On radiation reaction and the [x,p ] commutator for an accelerating charge

TL;DR

This paper explores the relationship between radiation reaction forces and quantum commutation relations for an accelerating charge, emphasizing the importance of relativistic effects in maintaining the canonical commutation relation.

Contribution

It demonstrates that the full relativistic radiation reaction must be considered to preserve the [x,p]=iħ commutation relation for an accelerating electron.

Findings

Full relativistic radiation reaction is necessary for consistent commutation relations.

The relativistic radiation reaction term aligns with the expected quantum mechanical behavior.

The study clarifies the connection between radiation forces and quantum operators under acceleration.

Abstract

We formally state the connection between the relativistic part of the radiation reaction and the Poynting Robertson force term, $-Rv/c^2$, where $R$ is power radiated. Then we address the question, does $[x,p]=i \hb$ for an accelerating charge ? The full radiation reaction term is used, which includes the relativistic term (von Laue vector.). We show that the full relativistic radiation reaction term must be taken into account if a commutation relation between $x$ and $p$ is to hold for an electron under uniform acceleration, consistent with the expectation values of $x^2$ and $p^2$.