Thermal quantum electrodynamics of Coulomb fluids : path integral methods

We present a formulation of the theory of charges in equilibrium with the radiation field based on a joint functional representation, combining the Feynman-Kac-Ito path integral for the particles with the bosonic integral for photons. In this formalism cluster expansion techniques of classical statistical mechanics become operative.They provide an alternative to the usual Feynman diagrammatics in many-body problems, which is not perturbative with respect to the coupling constant. As an application we show that the effective Coulomb interaction between quantum charges is partially screened by thermalized photons at large distances as the result of a subtle conspiracy between matter and field Planck constants.