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Universe
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Universe: Feature Papers 2023—Field Theory
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Universe: Feature Papers 2023—Field Theory

A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Field Theory".

Deadline for manuscript submissions: closed (29 February 2024) | Viewed by 19552

Special Issue Editor

Prof. Dr. Gerald B. Cleaver

E-Mail Website
Guest Editor
Early Universe Cosmology and Strings (EUCOS) Group, Center for Astrophysics, Space Physics and Engineering Research (CASPER), Baylor University, Waco, TX 76798, USA
Interests: quantum field theory; quantum gravity; quantum cosmology; traversable wormholes; Casimir effect; quantum information theory; quantum thermodynamics; philosophical foundations of quantum mechanics; multiverse concepts
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue aims to cover topics, original research, and peer-reviewed articles related to the latest research and developments in the wide-ranging realm of field theory. Field theory is an interdisciplinary subject and covers a vast domain of topics, including both theoretical and experimental issues. Potential topics include, but are not limited to, the following:

  • Classical field theory;
  • Quantum field theory, including string field theory;
  • Field theory of scalars, spinors, vectors, and higher rank tensors;
  • Abelian gauge fields and quantum electromagnetics;
  • Non-abelian gauge fields;
  • Weak interactions;
  • Strong interactions;
  • Standard model of physics;
  • Unified field theory;
  • Grand unified field theory;
  • Supersymmetric field theory;
  • Perturbative field theory;
  • Non-perturbative field theory;
  • Feynman diagrams;
  • Conformal field theory;
  • Continuous random fields;
  • Spontaneous symmetry breakdown;
  • Statistical field theory of many-body systems;
  • Spacetime symmetries;
  • Internal symmetries;
  • The vacuum;
  • Renormalization;
  • (Dynamics) Casimir effect.

You are invited to send short proposals for submissions of feature papers to our Editorial Office ([email protected]). They will first be evaluated by Editors, and the selected papers will be thoroughly and rigorously peer reviewed.

Prof. Dr. Gerald B. Cleaver
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Universe is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (14 papers)

