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Foundational Aspects of Gauge Field Theory

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Astrophysics, Cosmology, and Black Holes".

Deadline for manuscript submissions: 20 June 2025 | Viewed by 1664

Special Issue Editor


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Guest Editor
1. DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
2. INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
Interests: theoretical high-energy physics; fundamental symmetries; supergravity; modified gravity; gauge field theory; relational formalism; differential geometry
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Special Issue Information

Dear Colleagues,

This Special Issue explores the foundational aspects of gauge field theory, with a focus on gauge symmetries and gauge invariance, examining the significance of gauge principles and the implications of pursuing relational gauge-invariant approaches. In this context, symmetry reduction techniques are frequently adopted, either tacitly or in an explicit way, to detect and describe physical degrees of freedom. In fact, these tools can offer a beneficial interplay between geometric and physical insights in gauge field theory. The proposed investigation extends across various domains within physics, with possible implications in, e.g., cosmology, quantum gravity, and black hole physics, including holography, Carroll symmetries, Hawking radiation, the information paradox, soft hair and scalar charges, quantum (sub)systems, and entanglement entropy. We welcome both review and original research papers that delve into the aforementioned aspects.

Dr. Lucrezia Ravera
Guest Editor

Manuscript Submission Information

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Keywords

  • gauge field theory
  • gauge symmetries
  • spacetime symmetries
  • gravity theories
  • gauge-invariant approaches
  • fundamental symmetries
  • cosmology
  • quantum gravity
  • black holes
  • entanglement entropy

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Published Papers (2 papers)

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Research

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14 pages, 269 KiB  
Article
Boson–Fermion Algebraic Mapping in Second Quantization
by Fabio Lingua, Diego Molina Peñafiel, Lucrezia Ravera and Sebastián Salgado
Entropy 2024, 26(12), 1067; https://doi.org/10.3390/e26121067 - 8 Dec 2024
Viewed by 699
Abstract
We present an algebraic method to derive the structure at the basis of the mapping of bosonic algebras of creation and annihilation operators into fermionic algebras, and vice versa, introducing a suitable identification between bosonic and fermionic generators. The algebraic structure thus obtained [...] Read more.
We present an algebraic method to derive the structure at the basis of the mapping of bosonic algebras of creation and annihilation operators into fermionic algebras, and vice versa, introducing a suitable identification between bosonic and fermionic generators. The algebraic structure thus obtained corresponds to a deformed Grassmann-type algebra, involving anticommuting Grassmann-type variables. The role played by the latter in implementing gauge invariance in second quantization within our procedure is then discussed. This discussion includes the application of the mapping to the case of the bosonic and fermionic harmonic oscillator Hamiltonians. Full article
(This article belongs to the Special Issue Foundational Aspects of Gauge Field Theory)

Review

Jump to: Research

25 pages, 634 KiB  
Review
Mean Field Approaches to Lattice Gauge Theories: A Review
by Pierpaolo Fontana and Andrea Trombettoni
Entropy 2025, 27(3), 250; https://doi.org/10.3390/e27030250 - 27 Feb 2025
Viewed by 462
Abstract
Due to their broad applicability, gauge theories (GTs) play a crucial role in various areas of physics, from high-energy physics to condensed matter. Their formulations on lattices, lattice gauge theories (LGTs), can be studied, among many other methods, with tools coming from statistical [...] Read more.
Due to their broad applicability, gauge theories (GTs) play a crucial role in various areas of physics, from high-energy physics to condensed matter. Their formulations on lattices, lattice gauge theories (LGTs), can be studied, among many other methods, with tools coming from statistical mechanics lattice models, such as mean field methods, which are often used to provide approximate results. Applying these methods to LGTs requires particular attention due to the intrinsic local nature of gauge symmetry, how it is reflected in the variables used to formulate the theory, and the breaking of gauge invariance when approximations are introduced. This issue has been addressed over the decades in the literature, yielding different conclusions depending on the formulation of the theory under consideration. In this article, we focus on the mean field theoretical approach to the analysis of GTs and LGTs, connecting both older and more recent results that, to the best of our knowledge, have not been compared in a pedagogical manner. After a brief overview of mean field theory in statistical mechanics and many-body systems, we examine its application to pure LGTs with a generic compact gauge group. Finally, we review the existing literature on the subject, discussing the results obtained so far and their dependence on the formulation of the theory. Full article
(This article belongs to the Special Issue Foundational Aspects of Gauge Field Theory)
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