What is it about?
Symbolic computation provides excellent tools for the analysis and manipulation of the physical quantities involved in many-bodied systems. Analytical derivations are extremely valuable but not feasible to perform manually. Presented are algorithms expressed in the Maple symbolic computation system which map the relativistic time delays, the Liénard-Wiechert potentials and their resulting forces into equivalent formulations expressed in terms of only one time variable. Maple was used to expand each of the resulting expressions in a power series in 1/c to a high-order and to sum these series beyond their radius of convergence by the method of Padé rational function approximations.
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Why is it important?
This paper shows how to use the Maple computer algebra system how to make 1/c expansions of retarded and advanced Liénard=Wiechert potentials. It also shows the equivalence of the retarded potential of particle i acting on particle j with the advanced potential of particle j acting on i. This allowed is to rewrite the Fokker-Wheeler-Feynman time-symmetric theory in terms of retarded potentials only. This demonstrates that this theory can be made causal after all.
Perspectives
This puts the Darwin Lagrangian and the Breit Hamiltonian on a firm footing. It also allows to contemplate getting solutions to the 2-body Dirac equation. A by-product of this theory was in modeling MEV energy resonances of heavy-ion collisions known as the 'Darmstadt Monster'.
Dr Tony Cyril Scott
RWTH-Aachen University
Read the Original
This page is a summary of: Resolution of many particle electrodynamics by symbolic manipulation, Computer Physics Communications, January 1989, Elsevier,
DOI: 10.1016/0010-4655(89)90009-x.
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