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

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 λ_{0}Ψ^{0}+λ_{1}Ψ^{1}+λ_{2}Ψ^{2}+ lambda_{3}Ψ^{3} is investigated, several particular cases, plane waves and cylindrical waves, are considered in detail.

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

References in corpus (2)

• Maxwell Equations in Complex Form of Majorana - Oppenheimer, Solutions with Cylindric Symmetry in Riemann S_{3} and Lobachevsky H_{3} Spaces
• Majorana-Oppenheimer approach to Maxwell electrodynamics in Riemannian space-time

Cited by in corpus (1)

• A new matrix representation of the Maxwell equations based on the Riemann-Silberstein-Weber vector for a linear inhomogeneous medium