Covariant propagator of the Rarita-Schwinger field in the nuclear medium

A formalism for representing the fully relativistic propagator of the Rarita-Schwinger field in the nuclear medium is developed. Using a convenient basis for expanding the propagator it is shown that it can be represented by 40 energy and momentum dependent quantities which can be decomposed into a 2×2 and a 6×6 matrix. In this way calculations reduce to matrix multiplication. Using the presented formalism the full relativistically covariant contribution of the pion-nucleon loop to the isobar self energy and propagator in isospin-symmetric spin-saturated nuclear medium is computed. Utilizing this propagator the photoabsorption cross section on in-medium nucleons in the isobar region is calculated and the result compared with experimental data.