O movimento de partículas em configurações estáticas de teorias de Yang-Mills - Amorim, Bernardo Corrêa (2020)
This work is focused on the study of some aspects related to static magnetic field solutions in Yang-Mills theory, as well as the movement of particles with non-abelian electric charge under the action of this field. The Wu and Yang magnetic monopole configuration is discussed in detail and we review the problem of defining charges in non-abelian gauge theories in this context, where we demonstrate from the construction of the integral Yang-Mills equations that there is a magnetic source associated with this configuration, and we calculate its magnetic charge, dynamically conserved and invariant under local gauge transformations. We present the trajectories of a particle with non-abelian electric charge in interaction with the Wu and Yang monopole, calculated numerically. Finally, we review the configuration given by ’t Hooft and Polyakov ansatz, also considering the abelianization of the gauge field and the definition of the magnetic charge from the topology of the Higgs field in vacuum. We also show, for this case, numerical solutions for the trajectories of a particle with non-abelian electric charge in the presence of this magnetic field. By discussing the movement of charged particles under non-abelian magnetic fields we give some insights on the problem of the non-abelian charge and show that ’t Hooft and Polyakov configuration has the same charge as the Wu and Yang Monopole, when observed from far away.