Basic systems of orthogonal functions for space-time multivectors |
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Authors: | Alexander A Chernitskii |
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Institution: | (1) Saint Petersburg Electrotechnical University, Prof. Popov str. 5, St. Petersburg, 197376, Russia |
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Abstract: | 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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