A geometric analysis of the Maxwell field in a vicinity of a multipole particle and new special functions

Details A geometric analysis of the Maxwell field in a vicinity of a multipole particle and new special functions A geometric analysis of the Maxwell field in a vicinity of a multipole particle and new special functions

2007-08-16

arxiv.org/abs/0708.2174v1

J. Geom. Phys. 59 (2009) 693-709 (slightly shortened and modified version, slightly changed title)

Physics

Classical Physics

33 pages, LaTeX file

Scientific paper

10.1016/j.geomphys.2009.02.007

A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies considerably the equations. The solution is given in terms of a series, where a new family of special functions arises in a natural way. Singular behaviour of the field near to the particle may be analyzed this way up to an arbitrary order. Application to the self-interaction problems in classical electrodynamics is discussed.

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