Review on Quantum Field Theory

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 8081

Special Issue Editors


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Guest Editor
1. Bogoliubov Laboratory of Theoretical Physics, Institute for Nuclear Research, 141980 Dubna, Russia
2. Faculty of Sciences, P.J. Šafárik University, Moyzesova 16, 040 01 Košice, Slovakia
3. Institute of Experimental Physics, SAS, Watsonova 47, 040 01 Košice, Slovakia
Interests: quantum field theory; symmetries and their breaking; non-linear dynamics; phase transitions
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Guest Editor
Department of Military Technology, National Defence University, 00861 Helsinki, Finland
Interests: quantum dynamics; extreme states of matter; quantum statistical mechanics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Quantum field theory (QFT) is not only a powerful mathematical tool for calculating representative physical quantities, but also a theoretical platform and a rigorous scientific language for a compact description of physical reality. Historically, the first example of such a description was quantum electrodynamics. At present, QFT constitutes the “first principles” on which the standard model is based, which describes the world of elementary particles in a unified manner. However, from a methodological point of view, QFT methods have a wider scope. Their application to the description of phase transitions and other stochastic systems of classical physics have generated a strong push for further improvement and opened up their previously unknown possibilities for calculating important, physically measurable quantities in the study of various phase transitions, transport phenomena in random media, and even the universal properties of hydrodynamic turbulence.

Thus, to date, QFT methods have been used to solve an extremely wide range of physical problems covering both quantum and classical physics.

The purpose of this Special Issue is to highlight, through review articles, the latest developments in QFT using, in particular, the computational capabilities of modern powerful computers.

Significant attention is paid to new achievements in the Standard model and beyond, problems of renormalizability and anomalies, multi-loop calculations, the technique of resumption of asymptotic series, and non-perturbative methods for calculating functional integrals, including calculations on lattices. One of the most important goals is highlighting achievements in solving problems of non-equilibrium closed and open systems using QFT and functional integration methods. Achievements in the study of directed percolation, kinetics of chemical reactions and growth boundaries, which are systems describing wide classes of universality of physical processes, are examples thereof. Problems of violation of the famous Kolmogorov scaling in the developed hydrodynamic turbulence, which is a consequence of its important property intermittency or multifractality, are also considered.

All of the physical systems mentioned above have symmetries affecting their dynamics. The higher the degree of symmetry, the wider the class of physical processes described in a unified manner. In high-energy physics, this manifests itself in the existence of multiplets of elementary particles with the same dynamics. In complex classical systems, universality classes are found, each with different microscopic structures but common universal behavior on large scales. In theoretical models based on the postulates of quantum field theory, possibilities for describing symmetry properties are at the outset.

Prof. Dr. Michal Hnatič
Dr. Juha Honkonen
Guest Editors

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Keywords

  • renormalization
  • anomalies
  • renormalization group
  • multi-loop calculations
  • lattice calculations
  • complex systems
  • phase transitions
  • turbulence

Published Papers (9 papers)

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20 pages, 602 KiB  
Article
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 1049
Abstract
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  
Review
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 710
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  
Review
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
Viewed by 793
Abstract
We review several variants of three-dimensional quantum electrodynamics (QED3) with Nf fermion (or boson) flavors, including fermionic (or spinorial) QED3, bosonic (or scalar) QED3, N=1 supersymmetric QED and also models of reduced QED (supersymmetric [...] Read more.
We review several variants of three-dimensional quantum electrodynamics (QED3) with Nf fermion (or boson) flavors, including fermionic (or spinorial) QED3, bosonic (or scalar) QED3, 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-Nf 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/Nf 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  
Review
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 998
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  
Review
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
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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  
Review
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 790
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  
Review
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 674
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  
Review
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 751
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=mπ/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  
Review
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 797
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 A0-field. Full article
(This article belongs to the Special Issue Review on Quantum Field Theory)
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