Functional integral mean field expansions for nuclear many fermion systems

We present a careful analysis of the auxiliary field functional integral formalism for many fermion systems. We examine the limiting procedure used in construction of such integrals and show that a wide flexibility exists with respect to the choice of the one-body field representation upon which mean field expansions are made. We demonstrate the utility of this flexibility in the context of the evaluation of the grand canonical partition function. We examine the zero order. RPA and certain higher-order terms. The above-mentioned flexibility is reflected in the dependence of the results on a trial two-body interaction, different choices of which produce Hartree, Fock, HartreeFock or other forms of the mean field expansions. A standard variational procedure selects the Hartree-Fock as the optimal choice. With this choice we find certain corrections to previously reported RPA contribution for the Hartree mean field. We also indicate the relevance of our formulation for the recent applications of the functional integral mean field approach to nuclear dynamical problems.