Quantum Scalar-Field Propagator in a Stochastic Gravitational-Plane Wave

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 ω4γ−1 (0≤γ<1), then the equal-time propagator of the scalar field behaves as p−11−γ for large momenta. We discuss models of quantum-field theory where such anomalous behavior can appear.