Screened activity expansion for the pressure of a quantum multi-component plasma and consistency with the local charge neutrality

We consider a quantum multi-component plasma made of point charged particles interacting via the two-body Coulomb potential. Within the Feynman-Kac path integral representation of the system in terms of a classical gas of loops, we derive screened activity series for the pressure in the grand-canonical ensemble. The method is based on the Abe-Meeron summations which remove all long-range Coulomb divergences. Moreover, we show that the particle densities can be inferred from the diagrammatic series for the pressure, through partial differentiations with respect to suitable effective activities, consistently with the local charge neutrality. We briefly argue how these results can be used for including, in the equation of state at moderately low densities, the contributions of recombined entities made with three or more particles.