The Propagator Matrix Reloaded

TL;DR

This paper clarifies how to correctly incorporate interactions in initial conditions for quantum field theories in non-trivial backgrounds, showing that interactions cannot be ignored at finite temperature.

Contribution

It provides a clear derivation of a formalism that includes interactions in initial conditions for quantum field theories in curved spacetimes and finite temperature.

Findings

Interactions in initial conditions are essential at finite temperature.

Quantum field theories are not free in the infinite past under these conditions.

The formalism corrects misconceptions in existing literature.

Abstract

The standard way to perform calculations for quantum field theories involves the S-matrix and the assumption that the theory is free at past and future infinity. However, this assumption may not hold for field theories in non-trivial backgrounds such as curved spacetimes or finite temperature. In fact, even in the simple case of finite temperature Minkowski spacetime, there are a lot of misconceptions and confusion in the literature surrounding how to correctly take interactions into account when setting up the initial conditions. The objective of this work is to clear up these misconceptions and provide a clean and simple derivation of a formalism which includes interactions in the initial conditions and assesses whether or not it is legitimate to ignore them. The ultimate conclusion is that we cannot ignore them: quantum field theories at finite temperature are not free in the infinite past.