Convergence of \(\text{U}(1)_ 3\) lattice gauge theory to its continuum limit
type: Item
instance of: scholarly article
title: Convergence of \(\text{U}(1)_ 3\) lattice gauge theory to its continuum limit
zbMATH Open document ID: 0571.60011
DOI: 10.1007/BF01210842
author: Leonard Gross
published in: Communications in Mathematical Physics
publication date: 1983-01-01T00:00:00Z
review text: Lattice approximations of the free Euclidean electromagnetic field in three space-time dimensions are considered, extending results of \textit{K. G. Wilson} [Confinement of quarks, Phys. Rev. D 10, 2445--2450 (1974)]: The compact \(\text{U}(1)_ 3\) lattice gauge theory in three dimensions converges to the electromagnetic field (in the sense of convergence of the characteristic functional of the field variables \(F_{u,v})\) for the Villain action, and for the Wilson action on the electric sector. There are no monopoles when starting with the Villain action, and the same holds starting with the spin wave approximation of the Wilson action, so that it is conjectured that there are no monopoles in the continuum limit of the Wilson action.
Mathematics Subject Classification ID: 81T25
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 3911366
zbMATH Keywords: Lattice approximations
zbMATH Keywords: Euclidean electromagnetic field
zbMATH Keywords: lattice gauge theory
zbMATH Keywords: Villain action
zbMATH Keywords: Wilson action
MaRDI profile type: Publication
cites work: Q4129338
cites work: Q4118602
cites work: Q4185090
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cites work: Q5513660
cites work: Correlation inequalities and contour estimates
description: scientific article; zbMATH DE number 3911366