Fermionic excitations at finite temperature and density

We study fermionic excitations in a hot and dense strongly interacting medium consisting of quarks and (pseudo-)scalar mesons. In particular, we use the two-flavor quark-meson model in combination with the functional renormalization group (FRG) approach, which allows to take into account the effects from thermal and quantum fluctuations. The resulting fermionic excitation spectrum is investigated by calculating the quark spectral function at finite temperature, quark chemical potential, and spatial momentum. This involves an analytic continuation from imaginary to real energies by extending the previously introduced analytically continued FRG method to the present case. We identify three different collective excitations in the medium: the ordinary thermal quark, the plasmino mode, and an ultrasoft "phonino" mode. The dispersion relations of these modes are extracted from the quark spectral function. When compared to corresponding results from an FRG-improved one-loop calculation, a remarkable agreement has been found.