Effective dynamics of a classical point charge

TL;DR

This paper derives the effective dynamics of a classical point charge using a quantum-inspired formalism, revealing cutoff-dependent effects, acausality at small scales, and parallels with quantum anomalies and symmetry breaking.

Contribution

It introduces a new derivation of the point charge's effective Lagrangian within the closed time path formalism, highlighting cutoff effects and the emergence of acausality.

Findings

A cutoff-dependent linearized equation of motion is obtained.

No runaway trajectories are observed in the effective dynamics.

The radiation reaction force exhibits a pole similar to the Landau pole.

Abstract

The effective Lagrangian of a point charge is derived by eliminating the electromagnetic field within the framework of the classical closed time path formalism. The short distance singularity of the electromagnetic field is regulated by an UV cutoff. The Abraham-Lorentz force is recovered and its similarity to anomalies is underlined. The full cutoff-dependent linearized equation of motion is obtained, no runaway trajectories are found but the effective dynamics shows acausality if the cutoff is beyond the classical charge radius. The strength of the radiation reaction force displays a pole in its cutoff-dependence in a manner reminiscent of the Landau-pole of perturbative QED. Similarity between the dynamical breakdown of the time reversal invariance and dynamical symmetry breaking is pointed out.