Spin Particle with a Color Charge in a Color Field in Riemann-Cartan Space

TL;DR

This paper derives a comprehensive set of equations describing the motion of a classical spin particle with a color charge in a non-Abelian color and gravitational field within Riemann-Cartan space, extending existing models.

Contribution

It introduces a new hydrodynamic and equations of motion framework for spin particles with color charge in complex gravitational and gauge fields, generalizing previous equations like Wong and Tamm-Good.

Findings

Derived a hydrodynamic Euler-type equation for a perfect spin fluid with color charge.

Formulated equations of motion for a spin particle in combined color and gravitational fields.

Generalized Wong, Tamm-Good, and Bargmann-Michel-Telegdi equations.

Abstract

On the basis of the method of Cartan exterior forms and extended Lie derivatives, a hydrodynamic equation of the Euler type that describes a perfect spin fluid with an intrinsic color charge in an external non-Abelian color field in Riemann-Cartan space is derived from the energy-momentum quasiconservation law. This equation is used to obtain a self-consistent set of equations of motion for a classical test particle with a spin and a color charge in a color field combined with a gravitational field characterized by curvature and torsion. The resulting equations generalize the Wong equation, which describes the motion of a particle with an isospin, and the Tamm-Good and Bargmann-Michel-Telegdi equations, which describe the evolution of a charged-particle spin in an electromagnetic field.