Rules for diagrams in thermal field theories.

Abstract

Sets of rules are proposed that allow one to write down the amplitude associated with a diagram at temperature $T$ once the energy running around each loop has been summed over, in the imaginary-time formalism. Alternative forms are given: one is based on tree diagrams, another one on possible intermediate states. A close analogy to the $T=0$ case is obtained. The amplitude's analytic structure is explicit. A factorization property is found for the $N$-point imaginary-time Green functions.