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On the Wilson criterion
Yu. M. Zinoviev Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
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.
Received: 15.04.1998
Citation:
Yu. M. Zinoviev, “On the Wilson criterion”, TMF, 118:1 (1999), 67–73; Theoret. and Math. Phys., 118:1 (1999), 54–59
Linking options:
https://www.mathnet.ru/eng/tmf686https://doi.org/10.4213/tmf686 https://www.mathnet.ru/eng/tmf/v118/i1/p67
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