Supersymmetric Hubbard operators

We develop a supersymmetric representation of the Hubbard operator which unifies the slave boson and slave fermion representations into a single $U\left(1\right)\mathrm{}\times SU\left(1\mathrm{}|1\right)$ gauge theory, a group with larger symmetry than the product of two $U\left(1\right)\mathrm{}$ 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 $\mathrm{SP}\left(N\right)\mathrm{}$ group to yield a locally supersymmetric large-$N$ formulation of the $t-J$ model.