Communications in Mathematical Physics

, Volume 82, Issue 4, pp 545–606

Proof of confinement of static quarks in 3-dimensionalU(1) lattice gauge theory for all values of the coupling constant

  • Markus Göpfert
  • Gerhard Mack

DOI: 10.1007/BF01961240

Cite this article as:
Göpfert, M. & Mack, G. Commun.Math. Phys. (1982) 82: 545. doi:10.1007/BF01961240


We study the 3-dimensional pureU(1) lattice gauge theory with Villain action which is related to the 3-dimensional ℤ-ferromagnet by an exact duality transformation (and also to a Coulomb system). We show that its string tension α is nonzero for all values of the coupling constantg2, and obeys a bound α≧const·mDβ−1 for smallag2, with β=4π2/g2 and\(m_D^2 = (2{\beta \mathord{\left/ {\vphantom {\beta a}} \right. \kern-\nulldelimiterspace} a}^3 )e^{ - \beta \upsilon _{Cb} {{(0)} \mathord{\left/ {\vphantom {{(0)} 2}} \right. \kern-\nulldelimiterspace} 2}} (a = lattice spacing)\). A continuum limita→0,mD fixed, exists and represents a scalar free field theory of massmD. The string tension αmD−2 in physical units tends to ∞ in this limit. Characteristic differences in the behaviour of the model for large and small coupling constantag2 are found. Renormalization group aspects are discussed.

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Markus Göpfert
    • 1
  • Gerhard Mack
    • 1
  1. 1.II. Institut für Theoretische Physik der Universität HamburgHamburg 50Federal Republic of Germany

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