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New Equation of Motion for Classical Charged Particles

Mo, Tse Chin and Papas, C. H. (1971) New Equation of Motion for Classical Charged Particles. Physical Review D, 4 (12). pp. 3566-3571. ISSN 2470-0010. doi:10.1103/PhysRevD.4.3566.

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With the intuitive new ideas that (1) in classical electrodynamics, radiation reaction should be expressible by the external field and the charge's kinematics, (2) a charge experiences, in addition to the Lorentz forces, another "small" external force e_1F^(μλ)̇u_λ proportional to its acceleration, and (3) inertia plus radiation is balanced by these two external forces, we propose the new equation of motion, ṁu^μ − ((2e^3)/3m)F^(λα)_(ext)̇u_λu_αu^μ = eF^(μλ)_(ext)u_λ + e_1F^(μλ)_(ext)̇u_λ, where mass conservation requires e_1 = (2e^3)/3m. (The particle's spin is not considered in this work.) This equation for a classical charge is free from all the well-known difficulties of the Lorentz-Dirac equation. It conserves energy and momentum in a modified form in which the energy-momentum tensor contains a part t^(μν)(x) made of a new field-charge interaction φ^μ(x), in addition to the conventional "local" part made of F^(μν)_(ret)(x) and F^(μν)_(ext)(x) only, and therefore it no longer satisfies the conventional "local" conservation laws. It predicts correct radiation damping, as demonstrated here by applying it to various cases of basic physical importance. Also, it implies that a massless particle follows a null geodesic and cannot interact with the electromagnetic field whether it be charged or not; this implication may add a new degree of freedom to the charge-conservation law.

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Additional Information:© 1971 American Physical Society. (Received 15 March 1971) The authors wish to thank Professor R. P. Feynman for enlightening discussions during this work. Also we thank Professor R. V. Langmuir, Professor J. Mathews, and Professor R. L. Walker for their comments; and Professor J. K. Knowles and Professor E. Sternberg for the proof included in the Appendix. Support from the U. S. Air Force Office of Scientific Research under Grant No. AFOSR-70-1935 is gratefully acknowledged.
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Air Force Office of Scientific Research (AFOSR)AFOSR-70-1935
Issue or Number:12
Record Number:CaltechAUTHORS:20170814-120616863
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80356
Deposited By: George Porter
Deposited On:14 Aug 2017 20:10
Last Modified:15 Nov 2021 19:30

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