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 TMF: Year: Volume: Issue: Page: Find

 TMF, 1999, Volume 118, Number 1, Pages 67–73 (Mi tmf686)

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.

DOI: https://doi.org/10.4213/tmf686

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English version:
Theoretical and Mathematical Physics, 1999, 118:1, 54–59

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Document Type: Article

Citation: Yu. M. Zinoviev, “On the Wilson criterion”, TMF, 118:1 (1999), 67–73; Theoret. and Math. Phys., 118:1 (1999), 54–59

Citation in format AMSBIB
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