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Research

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19 pages, 425 KiB  
Article
Finite Time Path Field Theory Perturbative Methods for Local Quantum Spin Chain Quenches
by Domagoj Kuić, Alemka Knapp and Diana Šaponja-Milutinović
Universe 2024, 10(10), 384; https://doi.org/10.3390/universe10100384 - 30 Sep 2024
Abstract
We discuss local magnetic field quenches using perturbative methods of finite time path field theory (FTPFT) in the following spin chains: Ising and XY in a transverse magnetic field. Their common characteristics are: (i) they are integrable via mapping to a second quantized [...] Read more.
We discuss local magnetic field quenches using perturbative methods of finite time path field theory (FTPFT) in the following spin chains: Ising and XY in a transverse magnetic field. Their common characteristics are: (i) they are integrable via mapping to a second quantized noninteracting fermion problem; and (ii) when the ground state is nondegenerate (true for finite chains except in special cases), it can be represented as a vacuum of Bogoliubov fermions. By switching on a local magnetic field perturbation at finite time, the problem becomes nonintegrable and must be approached via numeric or perturbative methods. Using the formalism of FTPFT based on Wigner transforms (WTs) of projected functions, we show how to: (i) calculate the basic “bubble” diagram in the Loschmidt echo (LE) of a quenched chain to any order in the perturbation; and (ii) resum the generalized Schwinger–Dyson equation for the fermion two-point retarded functions in the “bubble” diagram, hence achieving the resummation of perturbative expansion of LE for a wide range of perturbation strengths under certain analyticity assumptions. Limitations of the assumptions and possible generalizations beyond it and also for other spin chains are further discussed. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2023—Field Theory)
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12 pages, 300 KiB  
Article
Quantum de Sitter Geometry
by Mohammad Vahid Takook
Universe 2024, 10(2), 70; https://doi.org/10.3390/universe10020070 - 2 Feb 2024
Cited by 2 | Viewed by 1897
Abstract
Quantum de Sitter geometry is discussed using elementary field operator algebras in Krein space quantization from an observer-independent point of view, i.e., ambient space formalism. In quantum geometry, the conformal sector of the metric becomes a dynamical degree of freedom, which can be [...] Read more.
Quantum de Sitter geometry is discussed using elementary field operator algebras in Krein space quantization from an observer-independent point of view, i.e., ambient space formalism. In quantum geometry, the conformal sector of the metric becomes a dynamical degree of freedom, which can be written in terms of a massless minimally coupled scalar field. The elementary fields necessary for the construction of quantum geometry are introduced and classified. A complete Krein–Fock space structure for elementary fields is presented using field operator algebras. We conclude that since quantum de Sitter geometry can be constructed by elementary fields operators, the geometry quantum state is immersed in the Krein–Fock space and evolves in it. The total number of accessible quantum states in the universe is chosen as a parameter of quantum state evolution, which has a relationship with the universe’s entropy. Inspired by the Wheeler–DeWitt constraint equation in cosmology, the evolution equation of the geometry quantum state is formulated in terms of the Lagrangian density of interaction fields in ambient space formalism. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2023—Field Theory)
8 pages, 275 KiB  
Article
Consistent Couplings between a Massive Spin-3/2 Field and a Partially Massless Spin-2 Field
by Nicolas Boulanger, Guillaume Lhost and Sylvain Thomée
Universe 2023, 9(11), 482; https://doi.org/10.3390/universe9110482 - 15 Nov 2023
Cited by 2 | Viewed by 1339
Abstract
We revisit the problem of constructing consistent interactions between a massive spin-3/2 field and a partially massless graviton in four-dimensional (anti) de Sitter (A)dS4 spacetime. We use the Stueckelberg formulation of the action principle for these fields and find two non-trivial cubic [...] Read more.
We revisit the problem of constructing consistent interactions between a massive spin-3/2 field and a partially massless graviton in four-dimensional (anti) de Sitter (A)dS4 spacetime. We use the Stueckelberg formulation of the action principle for these fields and find two non-trivial cubic vertices with less than two derivatives when moving to the unitary gauge. One of the vertices is reminiscent of the minimal coupling of the massive spin-3/2 field to gravity, except that now the graviton is partially massless. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2023—Field Theory)
12 pages, 290 KiB  
Article
A New Approach to String Theory
by Albert Schwarz
Universe 2023, 9(10), 451; https://doi.org/10.3390/universe9100451 - 16 Oct 2023
Cited by 2 | Viewed by 1234
Abstract
In the present paper, we consider quantum theories obtained through the quantization of classical theories with first-class constraints assuming that these constraints form a Lie algebra. We show that in this case, one can construct physical quantities of a new type. We apply [...] Read more.
In the present paper, we consider quantum theories obtained through the quantization of classical theories with first-class constraints assuming that these constraints form a Lie algebra. We show that in this case, one can construct physical quantities of a new type. We apply this construction to string theory. We find that scattering amplitudes in critical bosonic closed string theory can be expressed in terms of physical quantities of the new type. Our techniques can also be applied to superstrings and heterotic strings. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2023—Field Theory)
7 pages, 235 KiB  
Article
Singularities of Scattering Matrices
by Albert Schwarz
Universe 2023, 9(10), 427; https://doi.org/10.3390/universe9100427 - 25 Sep 2023
Viewed by 1062
Abstract
Our main result is the analysis of singularities of the integrands of integrals representing the matrix elements of the scattering matrix and the inclusive scattering matrix in perturbation theory. These results are proven for any quantum field theory in any dimension. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2023—Field Theory)
10 pages, 255 KiB  
Article
The Quantum Yang–Mills Theory
by Dimitrios Metaxas
Universe 2023, 9(9), 423; https://doi.org/10.3390/universe9090423 - 20 Sep 2023
Cited by 1 | Viewed by 1064
Abstract
In axiomatic quantum field theory, the postulate of the uniqueness of the vacuum (a pure vacuum state) is independent from the other axioms and equivalent to the cluster decomposition property. The latter, however, implies a Coulomb or Yukawa attenuation of the interactions at [...] Read more.
