Uniformly Accelerated Charge in a Quantum Field: From Radiation Reaction to Unruh Effect

TL;DR

This paper develops a stochastic quantum field theory framework for uniformly accelerated charges, connecting radiation reaction, vacuum fluctuations, and the Unruh effect, and offers a causal, runaway-free semiclassical description.

Contribution

It introduces a novel stochastic approach to charge dynamics in quantum fields, deriving a causal Abraham-Lorentz-Dirac equation and linking classical and quantum phenomena.

Findings

Derived a modified Abraham-Lorentz-Dirac equation free of runaway solutions.

Established a stochastic model connecting radiation reaction and the Unruh effect.

Provided a derivation of the Unruh effect using worldline coordinates.

Abstract

We present a stochastic theory for the nonequilibrium dynamics of charges moving in a quantum scalar field based on the worldline influence functional and the close-time-path (CTP or in-in) coarse-grained effective action method. We summarize (1) the steps leading to a derivation of a modified Abraham-Lorentz-Dirac equation whose solutions describe a causal semiclassical theory free of runaway solutions and without pre-acceleration patholigies, and (2) the transformation to a stochastic effective action which generates Abraham-Lorentz-Dirac-Langevin equations depicting the fluctuations of a particle's worldline around its semiclassical trajectory. We point out the misconceptions in trying to directly relate radiation reaction to vacuum fluctuations, and discuss how, in the framework that we have developed, an array of phenomena, from classical radiation and radiation reaction to the Unruh effect, are interrelated to each other as manifestations at the classical, stochastic and quantum levels. Using this method we give a derivation of the Unruh effect for the spacetime worldline coordinates of an accelerating charge. Our stochastic particle-field model, which was inspired by earlier work in cosmological backreaction, can be used as an analog to the black hole backreaction problem describing the stochastic dynamics of a black hole event horizon.