Supersymmetric approach to the infinite U Hubbard Model

We present a preliminary discussion on the use of supersymmetric representation of the Hubbard operator which unifies the slave boson and slave fermion representations into a single $U(1)\times SU(1\mathrm{\mid }1)$ gauge theory to treat the physics of the infinite U Hubbard model. By looking for solutions to the Hamiltonian in which the spins can exist as both condensed ordered moments and as mobile charged carriers, we examine the possibility of a Nagaoka ferromagnetic phase at finite doping with a quantum critical point into the paramagnetic phase.