The Riemann-Silberstein vector in the Dirac algebra

Shahen Hacyan


It is shown that the Riemann-Silberstein vector, defined as ${\bf E} + i{\bf B}$, appears naturally in the $SL(2,C)$ algebraic representation of the electromagnetic field. Accordingly, a compact form of the Maxwell equations is obtained in terms of Dirac matrices, in combination with the null-tetrad formulation of general relativity. The formalism is fully covariant; an explicit form of the covariant derivatives is presented in terms of the Fock coefficients.


Maxwell equations; Dirac matrices algebra; spinors

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Revista Mexicana de Física

ISSN: 0035-001X

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