Quantum corrections to the Larmor radiation formula in scalar electrodynamics

TL;DR

This paper calculates quantum corrections to the classical Larmor radiation formula in scalar electrodynamics, revealing non-local time effects and differences based on the type of vector potential used for acceleration.

Contribution

It introduces a first-order quantum correction to the Larmor formula within scalar QED, considering different acceleration scenarios and highlighting non-local temporal effects.

Findings

Quantum corrections differ for different acceleration scenarios.

Corrections are non-local in time, contrasting with classical predictions.

Quantum effects depend on the nature of the vector potential.

Abstract

We use the semi-classical approximation in perturbative scalar quantum electrodynamics to calculate the quantum correction to the Larmor radiation formula to first order in Planck's constant in the non-relativistic approximation, choosing the initial state of the charged particle to be a momentum eigenstate. We calculate this correction in two cases: in the first case the charged particle is accelerated by a time-dependent but space-independent vector potential whereas in the second case it is accelerated by a time-independent vector potential which is a function of one spatial coordinate. We find that the corrections in these two cases are different even for a charged particle with the same classical motion. The correction in each case turns out to be non-local in time in contrast to the classical approximation.