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 quantum electrodynamics (QED) on a lattice with staggered Fermions. We show that every SU(NL) quantum antiferromagnet with spins in a particular fundamental representation of the SU(NL) Lie algebra and with nearest neighbor couplings on a bipartite lattice is exactly equivalent to the infinite coupling limit of lattice QED with the number of flavors of electrons related to NL and the dimension of spacetime, D + 1. There are NL 2component Fermions in D = 1, 2NL 2-component Fermions in D = 2 and 2NL 4-component Fermions in D = 3. We find that, for both compact and non-compact QED, when NL is odd the ground state of the strong coupling limit breaks chiral symmetry in any dimensions and for any NL and the condensate is an isoscalar mass operator. When NL is even, chiral symmetry is broken if D ≥ 2 and if NL is small enough and the order parameter is an isovector mass operator. We also find the exact ground state of the lattice Coulomb gas as well as a variety of related lattice statistical systems with long–ranged interactions.