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 theR-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 theR-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 theR-gauge Euclidean electrodynamics.
Similar content being viewed by others
References
K. G. Wilson,Phys. Rev. D.,10, 2445–2459 (1974).
J. Villain,J. Phys.,36, 581–590 (1975).
Yu. M. Zinov'ev,Theor. Math. Phys.,43, 481–490 (1980).
Yu. M. Zinoviev,Commun. Math. Phys.,168, 227–247 (1995).
Yu. M. Zinov'ev,Theor. Math. Phys.,49, 951–956 (1981).
Yu. M. Zinoviev,Theor. Math. Phys.,50, 135–143 (1982).
Author information
Authors and Affiliations
Additional information
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118, No. 1, pp. 67–73, January, 1999.
Rights and permissions
About this article
Cite this article
Zinoviev, Y.M. On the Wilson criterion. Theor Math Phys 118, 54–59 (1999). https://doi.org/10.1007/BF02557195
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02557195