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.