Algebraic description of the Maxwell field singularity in a neighbourhood of a multipole particle
Jerzy Kijowski and Marcin Koscielecki
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Submission date: 03. Mar. 2000
published in: Reports on mathematical physics, 47 (2001) 3, p. 301-311
DOI number (of the published article): 10.1016/S0034-4877(01)80045-8
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In paper  mathematical self-consistency of a new theory of interacting "electromagnetic field + pointlike particles" system was analyzed. It was proved that the the initial value problem for both field and particles is well posed. For that purpose the asymptotic behaviour of the field in a neighbourhood of the particle was necessary. It was obtained using symbolic calculus package based on MATHEMATICA. For purposes of an extended theory, where particles may get polarization due to interaction, or may carry an angular momentum (spin) the above description of the asymptotic field near to particles is not sufficient. In the present paper we propose a different algorithm, which enables us to solve the problem in a much simpler way. To implement practically our algorithm we have used packages of symbolic calculus of the program MAPLE V.
 H. P. Gittel, J. Kijowski, E. Zeidler:The Relativistic Dynamics of the Combined Particle-Field System in Nonlinear Renormalized Electrodynamics, Comm. Math. Phys. 198 (1998) p. 711 - 736