Abstract
By analytic continuation from a SU(2) gauge field solution, Wu and Yang [Phys. Rev. 13, 3233 (1976)] obtained a static and sourceless solution of gauge theory for the group SL(2,C) [also for SO(3,1)]. This field configuration resembles a dyon that carries an imaginary charge. We present here a scheme that allows us to derive consistently the equations describing the interaction between the Lorentz gauge field and particles in the classical limit. They look like Wong’s equations in which gauge field components and color charges are complex. The complex charges and complex gauge field components can be understood as auxiliary concepts, while the equations of motion of particles in the outer space as well as kinematical and dynamical characteristics of the motion are real. The obtained equations are applied to investigate the case of particles in the mentioned dyon field configuration. The expressions of total energy and angular momentum, as integrals of motion of particles, are derived. The equations of motion allow planar motions, for which an analytic description of orbits is carried out.
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