Relativistic dynamics for a particle carrying a non-Abelian charge in a non-Abelian background electromagnetic field

Abstract

We study the relativistic dynamics of a particle carrying a non-Abelian charge in the presence of a non-Abelian background electromagnetic field. To this end, we extract the non-Abelian Dirac Hamiltonian from a system describing the interaction between the Yang–Mills field and a spin-1/2 field. The dynamics of a particle with non-Abelian charge is quantized directly by analogy with its quantum theory. By choosing a suitable non-Abelian gauge field, we investigate the spectrum in two-dimensional space, paying particular attention to the role of the total angular momentum. Relativistic Landau levels are obtained explicitly by means of an analytical method. The wave functions of the system are obtained in terms of the generalized Laguerre polynomials. Interesting features of such models are discussed through the spectrum.