Pressure and Spectral Density of Fermions at Finite Temperature

The pressure of a fermion system is expressed as a mass integral over the full two-point spectral densities within the real time formalism by use of the Keldysh representation for the propagators. This simplifies the calculation significantly and allows a Dyson resummation. The expression is used to demonstrate that potential infrared divergences are rendered harmless. We apply it to check the pressures of an ideal fermion gas and of a chemically non-equilibrated quantum chromodynamics plasma.