Variational problem for the frenkel and the Bargmann-Michel-Telegdi (BMT) equations

We propose Lagrangian formulation for the particle with value of spin fixed within the classical theory. The Lagrangian is invariant under non-Abelian group of local symmetries. On this reason, all the initial spin variables turn out to be unobservable quantities. As the gauge-invariant variables for description of spin we can take either the Frenkel tensor or the Bargmann-Michel-Telegdi (BMT) vector. Fixation of spin within the classical theory implies O(h)-corrections to the corresponding equations of motion.