Supersymmetric Hubbard operators

We develop a supersymmetric representation of the Hubbard operator which unifies the slave boson and slave fermion representations into a single U(1)×SU(1\|1) gauge theory, a group with larger symmetry than the product of two U(1) gauge groups. These representations of the Hubbard operator can be used to incorporate strong Hund's interactions in multielectron atoms as a constraint. We show how this method can be combined with the SP(N) group to yield a locally supersymmetric large-N formulation of the t-J model.