Self-consistent approximations: application to a quasiparticle description of the thermodynamic properties of relativistic plasmas

We generalize the concept of conserving, Phi-derivable, approximations to relativistic field theories. Treating the interaction field as a dynamical degree of freedom, we derive the thermodynamical potential in terms of fully dressed propagators, an approach which allows us to resolve the entropy of a relativistic plasma into contributions from its interacting elementary excitations. We illustrate the derivation for a hot QED plasma of massless particles. We also discuss how the self-consistency of the treatment manifests itself into relationships between the contributions from interaction and matter fields.