Functional Treatment Of The Meson Exchange Currents.

Two alternative formulations of the meson exchange currents (MEC) and of the associated response to an electromagnetic field are derived in the path integral framework for a system of nucleons and pion with either a pseudoscalar or a pseudovector interaction. In the first approach, by integrating out the pionic and the electromagnetic fields configurations, we deduce a fermionic effective action SeffF leading, in conventional perturbation theory, to the standard expression for the MEC. In the second one, instead, by integrating out the fermions and electromagnetic fields configuration, we obtain a bosonic effective action SeffB. We evaluate the functional generator ZC associated to the latter in the stationary phase approximation (mean field) plus leading order quantum fluctuations. The corresponding response, most suited to deal with the physics at high energies and densities, includes RPA dressed pion propagators, the exchange interaction between the particle and the hole, the full variety of the two particles-two holes diagrams as well as the so-called bubbles into bubble (to leading order) and the nucleon self-energy (to infinite order). Thus the functional expansion, closely related to the loop expansion of the field theory, yields an unambiguous prescription for the diagrams to be kept in order to achieve a consistent many-body description of the response of a system of pions and nucleons to an electromagnetic field.