Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

摘要

We review the recent results on development of vectormodels of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic fields. The formalism is developed starting fromthe Lagrangian variational problem, which implies both equations ofmotion and constraints which should be presented in a model of spinning particle.We present a detailed analysis of the resulting theory and show that it has reasonable properties on both classical and quantum level. We describe a number of applications and show how the vector model clarifies some issues presented in theoretical description of a relativistic spin: (A) one-particle relativistic quantum mechanics with positive energies and its relation with the Dirac equation and with relativistic Zitterbewegung; (B) spin-induced noncommutativity and the problem of covariant formalism; (C) three-dimensional acceleration consistent with coordinate-independence of the speed of light in general relativity and rainbow geometry seen by spinning particle; (D) paradoxical behavior of theMathisson-Papapetrou-Tulczyjew-Dixon equations of a rotating body in ultrarelativistic limit, and equations with improved behavior.