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

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Abstract

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 λ0Ψ0 + λ1Ψ1 + λ2Ψ2 + λ3Ψ3 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.

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  1. Institute of Physics, National Academy of Sciences of Belarus, 68 Nezavisimosti ave., Minsk, 220072, Belarus

    V. V. Kisel, E. M. Ovsiyuk, V. M. Red’kov & N. G. Tokarevskaya

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  1. V. V. Kisel
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  2. E. M. Ovsiyuk
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  3. V. M. Red’kov
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  4. N. G. Tokarevskaya
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Correspondence to V. M. Red’kov.

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Kisel, V.V., Ovsiyuk, E.M., Red’kov, V.M. et al. Maxwell equations in complex form, squaring procedure and separating the variables. Ricerche mat. 60, 1–14 (2011). https://doi.org/10.1007/s11587-010-0092-7

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