Non-perturbative behavior of the Pomeranchuk quantum phase transition of a nematic Fermi fluid

A nematic phase of an electron gas was predicted by Oganesyan et. al.[1] using a mean field approach by tuning the quadrupolar Landau paremeter $F_2$ to the Pomeranchuk quantum critical point at $F_2\sim-1$. We will present a study of the behavior at this QCP beyond the perturbative results of [1] using non- perturbative methods of higher dimensional bosonization. We extend the results on the Fermion residue calculated by Castro Neto and Fradkin for the Landau fermi liquid phase[2] to this case and present a calculation of the Fermion Green's Function at the critical point. [1] Oganesyan, V., Kivelson, S. A., and Fradkin, E., Phys. Rev. B. {\bf 64} 195109 (2001) [2] Castro Neto, A. H., Fradkin, E. H., Phys. Rev. B. {\bf 51} 4084 (1995)