In axiomatic quantum field theory, the postulate of the uniqueness of the vacuum (a pure vacuum state) is independent from the other axioms and equivalent to the cluster decomposition property. The latter, however, implies a Coulomb or Yukawa attenuation of the interactions at growing distances and hence cannot accommodate the confining properties of the strong interaction. Thesolution of the Yang–Mills quantum theory given previously uses an auxiliary field to incorporate Gauss’s law and demonstrates the existence of two separate vacua, the perturbative and the confining vacuum, therefore resulting in a mixed vacuum state, deriving confinement, as well as the related, expected properties of the strong interaction. The existence of multiple vacua is, in fact, expected by the axiomatic, algebraic quantum field theory, via the decomposition of the vacuum state to eigenspaces of the auxiliary field. The general vacuum state is a mixed quantum state, and the cluster decomposition property does not hold. Because of the energy density difference between the two vacua, the physics of the strong interactions does not admit a Lagrangian description. I clarify the above remarks related to the previous solution of the Yang–Mills interaction and conclude with some discussion a criticism of a related mathematical problem and some tentative comments regarding the spin-2 case. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2023—Field Theory)
10 pages, 280 KiB  
Article
Universality in the Exact Renormalization Group: Comparison to Perturbation Theory
by José Gaite
Universe 2023, 9(9), 409; https://doi.org/10.3390/universe9090409 - 7 Sep 2023
Cited by 2 | Viewed by 1028
Abstract
Various formulations of the exact renormalization group can be compared in the perturbative domain, in which we have reliable expressions for regularization-independent (universal) quantities. We consider the renormalization of the λϕ4 theory in three dimensions and make a comparison between the [...] Read more.
Various formulations of the exact renormalization group can be compared in the perturbative domain, in which we have reliable expressions for regularization-independent (universal) quantities. We consider the renormalization of the λϕ4 theory in three dimensions and make a comparison between the sharp-cutoff regularization method and other more recent methods. They all give good results, which only differ by small non-universal terms. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2023—Field Theory)
21 pages, 375 KiB  
Article
Super Riemann Surfaces and Fatgraphs
by Albert S. Schwarz and Anton M. Zeitlin
Universe 2023, 9(9), 384; https://doi.org/10.3390/universe9090384 - 26 Aug 2023
Cited by 1 | Viewed by 959
Abstract
Our goal is to describe superconformal structures on super Riemann surfaces (SRSs) based on data assigned to a fatgraph. We start from the complex structures on punctured (1|1)-supermanifolds, characterizing the corresponding moduli and the deformations using Strebel differentials [...] Read more.
Our goal is to describe superconformal structures on super Riemann surfaces (SRSs) based on data assigned to a fatgraph. We start from the complex structures on punctured (1|1)-supermanifolds, characterizing the corresponding moduli and the deformations using Strebel differentials and certain Čech cocycles for a specific covering, which we reproduce from fatgraph data, consisting of U(1)-graph connection and odd parameters at the vertices. Then, we consider dual (1|1)-supermanifolds and related superconformal structures for N=2 super Riemann surfaces. The superconformal structures, N=1 SRS, are computed as the fixed points of involution on the supermoduli space of N=2 SRS. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2023—Field Theory)
17 pages, 1311 KiB  
Article
Maxwell Field of a Charge in Hyperbolic Motion
by Ramón Serrano Montesinos and Juan Antonio Morales-Lladosa
Universe 2023, 9(6), 286; https://doi.org/10.3390/universe9060286 - 10 Jun 2023
Viewed by 1169
Abstract
We conduct a detailed study of the electromagnetic field produced by a massive point particle undergoing hyperbolic (uniformly accelerated) motion in Minkowski space-time. Starting from the Liénard–Wiechert solution and using a covariant notation, we obtain and analyse the main quantities that describe this [...] Read more.
We conduct a detailed study of the electromagnetic field produced by a massive point particle undergoing hyperbolic (uniformly accelerated) motion in Minkowski space-time. Starting from the Liénard–Wiechert solution and using a covariant notation, we obtain and analyse the main quantities that describe this field. We identify the space-time region to which this solution is restricted and write a solution valid in the whole of space-time. Finally, we verify that this solution satisfies Maxwell’s equations in the sense of distributions. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2023—Field Theory)
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13 pages, 293 KiB  
Article
Functional Integrals in Geometric Approach to Quantum Theory
by Igor Frolov and Albert Schwarz
Universe 2023, 9(5), 231; https://doi.org/10.3390/universe9050231 - 15 May 2023
Viewed by 866
Abstract
In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal of this paper is to prove corresponding results in geometric approach to quantum theory. We apply these results to the formalism of L-functionals. [...] Read more.
In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal of this paper is to prove corresponding results in geometric approach to quantum theory. We apply these results to the formalism of L-functionals. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2023—Field Theory)
11 pages, 293 KiB  
Article
Scattering in Algebraic Approach to Quantum Theory—Jordan Algebras
by Albert Schwarz
Universe 2023, 9(4), 173; https://doi.org/10.3390/universe9040173 - 31 Mar 2023
Cited by 2 | Viewed by 987
Abstract
Using the geometric approach, we formulate a quantum theory in terms of Jordan algebras. We analyze the notion of a (quasi)particle (=elementary excitation of translation-invariant stationary state) and the scattering of (quasi)particles in this framework. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2023—Field Theory)
13 pages, 305 KiB  
Article
Scattering in Geometric Approach to Quantum Theory
by Albert Schwarz
Universe 2022, 8(12), 663; https://doi.org/10.3390/universe8120663 - 16 Dec 2022
Cited by 7 | Viewed by 3702
Abstract
We define inclusive scattering matrix in the framework of a geometric approach to quantum field theory. We review the definitions of scattering theory in the algebraic approach and relate them to the definitions in the geometric approach. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2023—Field Theory)
15 pages, 311 KiB  
Article
Scattering in Algebraic Approach to Quantum Theory—Associative Algebras
by Albert Schwarz
Universe 2022, 8(12), 660; https://doi.org/10.3390/universe8120660 - 15 Dec 2022
Cited by 7 | Viewed by 1093
Abstract
The definitions of scattering matrix and inclusive scattering matrix in the framework of formulation of quantum field theory in terms of associative algebras with involution are presented. The scattering matrix is expressed in terms of Green functions on shell (LSZ formula), and the [...] Read more.
The definitions of scattering matrix and inclusive scattering matrix in the framework of formulation of quantum field theory in terms of associative algebras with involution are presented. The scattering matrix is expressed in terms of Green functions on shell (LSZ formula), and the inclusive scattering matrix is expressed in terms of generalized Green functions on shell. The expression for inclusive scattering matrix can be used also for quasi-particles (for elementary excitations of any translation-invariant stationary state, for example, for elementary excitations of equilibrium state). An interesting novelty is the consideration of associative algebras over real numbers. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2023—Field Theory)

