Causality in relativistic many body theory

The stability of the nuclear matter system with respect to density fluctuat ions is examined exploring in detail. the pole structure of the electronucl ear response functions. Making extensive use of the method of dispersion in tegrals we calculate the full polarization propagator not only for real ene rgies in the spacelike and timelike regime but also in the whole complex en ergy plane. The latter proved to be necessary in order to identify unphysic al causality violating poles which are the consequence of the neglect of va cuum polarization. On the contrary it is shown that Dirac sea effects stabi lize the nuclear matter system, shifting the unphysical pole from the upper energy plane back to the real axis. The exchange of strength between these real timelike collective excitations and the spacelike energy regime is sh own to lead to a reduction of the quasielastic peak as it is seen in electr on scattering experiments. Neglecting vacuum polarization one also obtains a reduction of the quasielastic peak but in this case the strength is partl y shifted to the causality violating pole mentioned above which consequentl y cannot be considered as a physical reliable result. Our investigation of the response function in the energy region above the threshold of nucleon-a ntinucleon production leads to another remarkable result. Treating the nucl eons as pointlike Dirac particles we show that far any isospin-independent NN interaction random phase approximation correlations provide a reduction of the production amplitude for pp pairs by a factor of 2. [S0556-2813(99)0 5905-1].