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

Classical and quantum radiation reaction in conformally flat spacetime