Covariant description of dynamical processes in relativistic nuclear matter.

Abstract

We report results of covariant calculations of density-dependent polarization processes in relativistic nuclear matter. We consider the polarization induced by those mesons that play an important role in the boson-exchange model of nuclear forces (\ensuremath{\sigma},\ensuremath{\pi},\ensuremath{\rho},\ensuremath{\omega}). After obtaining the polarization operators, we construct the propagators for these mesons. The covariant nature of the calculation greatly clarifies the structure of the polarization operators and associated Green's functions. (In addition to the meson momentum, these quantities depend upon another four-vector, ${\mathrm{\ensuremath{\eta}}}^{\mathrm{\ensuremath{\mu}}}$, that describes the uniform motion of the medium.) In the case of the pion, we show that the same results are obtained for pseudovector or pseudoscalar coupling to the nucleon, if the associated Lagrangians are related by chiral transformations. Of particular interest are the extremely large values found for the polarization operators of the omega and sigma mesons. It is also found that the coupling of the sigma and omega fields through the polarization process is also extremely large. (Because of these results one cannot usefully consider the sigma and omega fields as independent degrees of freedom in nuclear matter.) We describe methods for reorganizing the calculation of ring diagrams in which we group those diagrams that exhibit strong cancellations. We also comment on the implication of our results for nuclear structure studies.