Covariant Feynman rules at finite temperature: Time-path formulation.

Abstract

A path-integral (time-path) formulation is used to derive Feynman rules for relativistic many-body systems at finite temperature and density. The generating functional of propagators is written in a form that involves evolution along contours in the complex time plane. Controversies regarding the factorization of this generating functional into separate contributions from real and imaginary times are resolved. The time paths are generalized to manifestly covariant form, and the distinction between evolution in the canonical and grand-canonical Heisenberg pictures is discussed. This unified path-integral approach produces manifestly covariant Feynman rules for both real and imaginary times, which were applied to hadronic field theories of hot, dense nuclear matter in an earlier paper.