Maxwell equations in matrix form, squaring procedure, separating the variables, and structure of electromagnetic solutions

Details Maxwell equations in matrix form, squaring procedure, separating the variables, and structure of electromagnetic solutions Maxwell equations in matrix form, squaring procedure, separating the variables, and structure of electromagnetic solutions

2009-06-08

arxiv.org/abs/0906.1434v1

Ric. Mat.60: 1-14,2011

Physics

Mathematical Physics

26 pages 16 International Seminar NCPC, May 19-22, 2009, Minsk, Belarus

Scientific paper

10.1007/s11587-010-0092-7

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.

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