Loop corrections in Minkowski spacetime away from equilibrium. Part I. Late-time resummations

TL;DR

This paper investigates the late-time behavior of loop corrections to unequal-time correlators in Minkowski spacetime, revealing secular growth and employing resummation techniques to understand their decay patterns.

Contribution

It introduces a late-time in-in path integral approach and develops the Weisskopf-Wigner resummation method for Minkowski correlators, providing exact exponentiation of secular growth.

Findings

Correlators exhibit linear or logarithmic growth depending on interaction dimension.

Resummation yields exponential or polynomial decay of correlators.

Results suggest universal late-time behavior based on interaction strength dimensions.

Abstract

Loop corrections to unequal-time correlation functions in Minkowski spacetime exhibit secular growth due to a breakdown of time-dependent perturbation theory. This is analogous to secular growth in equal-time correlators on time-dependent backgrounds, except that in Minkowski the divergences must not signal a real IR issue. In this paper, we calculate the late-time limit of the two-point correlator for different massless self-interacting scalar quantum field theories on a Minkowski background. We first use a late-time version of the in-in path integral starting in the vacuum of the free theory; in this limit, the calculation, including UV renormalization, reduces to that in in-out. We find linear or logarithmic growth in time, depending on whether the interaction strength is dimension-one or dimensionless, respectively. We next develop the Weisskopf-Wigner resummation method, that proceeds by demanding unitarity within a truncated Hilbert space, to calculate the resummed correlator and find that it gives an exact exponentiation of the late-time perturbative result. The resummed (unequal-time) correlator thus decays with an exponential or polynomial time-dependence, which is suggestive of `universal' behavior that depends on the dimensions of the interaction strength.