Fermion dynamics in presence of non abelian monopoles

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.