The uniform quantized electron gas revisited

In this work we continue and extend our recent work on the correlation energy of the quantized electron gas of uniform density at temperature $T=0$. As before we utilize the methods, properties, and results obtained by means of classical statistical mechanics. These were extended to quantized systems via the Feynman path integral formalism. The latter translates the quantum problem into a classical polymer problem in four dimensions. Again the well known RPA (random phase approximation) is recovered as a basic result which we then modify and improve upon. Here we will we focus upon thermodynamic self-consistency. Our numerical calculations exhibit a remarkable agreement with well known results of a standard parametrization of Monte Carlo correlation energies.