Quantum scalar field propagator in a stochastic gravitational plane wave

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 ${\omega }^{4\gamma -1}$ ($0\le \gamma <1$) 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.

arXiv comment14 pages,substantially revised version

References in corpus (18)

• Quantum Gravity at a Lifshitz Point
• Tests of general relativity with GW150914
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Spectral Dimension of the Universe
• Inflation and squeezed quantum states
• Stochastic Gravitational Wave Backgrounds
• Eikonal Quantum Gravity and Planckian Scattering
• Gravitational-wave cosmology across 29 decades in frequency
• Scattering at Planckian Energies
• Gravitons and Lightcone Fluctuations
• Dimension and Dimensional Reduction in Quantum Gravity
• Signatures of the Quantization of Gravity at Gravitational Wave Detectors
• Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data
• Lightcone fluctuations in flat spacetimes with nontrivial topology
• Gravitons and Lightcone Fluctuations II: Correlation Functions
• Spacetime foam: a review
• Propagating gravitons vs. dark matter in asymptotically safe quantum gravity
• Universal regular short distance behavior from an interaction with a scale invariant gravity