Retarded-advanced N-point Green functions in thermal field theories

Abstract

The general relationship between a retarded-advanced Green function of the real time formalism and analytical continuations of the imaginary time amplitude is obtained via perturbation theory. A 4-point RA function is, at most, a linear combination of three analytical continuations, and a 5-point RA function of seven continuations. The RA functions are written as the sum of one analytical continuation plus discontinuities across single momentum-transfer variables. These discontinuities correspond to process where particles are on-shell in an intermediate state with a thermal statistical weight. For the 3-point function, the difference between the real parts od two different analytical continuations is a double discontinuity. This is expressed in terms of three one-particle decay amplitudes. Feynman rules in the (R, A) basis introduce a new feature, the flow of infinitesimal ϵ, which obeys the Kirchoff laws.