Classical and quantum radiation reaction in conformally flat spacetime

TL;DR

This paper explores the quantum and classical radiation reaction of a charged scalar particle in conformally flat spacetime, showing the classical limit correspondence and analyzing one-loop quantum corrections and their breakdown at quantum levels.

Contribution

It demonstrates the classical-quantum correspondence of radiation reaction in conformally flat spacetime and examines the effects of one-loop QED corrections, highlighting the breakdown of conformal equivalence at quantum level.

Findings

Classical radiation reaction matches quantum predictions as   0.

One-loop QED corrections alter the mass and Maxwell's equations in Model A.

Conformal equivalence breaks down at one-loop quantum corrections.

Abstract

We investigate the physics of a charged scalar particle moving in conformally flat spacetime with the conformal factor depending only on time in the framework of quantum electrodynamics (QED). In particular, we show that the radiation-reaction force derived from QED agrees with the classical counterpart in the limit $\hbar \to 0$ using the fact that to lowest order in $\hbar$ the charged scalar field theory with mass $m$ in conformally flat spacetime with conformal factor $\Omega(t)$, which we call Model B, is equivalent to that in flat spacetime with a time-dependent mass $m\Omega(t)$, which we call Model A, at tree level in this limit. We also consider the one-loop QED corrections to these two models in the semi-classical approximation. We find nonzero one-loop corrections to the mass and Maxwell's equations in Model A at order $\hbar^{-1}$. This does not mean, however, that the corresponding one-loop corrections in Model B are nonzero because the equivalence of these models through a conformal transformation breaks down at one loop. We find that the one-loop corrections vanish in the limit $\hbar \to 0$ in Model B.