N-quantum approach to quantum field theory at finite T and $\mu$: the NJL model

Abstract

We extend the N-quantum approach to quantum field theory to finite temperature ($T$) and chemical potential ($\mu$) and apply it to the NJL model. In this approach the Heisenberg fields are expressed using the Haag expansion while temperature and chemical potential are introduced simultaneously through a generalized Bogoliubov transformation. Known mean field results are recovered using only the first term in the Haag expansion. In addition, we find that at finite T and in the broken symmetry phase of the model the mean field approximation can not diagonalize the Hamiltonian. Inclusion of scalar and axial vector diquark channels in the SU(2)${}_{rmf}$ $otimes$ SU(3)${}_{\mathrm{c}}$ version of the model can lead to a lowering of the vacuum energy density. We discuss how to go beyond the mean field approximation by including higher order terms in the Haag expansion.

Comments: 14 pages including 2 eps figures. Modified sentences on the lowering of the vacuum energy density