Review

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86 pages, 692 KiB  
Review
Quantum Mechanics and Quantum Field Theory: Algebraic and Geometric Approaches
by Igor Frolov and Albert Schwarz
Universe 2023, 9(7), 337; https://doi.org/10.3390/universe9070337 - 17 Jul 2023
Cited by 3 | Viewed by 1458
Abstract
This is a non-standard exposition of the main notions of quantum mechanics and quantum field theory, including recent results. It is based on the algebraic approach in which the starting point is a star-algebra and on the geometric approach in which the starting [...] Read more.
This is a non-standard exposition of the main notions of quantum mechanics and quantum field theory, including recent results. It is based on the algebraic approach in which the starting point is a star-algebra and on the geometric approach in which the starting point is a convex set of states. Standard formulas for quantum probabilities are derived from decoherence. This derivation allows us to go beyond quantum theory in the geometric approach. Particles are defined as elementary excitations of the ground state (and quasiparticles as elementary excitations of any translation invariant state). The conventional scattering matrix does not work for quasiparticles (or even for particles if the theory does not have particle interpretation). The analysis of scattering in these cases is based on the notion of an inclusive scattering matrix, which is closely related to inclusive cross-sections. It is proven that the conventional scattering matrix can be expressed in terms of Green functions (LSZ formula) and the inclusive scattering matrix can be expressed in terms of generalized Green functions that appear in the Keldysh formalism of non-equilibrium statistical physics. The derivation of the expression of the evolution operator and other physical quantities in terms of functional integrals is based on the notion of the symbol of an operator; these arguments can be applied in the geometric approach as well. In particular, this result can be used to provide a simple derivation of the diagram technique for generalized Green functions. The notion of an inclusive scattering matrix makes sense in the geometric approach, although it seems that a definition of the conventional scattering matrix cannot be provided in this situation. The geometric approach is used to show that quantum mechanics and its generalizations can be considered as classical theories where our devices are able to measure only a part of the observables. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2023—Field Theory)
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