Conformal behavior of the Lorentz-Dirac equation and Machian particle dynamics

It is shown that the self-interaction force on a pointlike electric charge in curved space-time has conformal weight −1. Motivated by this result, a conformally covariant version of the Lorentz–Dirac equation is presented, where the particle mass is treated as a position- and time-dependent quantity. This feature suggests that the underlying dynamics is Machian.