The equations of motion for a classical color particle in background non-Abelian bosonic and fermionic fields

TL;DR

This paper develops a comprehensive framework for the equations of motion of a classical color-charged particle interacting with non-Abelian gauge and fermionic background fields, emphasizing gauge invariance and the infinite interaction terms involved.

Contribution

It constructs a general action for a classical color particle in non-Abelian backgrounds, including both gauge and fermionic fields, and derives gauge-covariant currents and sources.

Findings

Infinite interaction terms are generally required in the Lagrangian.

Constructed gauge-covariant currents match previous heuristic results.

Provided a systematic method for deriving equations of motion in non-Abelian backgrounds.

Abstract

Based on the most general principles of reality, gauge and reparametrization invariance, a problem of constructing the action describing dynamics of a classical color-charged particle interacting with background non-Abelian gauge and fermion fields is considered. The cases of the linear and quadratic dependence of a Lagrangian on a background fermion field are discussed. It is shown that in both cases in general there exists an infinite number of interaction terms, which should be included in the Lagrangian in question. From a simple iteration scheme, examples of the construction of the first few gauge-covariant currents and sources induced by a moving particle with non-Abelian charge are given. It is shown that these quantities, by a suitable choice of parameters, exactly reproduce additional currents and sources previously obtained in [Yu.A. Markov, M.A. Markova, Nucl. Phys. A 784 (2007) 443] on the basis of heuristic considerations.