Sign of the Feynman propagator and irreversibility

For the interacting Feynman propagator delta(F,int)(x,y) of scalar electrodynamics, we show that the sign property, Rei delta(F,int) >= 0, may hinge on the reversibility of time evolution. In contrast, Imi delta(F,int) is indeterminate. When we switch to reduced dynamics under the weak coupling approximation, the positive semidenite sign of Rei delta(F,int) is generally lost, unless we impose severe restrictions on the Kraus operators that govern time evolution. With another approximation, the rotating wave approximation, we may recover the sign by restricting the test functions to exponentials under certain conditions.

Automated summary

In this paper, we investigate the sign property of the interacting Feynman propagator in scalar electrodynamics, and find that it may depend on the reversibility of time evolution. The positive semidenite sign is generally lost under the weak coupling approximation, but can be recovered by restricting the test functions under certain conditions using the rotating wave approximation.