Effect of polarization on a spin particle trajectory

Abstract

It is demonstrated that the problem of determining the parameters of trajectories of spin particles and beam of rays in the case of radiation with allowance for polarization is reduced to a variational problem with higher derivatives. It is demonstrated that in the limit of small values of the curvature and torsion, the higher derivatives can be expressed through the parameters of the medium. In this case, the curvature and torsion together with the polarization projection onto the trajectory determine an analog of the 4-potential which in its turn specifies an analog of the electromagnetic field tensor where the projection of polarization onto the trajectory plays the role of charge for a charged particle. It is demonstrated that the Magnus optical effect for dissipative solitons is determined not only by helicity σ, but also by topological index m (by the projection of the orbital soliton momentum onto the soliton trajectory). In an inhomogeneous medium, a relationship between the Magnus optical effect and nonholonomicity of the field of unit vectors tangent to the trajectory is established.