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Communications in Mathematical Physics

, Volume 168, Issue 2, pp 227–247 | Cite as

U(1) gauge theory on a torus

  • Yu. M. Zinoviev
Article

Abstract

U(1) gauge theory with the Villain action on a cubic lattice approximation of three- and four-dimensional torus is considered. As the lattice spacing approaches zero, provided the coupling constant correspondingly approaches zero, the naturally chosen correlation functions converge to the correlation functions of theR-gauge electrodynamics on three- and four-dimensional torus. When the torus radius tends to infinity these correlation functions converge to the correlation functions of theR-gauge Euclidean electrodynamics.

Keywords

Neural Network Statistical Physic Correlation Function Complex System Gauge Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Wilson, K.G.: Confinement of quarks. Phys. Rev.D10, 2445–2459 (1974)Google Scholar
  2. 2.
    Villain, J.: Theory of one- and two-dimensional magnets with an easy magnetization plane. 2. The planar, classical, two-dimensional magnet. J. Phys.36, 581–590 (1975)Google Scholar
  3. 3.
    Gross, L.: Convergence ofU(1)3 lattice guage theory to its continuum limit. Commun. Math. Phys.92, 137–162 (1983)Google Scholar
  4. 4.
    Driver, B.K.: Convergence ofU(1)4 lattice gauge theory to its continuum limit. Commun. Math. Phys.110, 479–501 (1987)Google Scholar
  5. 5.
    Zinoviev, Yu.M.: Duality in the abelian guage lattice theories. Theor. Math. Phys.43, 481–490 (1980)Google Scholar
  6. 6.
    Zinoviev, Yu.M.: LatticeR-guage theories. Theor. Math. Phys.49, No. 2 (1981)Google Scholar
  7. 7.
    Zinoviev, Yu.M.:R-gauge theories. Theor. Math. Phys.50, 135–143 (1982)Google Scholar
  8. 8.
    de Rham, G.: Variétés différentiables. Paris: Hermann, 1955Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Yu. M. Zinoviev
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

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