2017•EUROPEAN RESEARCHOpen access

A NEW FORM OF THE ANTISYMMETRIC TENSOR AND THE COMPLETE SYSTEM OF EQUATIONS OF THE ELECTROMAGNETIC FIELD

Yuriy A. Spirichev

Open full text 0 citations

Abstract

а new form of the equivalent representation of the canonical antisymmetric tensor of the electromagnetic field is obtained.This form of representation is based on the decomposition of the 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 a 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.

Open-access reader

About this research paper

What this paper is about

а new form of the equivalent representation of the canonical antisymmetric tensor of the electromagnetic field is obtained.This form of representation is based on the decomposition of the 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 a 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.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

а new form of the equivalent representation of the canonical antisymmetric tensor of the electromagnetic field is obtained.This form of representation is based on the decomposition of the 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 a 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, Electromagnetic field, Maxwell stress tensor, Maxwell's equations in curved spacetime, Symmetric tensor, Tensor (intrinsic definition)

Related papers

Back to paper searchBrowse research topicsOriginal source
A NEW FORM OF THE ANTISYMMETRIC TENSOR AND THE COMPLETE SYSTEM OF EQUATIONS OF THE ELECTROMAGNETIC FIELD — Research Paper | ScholarLens