Variational Resolution of the Abraham-Lorentz-Dirac Equation Pathologies
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.
Cite
@article{arxiv.2505.02870,
title = {Variational Resolution of the Abraham-Lorentz-Dirac Equation Pathologies},
author = {Duje Bonacci},
journal= {arXiv preprint arXiv:2505.02870},
year = {2025}
}
Comments
PRL style paper, recently submitted. 5 pages of the core derivations and discussion and 3 pages of appendices. Al comments welcome. Updated version with some clarified argumentation in the appendices and some additional experimentally relevant references added