The Riemann-Silberstein vector in the Dirac algebra

Shahen Hacyan

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arXiv · 1811.09684

The Riemann-Silberstein vector in the Dirac algebra

Shahen Hacyan

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Abstract

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 erivatives is presented in terms of the Fock coefficients.

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Shahen Hacyan. 2018-11-12. The Riemann-Silberstein vector in the Dirac algebra. https://arxiv.org/abs/1811.09684

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