On the Wilson criterion
Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 1, pp. 67-73
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The $U(1)$-gauge theory with the Villain action is considered in a cubic lattice approximation of three- and four-dimensional tori. As the lattice spacing tends to zero, the naturally defined correlation functions converge to the correlation functions of the $\mathbf R$-gauge electrodynamics on three- and four-dimensional tori only for a special scaling, which depends on the correlation functions. Another scaling gives degenerate continuum limits. The Wilson criterion for the confinement of charged particles is fulfilled for the $\mathbf R$-gauge electrodynamics on a torus. If the radius of the initial torus tends to infinity, then the correlation functions converge to the correlation functions of the $\mathbf R$-gauge Euclidean electrodynamics.
@article{TMF_1999_118_1_a4,
author = {Yu. M. Zinoviev},
title = {On the {Wilson} criterion},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {67--73},
publisher = {mathdoc},
volume = {118},
number = {1},
year = {1999},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1999_118_1_a4/}
}
Yu. M. Zinoviev. On the Wilson criterion. Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 1, pp. 67-73. http://geodesic.mathdoc.fr/item/TMF_1999_118_1_a4/