2009/05/14 by Samuel E. Gralla, Abraham I. Harte, Robert M. Wald · 1 voice · 3 citations
Physics and Astronomy · #Experimental and Theoretical Physics Studies #Quantum and Classical Electrodynamics #Relativity and Gravitational Theory #gr-qc #hep-th #physics.class-ph
paper · pdf · doi:10.1103/physrevd.80.024031
openalex publication_date 2009/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
During the past century, there has been considerable discussion and analysis of the motion of a point charge in an external electromagnetic field in special relativity, taking into account ``self-force'' effects due to the particle's own electromagnetic field. We analyze the issue of ``particle motion'' in classical electromagnetism in a rigorous and systematic way by considering a one-parameter family of solutions to the coupled Maxwell and matter equations corresponding to having a body whose charge-current density Ja(\ensuremathλ) and stress-energy tensor Tab(\ensuremathλ) scale to zero size in an asymptotically self-similar manner about a worldline \ensuremathγ as \ensuremathλ\ensuremath→0. In this limit, the charge, q, and total mass, m, of the body go to zero, and q/m goes to a well-defined limit. The Maxwell field Fab(\ensuremathλ) is assumed to be the retarded solution associated with Ja(\ensuremathλ) plus a homogeneous solution (the ``external field'') that varies smoothly with \ensuremathλ. We prove that the worldline \ensuremathγ must be a solution to the Lorentz force equations of motion in the external field Fab(\ensuremathλ=0). We then obtain self-force, dipole forces, and spin force as first-order perturbative corrections to the center-of-mass motion of the body. We believe that this is the first rigorous derivation of the complete first-order correction to Lorentz force motion. We also address the issue of obtaining a self-consistent perturbative equation of motion associated with our perturbative result, and argue that the self-force equations of motion that have previously been written down in conjunction with the ``reduction of order'' procedure should provide accurate equations of motion for a sufficiently small charged body with negligible dipole moments and spin. (There is no corresponding justification for the non-reduced-order equations.) We restrict consideration in this paper to classical electrodynamics in flat spacetime, but there should be no difficulty in extending our results to the motion of a charged body in an arbitrary globally hyperbolic curved spacetime.