Maxwell equations in complex form, squaring procedure and separating the variables

The Riemann–Silberstein–Majorana–Oppenheimer complex approach to the Maxwell electrodynamics is investigated within the matrix formalism. Within the squaring procedure we construct four types of formal solutions of the Maxwell equations on the base of scalar D’Alembert solutions. General problem of...

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Bibliographic Details
Published in:Ricerche di matematica 2011-06, Vol.60 (1), p.1-14
Main Authors: Kisel, V. V., Ovsiyuk, E. M., Red’kov, V. M., Tokarevskaya, N. G.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Geometry
Mathematics
Mathematics and Statistics
Numerical Analysis
Probability Theory and Stochastic Processes
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Summary:The Riemann–Silberstein–Majorana–Oppenheimer complex approach to the Maxwell electrodynamics is investigated within the matrix formalism. Within the squaring procedure we construct four types of formal solutions of the Maxwell equations on the base of scalar D’Alembert solutions. General problem of separating physical electromagnetic solutions in the linear space λ 0 Ψ 0 + λ 1 Ψ 1 + λ 2 Ψ 2 + λ 3 Ψ 3 is investigated, the Maxwell equations reduce to a new form including parameters λ a . Several particular cases, plane waves and cylindrical waves, are considered in detail. Possible extension of the technique to a curved space–time models is discussed.
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-010-0092-7