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On Tensors and Equations of the Electromagnetic Field

Yuriy A. Spirichev

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Abstract

It is shown that the electromagnetic field is completely described by an asymmetric tensor of the second rank, which is a four-dimensional derivative of the electromagnetic potential. This tensor can be decomposed into the canonical antisymmetric and the new symmetric EMF tensor. From this tensor, in the form of its complete divergence, the EMF equations follow. One of them is an electromagnetic analog of the Lame equation for an elastic medium. It is shown that the longitudinal waves of the divergence of the vector potential propagate at a speed greater than the speed of light and do not have a magnetic component.

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What this paper is about

It is shown that the electromagnetic field is completely described by an asymmetric tensor of the second rank, which is a four-dimensional derivative of the electromagnetic potential. This tensor can be decomposed into the canonical antisymmetric and the new symmetric EMF tensor. From this tensor, in the form of its complete divergence, the EMF equations follow. One of them is an electromagnetic analog of the Lame equation for an elastic medium. It is shown that the longitudinal waves of the divergence of the vector potential propagate at a speed greater than the speed of light and do not have a magnetic component.

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Available abstract

It is shown that the electromagnetic field is completely described by an asymmetric tensor of the second rank, which is a four-dimensional derivative of the electromagnetic potential. This tensor can be decomposed into the canonical antisymmetric and the new symmetric EMF tensor. From this tensor, in the form of its complete divergence, the EMF equations follow. One of them is an electromagnetic analog of the Lame equation for an elastic medium. It is shown that the longitudinal waves of the divergence of the vector potential propagate at a speed greater than the speed of light and do not have a magnetic component.

Key concepts: Electromagnetic tensor, Antisymmetric tensor, Electromagnetic field, Tensor (intrinsic definition), Lanczos tensor, Physics, Divergence (linguistics), Maxwell stress tensor

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