Mean Field Approaches to Lattice Gauge Theories : A Review
Fontana, Pierpaolo (Universitat Autònoma de Barcelona. Departament de Física)
Trombettoni, Andrea (University of Trieste. Department of Physics)

Date:	2025
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 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.
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article de revisió ; recerca ; Versió publicada
Subject:	Lattice gauge theory ; Mean field theory ; Gauge-invariant approaches
Published in:	Entropy, Vol. 27, Issue 3 (March 2025) , art. 250, ISSN 1099-4300

DOI: 10.3390/e27030250
PMID: 40149175

25 p, 634.2 KB

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