Ultra-relativistic spinning particle and a rotating body in external fields

Abstract: We use the vector model of spinning particle to analyze the influence of spin-field coupling on the particle's trajectory in ultra-relativistic regime. The Lagrangian with minimal spin-gravity interaction yields the equations equivalent to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations of a rotating body. We show that they have unsatisfactory behavior in the ultra-relativistic limit. In particular, three-dimensional acceleration of the particle increases with velocity and becomes infinite in the ultra-relativistic limit. The reason is that in the equation for trajectory emerges the term which can be thought as an effective metric generated by the minimal spin-gravity coupling. Therefore we examine the non-minimal interaction through the gravimagnetic moment $\kappa$, and show that the theory with $\kappa=1$ is free of the problems detected in MPTD-equations. Hence the non-minimally interacting theory seem more promising candidate for description of a relativistic rotating body in general relativity. The Lagrangian for the particle in an arbitrary electromagnetic field in Minkowski space leads to generalized Frenkel and Bargmann-Michel-Telegdi equations. The particle with magnetic moment in electromagnetic field and the particle with gravimagnetic moment in gravitational field have very similar structure of equations of motion. In particular, the spin-electromagnetic coupling also produces an effective metric for the particle with anomalous magnetic moment. If we use the usual special-relativity notions for time and distance, then the critical speed, which the particle cannot exceed during its evolution in electromagnetic field, is different from the speed of light. This can be corrected assuming that the three-dimensional geometry should be defined with respect to the effective metric.