On the dynamics of classical particle with spin

TL;DR

This paper provides a covariant 4D framework for describing the dynamics of a free classical spinning particle in special relativity, introducing a new vector field to define mean spin and position variables.

Contribution

It introduces a novel covariant approach with a new vector field for classical spinning particles, clarifying the role of supplementary conditions like the Frenkel condition.

Findings

Frenkel condition unambiguously determines particle dynamics.

New vector field defines mean spin and position variables.

Complete covariant 4D description of spinning particles.

Abstract

The complete explicitly covariant 4-dimensional description of the dynamics of a free classical particle with spin within the framework of the special relativity theory is presented. The key point of our approach is the the introduction of the new vector field which enables to define the analogues of the mean spin and position variables. The supplementary conditions are discussed and it is demonstrated that the Frenkel condition unambiguously determines the dynamics of a spinning particle.