Radiation reaction for a massless charged particle

TL;DR

This paper develops effective equations of motion for a massless charged particle considering radiation back reaction, revealing unique divergence structures and higher-order dynamics compared to massive particles, with explicit corrections in homogeneous fields.

Contribution

It introduces the first derivation of effective equations for massless charged particles including radiation reaction, highlighting differences from massive cases and providing explicit radiative corrections.

Findings

Divergences in massless case are not all Lagrangian.

Effective equations are higher order than Lorentz-Dirac.

Explicit first radiative correction derived for homogeneous fields.

Abstract

We derive effective equations of motion for a massless charged particle coupled to the dynamical electromagnetic field having regard to the radiation back reaction. It is shown that unlike the massive case not all the divergences resulting from the self-action of the particle are Lagrangian, i.e. can be canceled out by adding appropriate counterterms to the original action. Besides, the order of renormalized differential equations governing the effective dynamics turns out to be greater than the order of the corresponding Lorentz-Dirac equation for a massive particle. For the case of homogeneous external field the first radiative correction to the Lorentz equation is explicitly derived via the reduction of order procedure.