Variational Resolution of the Abraham-Lorentz-Dirac Equation Pathologies

2025/05/04 by Duje Bonacci, Bonacci, Duje · 1 voice
Engineering · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Classical Physics (physics.class-ph) #Control and Stability of Dynamical Systems #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Quantum and Classical Electrodynamics #physics.class-ph #physics.soc-ph

paper · pdf · doi:10.48550/arxiv.2505.02870

openalex publication_date 2025/05/04 · arxiv published 2025/05/04 · openalex created_date 2025/10/10 · arxiv updated 2026/06/25 · openalex updated_date 2026/08/01

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.

Citations

• A Rigorous Derivation of Electromagnetic Self-force
• Analytic pulse design for selective population transfer in many-level quantum systems: optimizing the pulse duration
• Inducing complete population oscillations in systems with externally induced dipole moments
• Analytic pulse design for selective population transfer in many-level quantum systems: Maximizing the amplitude of population oscillations
• The motion of point particles in curved spacetime

Discussions

• Duje Bonacci: Variational Resolution of the Abraham-Lorentz-Dirac Equation Pathologies https://arxiv.org/abs/2505.02870 https://arxiv.org/pdf/2505.02870 https://arxiv.org/html/2505.02870 [bsky, 0 points, 1 comments]

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