Classical fermion dynamics in presence of non abelian monopoles

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 S Wong (1970, Il Nuovo Cimento LXV, 4 689), and the associated dynamics has been extensively investigated in I Alekseev (1988, Theoret. and Math. Phys. 77 1273), L G Feher (1984, Acta Physica Polonica 15 920). The classical limit of a spinning particle in an abelian was considered in A Davis and W Perkins (1989, Phys. Lett. B 228 37), where an interpretation of the celebrated Callan-Rubakov effect C G Callan (1982, Phys. Rev. D 26 2058); V A Rubakov (1982, Nucl. Phys. B 203 311), V A Rubakov and M S Serebryakov (1983, Nucl. Phys. B 218 240); V A Rubakov (1981, JETP Len. 33 644). 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 N Linden, A Macfarlane and J van Holten Czechoslovak (1996, J. Phys. 46 209), A Barducci, R Casalbuoni and L Lusanna (1977, Nuclear Physics B 124 93, A P Balachandran Per Salomson, B -S Skagerstam, and J -O Winnberg (1977, Phys. Rev. D 15 2308). 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.