On the theory of vector field with a symmetric affinors. Real vector field in the framework of the standard methods

TL;DR

This paper develops a theoretical framework for real vector fields with symmetric affinors, addressing their physical existence, gauge invariance, and implications for classical electrodynamics, offering new insights into the structure of electromagnetic fields.

Contribution

It introduces a novel theory of real vector fields incorporating symmetric derived affinors, highlighting their physical significance and gauge properties within classical electrodynamics.

Findings

Classical electromagnetic fields include independent physical components beyond antisymmetric parts.

The proposed theory maintains gauge invariance despite explicit gauge-noninvariant constituents.

Probabilistic interpretation issues are manageable with standard methods in indefinite-metric frameworks.

Abstract

Attention is drawn to the mathematical equality of rights of symmetrical constituents derived affinor of a vector field in relation to its antisymmetric constituents. In this regard, raises the question not only of equitable accounting, but and mainly question of the real existence of fields, represented by these constituents. In particular, we conclude that the classical electromagnetic field at any point of space-time accompanied, in the General case, independent physical field, defined symmetrical derived affinor of 4-potential of classical electrodynamics. Discussed, within the framework of the Bogolyubov and Shirkov axiomatic, a theory of real vector field, clearly and equitably taking into account the symmetric derived affinors this field and found a number of important distinguishing features this model. Despite accounting explicitly gauge-noninvariant constituents, the proposed theory has specialized gauge invariance, which provides, in particular, conservation of electric current. In this connection, the difficulties with the probabilistic interpretation, in the case of indefinite-metric version of the theory, are surmountable by standard methods. Finally, is proposed the physical content of the fields, defined of a symmetrical derived affinor of 4-potential of classical electrodynamics. Keywords: vector field, symmetrical derived affinor, gauge invariance.