A FUNCTIONAL INTEGRAL APPROACH TO THE THERMODYNAMICS OF THE σ-ω MODEL

Abstract

We study the σ-ω model for nuclear matter at finite temperature and density in the functional integral approach. Particular emphasis is put on the treatment of the degrees of freedom of the massive vector meson. Various ways to calculate the grand partition function for free massive vector particles are presented. Then we show how field theories of two mutually interacting fields can be alternatively formulated in terms of a theory containing one free field and a nonlocal self-interaction of the other field. For a perturbative expansion in powers of the coupling constant and in the mean-field approximation, this formulation gives the same results as the standard treatment, e.g., the loop-expansion scheme of the effective potential. However, in contrast to the latter, the mean-field approximation is now obtained in a very simple and physically obvious way which closely resembles the analogous derivation for statistical-mechanical systems. We apply our alternative formulation to the case of scalar and massive vector particles interacting with another field. Combining both cases and taking the nucleon field as the interaction partner, we finally arrive at the grand partition function for the σ-ω model in mean-field approximation.