corresponding instability is postponed to very large background fields and may be of relevance in the early universe, at best. We start with an introduction to the topic and display the necessary formulas and methods. Then, we consider the one-particle spectra of the fields in a magnetic background and the related Euler–Heisenberg Lagrangians. In addition, we discuss the potential instability connected with the anomalous moment of the electron. The main part is on the quantum correction to the energy in non-Abelian fields, including massive ones. Here, the focus is on so-called electroweak magnetism and the search for a classical solution of the field equations and their approximations by a lattice of flux tubes. Finally, we review approaches with non-homogeneous background fields and the background of an

A_{0}

-field. Full article

(This article belongs to the Special Issue Review on Quantum Field Theory)

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