Variational Resolution of the Abraham-Lorentz-Dirac Equation Pathologies

TL;DR

This paper introduces a variational approach based on proper-time to resolve the classical Abraham-Lorentz-Dirac equation's pathologies, such as runaway solutions and non-causality, without regularization.

Contribution

It develops a novel variational framework that derives the ALD equation from first principles, eliminating self-force issues and clarifying gauge invariance.

Findings

Elimination of runaway solutions and non-causal behavior.

Derivation of minimal coupling from first principles.

Establishment of gauge invariance as a consequence of the variational structure.

Abstract

We propose a structural variational resolution of the Abraham-Lorentz-Dirac (ALD) pathologies. By deriving the Variational Kinematic Constraint (VKC) and the Variational Dynamics Constraint (VDC) from the particle's proper-time perspective, we show that self-induced variations are forbidden and dynamics arise solely from first-order proper-time variations of external fields. Consequently, self-force terms are excluded at the variational level, eliminating runaway solutions and non-causal behavior without regularization. Our framework further provides a first-principles derivation of minimal coupling and reveals gauge invariance as a necessary consequence of proper-time-based variational structure.