SU(2) gauge invariance and order parameters in strongly coupled electronic systems

We show that the spin-{} Heisenberg model (the strong-coupling limit of the Hubbard model) is also the strong-coupling limit of an SU(2) lattice gauge theory with fermions. The local SU(2) gauge symmetry is manifest. The role of this gauge invariance is investigated in both the Hamiltonian and path-integral formulations. Off half-filling, our results reveal the existence of a lattice SU(2) bosonic matrix field which is a natural candidate for a condensate order parameter.