Electromagnetic and gravitational self-force on a relativistic particle from quantum fields in curved space

TL;DR

This paper derives quantum field theoretical equations for the self-force on relativistic particles due to electromagnetic and gravitational fields, incorporating quantum fluctuations and stochastic effects, with implications for gravitational wave signals.

Contribution

It provides a novel derivation of self-force equations from quantum fields in curved spacetime, including stochastic and noise-induced effects.

Findings

Regularization of divergent self-force using Green's function smearing

Derivation of Langevin equations with quantum fluctuation effects

Potential for noise-induced drift motions affecting gravitational waveforms

Abstract

We provide a quantum field theoretical derivation of the Abraham-Lorentz-Dirac (ALD) equation, describing the motion of an electric point charge sourcing an electromagnetic field, which back-reacts on the charge as a self-force, and the Mino-Sasaki-Tanaka-Quinn-Wald (MSTQW) equation describing the motion of a point mass with self-force interacting with the linearized metric perturbations caused by the mass off an otherwise vacuous curved background spacetime. We regularize the formally divergent self-force by smearing the direct part of the retarded Green's function and using a quasilocal expansion. We also derive the ALD-Langevin and the MSTQW-Langevin equations with a classical stochastic force accounting for the effect of the quantum fluctuations in the field, which causes small fluctuations on the particle trajectory. These equations will be useful for studying the stochastic motion of charges and small masses under the influence of both quantum and classical noise sources, derived either self-consistently or put in by hand phenomenologically. We also show that history-dependent noise-induced drift motions could arise from such stochastic sources on the trajectory that could be a hidden feature of gravitational wave forms hitherto unknown.