Equations of motion for a classical color particle in external non-Abelian fermionic and bosonic fields

On the basis of principles of gauge and reparametrization invariance of a real-valued Lagrangian, construction of the action describing the 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 the background fermion field are discussed. It is shown that, in both cases, there exist an infinite number of interaction terms. From an iteration scheme, examples of construction of the first few 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 obtained previously in [1] on the basis of heuristic considerations.