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

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