Dispersion relations at finite temperature and density for nucleons and pions

We calculate the nucleonic and pionic dispersion relations at finite temperature T and non-vanishing chemical potentials $({\mu }_f)$ in the context of an effective chiral theory that describes the strong and electromagnetic interactions for nucleons and pions. The dispersion relations are calculated in the broken chiral symmetry phase, where the nucleons are massive and pions are taken as massless. The calculation is performed at lowest order in the energy expansion, working in the framework of the real time formalism of thermal field theory in the Feynman gauge. These one-loop dispersion relations are obtained at leading order with respect to T and ${\mu }_f$. We also evaluate the effective masses of the quasi-nucleon and quasi-pion excitations in thermal and chemical conditions as the ones of a neutron star.