Fermion dynamics in presence of non abelian monopoles

TL;DR

This paper investigates the classical dynamics of a spinning, non-abelian charged particle interacting with a non-abelian monopole, revealing how spin and gauge interactions influence conservation laws and particle precession.

Contribution

It extends previous models by analyzing combined spin and non-abelian charge effects on particle dynamics and conservation laws in monopole fields.

Findings

Energy and angular momentum conservation are limited to specific conditions.

Non-abelian interactions break some classical conservation laws.

Particle precession differs from the abelian case under certain limits.

Abstract

In the present letter, the dynamics of a spin one-half particle with non abelian charge, interacting with a non abelian monopole like configuration, is studied. In the non spinning case, these equations correspond to the Wong ones [1], and the associated dynamics has been extensively studied in [2]-[3]. The classical limit of a spinning particle in an abelian was studied in [4], where an interpretation of the celebrated Callan-Rubakov effect [5]-[6] was obtained in purely classical terms. The present work studies an interpolating situation, in which spin and non abelian charges are turned on. The corresponding equations are obtaining by taking into account some earlier works about spinning particles [7]-[9]. The conservation laws are studied in this context, and it is found that energy and some generalization of angular momentum are conserved just in particular limits. This is a reflection that the non abelian interaction contains gauge field quartic interaction, which spoils the symmetries leading to these conservation laws. The precession of the particle is analyzed and compared with its abelian counterpart in this limit.