Loop corrections in Minkowski spacetime away from equilibrium. Part II. Finite-time results

TL;DR

This paper calculates finite-time two-point correlation functions for massless scalar quantum fields in Minkowski spacetime away from equilibrium, identifying necessary counterterms and analyzing late-time behavior.

Contribution

It provides a detailed method for UV renormalization of unequal-time correlators with arbitrary initial conditions in Minkowski space, including new initial state counterterms.

Findings

Late-time correlations grow linearly or logarithmically depending on interaction strength.

UV divergences are canceled by specific counterterms, confirming the consistency of the approach.

No true IR issues are present despite divergences in the correlation functions.

Abstract

Loop corrections to finite-time correlation functions in quantum field theories away from equilibrium can be calculated using the in-in path integral approach. In this paper, we calculate the unequal-time two-point correlator for different massless self-interacting scalar quantum field theories on a Minkowski background, starting the field evolution at an arbitrary initial time. We find the counterterms that need to be added to UV-renormalize the result, including usual in-out counterterms in the dynamics and additional initial state counterterms that are required to cancel all UV divergences. We find that the late-time limit of the renormalized correlation function exhibits a linear or logarithmic growth in time, depending on whether the interaction strength is dimension-one or dimensionless, respectively. The late-time correlations match those obtained in our companion paper and, as shown there, the divergences do not indicate a real IR issue, consistent with what one would expect in Minkowski.