Radiation reaction in quantum mechanics

TL;DR

This paper examines the classical limit of radiation reaction in quantum mechanics, revealing that the Lorentz-Dirac formula is incorrect in certain scenarios and proposing a corrected approach based on the Larmor formula.

Contribution

It identifies limitations of the Lorentz-Dirac radiation reaction formula and proposes a more accurate classical limit using the Larmor formula for energy loss.

Findings

Lorentz-Dirac formula predicts incorrect position shift in some cases

The correct classical limit aligns with the Larmor formula for energy loss

The discrepancy arises when acceleration is due to a time-independent potential

Abstract

The Lorentz-Dirac radiation reaction formula predicts that the position shift of a charged particle due to the radiation reaction is of first order in acceleration if it undergoes a small acceleration. A semi-classical calculation shows that this is impossible at least if the acceleration is due to a time-independent potential. Thus, the Lorentz-Dirac formula gives an incorrect classical limit in this situation. The correct classical limit of the position shift at the lowest order in acceleration is obtained by assuming that the energy loss at each time is given by the Larmor formula.