Derivation of the real-time formalism from first principles in thermal field theory

Abstract

By working out in detail simple and yet general enough examples, we compare the usual real time formalism (RTF) of thermal field theory and the exact formalism that follows from first principles and takes explicitly into account the vertical part of the time contour. We show how the RTF follows from the exact formalism when we consider correlation functions with at least one fixed real time argument. The so called “asymptotic condition” is shown to be irrelevant and the “n(k0) prescription” is automatically contained in the results. We then look at vacuum fluctuations and show that the exact formalism leads naturally to the imaginary time formalism.