SU(N) ANTIFERROMAGNETS AND THE PHASE-STRUCTURE OF QED IN THE STRONG-COUPLING LIMIT

We examine the strong coupling limit of both compact and non-compact q uantum electrodynamics (QED) on a lattice with staggered fermions. We show that every SU (N(L)) quantum antiferromagnet with spins in a part icular fundamental representation of the SU (N(L)) Lie algebra and wit h nearest neighbor couplings on a bipartite lattice is exactly equival ent to the infinite coupling limit of lattice QED with the number of f lavors of electrons related to N(L) and the dimension of space-time, D + 1. We find that, for both compact and non-compact QED, when N(L) is odd the ground state of the strong coupling limit breaks chiral symme try in any dimensions and for any N(L) and the condensate is an isosca lar mass operator. When N(L) is even, chiral symmetry is broken if D g reater-than-or-equal-to 2 and if N(L) is small enough; in this case th e order parameter is an isovector mass operator. We also find the exac t ground state of the lattice Coulomb gas as well as a variety of rela ted lattice statistical systems with long-range interactions.