Maxwell equations in matrix form, squaring procedure, separating the variables, and structure of electromagnetic solutions
Mathematical Physics
2011-09-28 v1 High Energy Physics - Theory
math.MP
Abstract
The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in vacuum is investigated within the matrix formalism. The matrix form of electrodynamics includes three real 4 \times 4 matrices. Within the squaring procedure we construct four formal solutions of the Maxwell equations on the base of scalar Klein -- Fock -- Gordon solutions. The problem of separating physical electromagnetic waves in the linear space \lambda_{0}\Psi^{0}+\lambda_{1}\Psi^{1}+\lambda_{2}\Psi^{2}+ lambda_{3}\Psi^{3} is investigated, several particular cases, plane waves and cylindrical waves, are considered in detail.
Keywords
Cite
@article{arxiv.0906.1434,
title = {Maxwell equations in matrix form, squaring procedure, separating the variables, and structure of electromagnetic solutions},
author = {V. V. Kisel and E. M. Ovsiyuk and V. M. Red'kov and N. G. Tokarevskaya},
journal= {arXiv preprint arXiv:0906.1434},
year = {2011}
}
Comments
26 pages 16 International Seminar NCPC, May 19-22, 2009, Minsk, Belarus