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

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.

31 pages, 5 figures. Added discussion on resummation in in-out vs. WW. Matches published version

References in corpus (4)

• Condensates and quasiparticles in inflationary cosmology: mass generation and decay widths
• On the Perturbative Stability of Quantum Field Theories in de Sitter Space
• Loop corrections in Minkowski spacetime away from equilibrium. Part II. Finite-time results
• Infrared dressing in real time: emergence of anomalous dimensions

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