Quantum scalar field propagator in a stochastic gravitational plane wave

TL;DR

This paper investigates how a stochastic gravitational plane wave affects the behavior of a scalar field propagator, revealing anomalous momentum dependence linked to the wave's spectral properties.

Contribution

It introduces a model connecting stochastic gravitational waves with scalar field propagator behavior, highlighting conditions for anomalous scaling in quantum field theory.

Findings

Scalar propagator scales as p^(-1/(1-γ)) at high momenta

Spectral spectrum influences the propagator's asymptotic behavior

Models of quantum field theory can exhibit such anomalous behavior

Abstract

A stochastic metric can appear in classical as well as in quantum gravity. We show that if the linearized stochastic Gaussian gravitational plane wave has the frequency spectrum $\omega^{4\gamma-1}$ ($0\leq \gamma<1$) then the equal-time propagator of the scalar field behaves as $p^{-\frac{1}{1-\gamma}}$for large momenta. We discuss models of quantum field theory where such anomalous behaviour can appear.