Classical Larmor formula through the Unruh effect for uniformly accelerated electrons

TL;DR

This paper demonstrates that the classical Larmor radiation formula for accelerated electrons can be derived from the quantum Unruh effect, showing their deep connection in the coaccelerated frame.

Contribution

It establishes a direct link between the classical Larmor formula and the quantum Unruh effect for uniformly accelerated charges, clarifying their relationship.

Findings

Larmor formula matches emission and absorption of Rindler photons.

Power and angular distribution are consistent with classical predictions.

Unruh effect is necessary to reproduce classical radiation in the quantum framework.

Abstract

We investigate the connection between the classical Larmor formula and the quantum Unruh effect by computing the emitted power by a uniformly accelerated charged particle and its angular distribution in the coaccelerated frame. We consider a classical particle accelerated with nonzero charge only for a finite period and then take the infinite-time limit after removing the effects due to the initial charging and final discharging processes. We show that the result found for the interaction rates agrees with previous studies in which the period of acceleration with nonzero charge was taken to be infinite from the beginning. We also show that the power and angular distribution of emission, which is attributed either to the emission or absorption of a Rindler photon in the coaccelerated frame, is given by the Larmor formula, confirming that, at tree level, it is necessary to take into account the Unruh effect in order to reproduce the classical Larmor radiation formula in the coaccelerated frame.