PROOF OF CHIRAL SYMMETRY-BREAKING IN STRONGLY COUPLED LATTICE GAUGE-THEORY

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 group U(N), N = 2,3,4, we prove that chiral long-range order exists at zero mass in four or more dimensions.