The Haldane bosonisation scheme and metallic states of interacting fermions in d spatial dimensions

We consider the Haldane bosonisation scheme in d spatial dimensions as applied to a realistic model of interacting fermions in d=2 and unequivocally demonstrate failure of this scheme in d > 1, specifically in d=2. In addition to tracing back this failure to its origin, we show that {\sl nothing} as regards the true metallic state of the model under consideration is known with any degree of certainty.Comment: 20 pages, no figure

Dynamical correlation functions expressed in terms of many-particle ground-state wavefunction; the dynamical self-energy operator

We present the explicit expressions for the (regularized) terms in the large-epsilon asymptotic series of in particular the self-energy operator pertaining to arbitrary systems of interacting spin-s fermions in d spatial dimensions and deduce a variety of exact results concerning the general properties of this operator. We give especial attention to systems of spin-1/2 fermions in d=3 interacting through the Coulomb potential. [Short Abstract]Comment: 119 pages, 6 postscript figures. Brought the text in conformity with the published version, and corrected the coefficients of A'(0) and A_s'(0) in appendix