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Symmetric and Asymmetric Tensors of the Electromagnetic Field

Yurii A. Spirichev

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Abstract

It is shown that the canonical antisymmetric tensor of the electromagnetic field can be associated with symmetric and asymmetric tensors, which are derived from decomposition of the antisymmetric tensor of general form into its elements: symmetric and antisymmetric parts. These tensors contain additional information about the electromagnetic field. d'Alembert wave equations for electromagnetic potential and derivatives of Lorenz gauge condition follow from antisymmetric tensor and Navier-Stokes dynamic equation for the electromagnetic potential follow from symmetric tensor. A harmonized system of field equations, including Maxwell's equations, follows from these three tensors.

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What this paper is about

It is shown that the canonical antisymmetric tensor of the electromagnetic field can be associated with symmetric and asymmetric tensors, which are derived from decomposition of the antisymmetric tensor of general form into its elements: symmetric and antisymmetric parts. These tensors contain additional information about the electromagnetic field. d'Alembert wave equations for electromagnetic potential and derivatives of Lorenz gauge condition follow from antisymmetric tensor and Navier-Stokes dynamic equation for the electromagnetic potential follow from symmetric tensor. A harmonized system of field equations, including Maxwell's equations, follows from these three tensors.

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Available abstract

It is shown that the canonical antisymmetric tensor of the electromagnetic field can be associated with symmetric and asymmetric tensors, which are derived from decomposition of the antisymmetric tensor of general form into its elements: symmetric and antisymmetric parts. These tensors contain additional information about the electromagnetic field. d'Alembert wave equations for electromagnetic potential and derivatives of Lorenz gauge condition follow from antisymmetric tensor and Navier-Stokes dynamic equation for the electromagnetic potential follow from symmetric tensor. A harmonized system of field equations, including Maxwell's equations, follows from these three tensors.

Key concepts: Antisymmetric tensor, Lanczos tensor, Electromagnetic tensor, Antisymmetric relation, Electromagnetic field, Symmetric tensor, Physics, Tensor (intrinsic definition)

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