Self-force with a stochastic component from radiation reaction of a scalar charge moving in curved spacetime

Abstract

We give a quantum field theoretical derivation of the scalar Abraham-Lorentz-Dirac (ALD) equation and the self-force for a scalar charged particle interacting with a quantum scalar field in curved spacetime. We regularize the causal Green's function using a quasi-local expansion in the spirit of effective field theory and obtain a regular expression for the self-force. The scalar ALD equation obtained in this way for the classical motion of the particle checks with the equation obtained by Quinn earlier [1]. We further derive a scalar ALD-Langevin equation with a classical stochastic force accounting for the effect of quantum fluctuations in the field, which causes small fluctuations on the particle trajectory. This equation will be useful for the study of stochastic motion of charges under the influence of both quantum and classical noise sources, derived either self-consistently (as done here) or put in by hand (with warnings). We show the possibility of secular effects from such stochastic influences on the trajectory that may impact on the present calculations of gravitational waveform templates.

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

“…Most of the treatment here parallels that in [13], which the reader is referred to for more details. We use units where c = G = 1, unless otherwise stated, and use the conventions of Misner, Thorne, and Wheeler [16] with signature (−, +, +, +).…”

“…This approach is taken in [5] for deriving the ALD equations in flat spacetime and is easily extended to motions in a curved spacetime [13] since the ultraviolet divergence is local in origin.…”

“…This is the usual divergence that results from considering interactions between a point-particle and arbitrarily high modes of a quantum field. We use the regularization introduced in [5] (in flat spacetime) and extended to scalar particle dynamics in curved spacetimes in [13].…”

“…This approach can be applied to the relation between Unruh radiation and ordinary radiation in accelerating detectors (see [6,11,12]). In a previous paper [13] we use the world line influence functional approach to obtain the equations of motion for a scalar charge coupled to a quantum scalar field in a curved spacetime. Our results for the classical motion agree with Quinn [14].…”

“…It must be regularized to obtain a finite and unambiguous self-force. We use a method introduced and developed in [5,13] that is inspired by effective field theory, which provides a natural way to quickly identify and renormalize this divergence. A high energy scale is introduced into the dynamics so that certain criteria on the magnitude of this scale and others must be met in order to have a dynamics consistent with our first principles derivations of (semi-classical) equations.…”