Communications in Mathematical Physics

, Volume 139, Issue 2, pp 395–431 | Cite as

Proof of chiral symmetry breaking in strongly coupled lattice gauge theory

  • Manfred Salmhofer
  • Erhard Seiler


We study chiral symmetry in the strong coupling limit of lattice gauge theory with staggered fermions and show rigorously that chiral symmetry is broken spontaneously in massless QED and the gauge-invariant Nambu-Jona-Lasinio model if the dimension of spacetime is at least four. The results for the chiral condensate as a function of the mass imply that the mean-field approximation is an upper bound for this observable which becomes exact as the dimension goes to infinity. For the model with gauge groupU(N),N=2,3,4, we prove that chiral long-range order exists at zero mass in four or more dimensions.


Neural Network Statistical Physic Complex System Gauge Theory Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Manfred Salmhofer
    • 1
  • Erhard Seiler
    • 1
  1. 1.Max-Planck-Institut für Physik und AstrophysikWerner-Heisenberg InstitutMünchen 40Federal Republic of Germany

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