Canonical approach to the propagation of elementary particles in a medium

Abstract

We discuss the canonical derivation of the Feynman rules for relativistic, real-time covariant calculations in field theory at finite temperature. The resulting rules are equivalent to the ones derived using the path-integral method, with the particular value zero for the time-path gauge parameter. The canonical approach complements the path-integral formulation in a way analogous to the relation between the operator and the path-integral formalisms in ordinary field theory. This is illustrated by a simple rederivation of the relations satisfied by the exact propagators of the theory. Special emphasis is given to formulate the results in a way readily useful for practical calculations, with particular attention to the connection between the effective action calculated with the Feynman rules and the classical field equations that are of interest for macroscopic physics. Several examples are provided to illustrate various aspects of the issues involved.