Basic systems of orthogonal functions for space-time multivectors

Details Basic systems of orthogonal functions for space-time multivectors Basic systems of orthogonal functions for space-time multivectors

2005-01-20

arxiv.org/abs/hep-th/0501161v2

Advances in Applied Clifford Algebras 15, No. 1, 27-53 (2005)

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, published version (correction of one misprint)

Scientific paper

Space-time multivectors in Clifford algebra (space-time algebra) and their application to nonlinear electrodynamics are considered. Functional product and infinitesimal operators for translation and rotation groups are introduced, where unit pseudoscalar or hyperimaginary unit is used instead of imaginary unit. Basic systems of orthogonal functions (plane waves, cylindrical, and spherical) for space-time multivectors are built by using the introduced infinitesimal operators. Appropriate orthogonal decompositions for electromagnetic field are presented. These decompositions are applied to nonlinear electrodynamics. Appropriate first order equation systems for cylindrical and spherical radial functions are obtained. Plane waves, cylindrical, and spherical solutions to the linear electrodynamics are represented by using the introduced orthogonal functions. A decomposition of a plane wave in terms of the introduced spherical harmonics is obtained.

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