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A New Form of the Antisymmetric Tensor and the Electromagnetic Field Equations

Yurii A. Spirichev

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Abstract

A new form of the equivalent representation of the canonical antisymmetric tensor of the electromagnetic field is described. This form of representation is based on the decomposition of an asymmetric tensor of a general form into a symmetric and antisymmetric part. It follows from this expansion that the canonical antisymmetric tensor of the electromagnetic field can be equivalently represented as the difference between an asymmetric tensor of general form and a symmetric tensor. Then Maxwell's equations can be written in the form of four-dimensional divergences of these tensors. From this representation, in addition to the Maxwell equations, new equations of the electromagnetic field also follow, expanding knowledge of it. One of these equations is the equation of motion of the electromagnetic field in the form of the dynamic Navier-Stokes equation.

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What this paper is about

A new form of the equivalent representation of the canonical antisymmetric tensor of the electromagnetic field is described. This form of representation is based on the decomposition of an asymmetric tensor of a general form into a symmetric and antisymmetric part. It follows from this expansion that the canonical antisymmetric tensor of the electromagnetic field can be equivalently represented as the difference between an asymmetric tensor of general form and a symmetric tensor. Then Maxwell's equations can be written in the form of four-dimensional divergences of these tensors. From this representation, in addition to the Maxwell equations, new equations of the electromagnetic field also follow, expanding knowledge of it. One of these equations is the equation of motion of the electromagnetic field in the form of the dynamic Navier-Stokes equation.

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Available abstract

A new form of the equivalent representation of the canonical antisymmetric tensor of the electromagnetic field is described. This form of representation is based on the decomposition of an asymmetric tensor of a general form into a symmetric and antisymmetric part. It follows from this expansion that the canonical antisymmetric tensor of the electromagnetic field can be equivalently represented as the difference between an asymmetric tensor of general form and a symmetric tensor. Then Maxwell's equations can be written in the form of four-dimensional divergences of these tensors. From this representation, in addition to the Maxwell equations, new equations of the electromagnetic field also follow, expanding knowledge of it. One of these equations is the equation of motion of the electromagnetic field in the form of the dynamic Navier-Stokes equation.

Key concepts: Antisymmetric tensor, Electromagnetic tensor, Lanczos tensor, Antisymmetric relation, Electromagnetic field, Maxwell's equations in curved spacetime, Tensor (intrinsic definition), Symmetric tensor

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