A general quantum-mechanical description of relativistic spin 1/2 particles and nuclei channeled in bent crystals is presented using the cylindrical system of coordinates. The previously derived Dirac equation in this system is supplemented with terms characterizing anomalous magnetic and electric dipole moments. For the general case, transformation into the Foldy-Wouthhuysen representation is performed, quantum-mechanical equations of the motion of particles and their spins are obtained, and their classical limit is found. The physical nature of the main features of the description of particles and nuclei in the cylindrical system of coordinates is determined.
An account is given of the Wigner concept of particle spin and velocity rotations and of the variation of the angle between them under Lorentz transformations with noncollinear velocities. It is shown that Moller's description of spin rotation can be reduced to the Wigner rotation, and Moller's formula for the angle of spin rotation in the curvilinear motion of a particle is corrected. The permutation asymmetry of the relativistic velocity addition law distinguishes the Wigner sequence of Lorentzian boosts by its applicability to the description of spin and velocity rotations in curvilinear motion.