Quantum spin dynamics in external classical fields

We study the quantum and classical dynamics of spinning particles in the framework of the general-relativistic covariant Dirac theory. The exact Foldy-Wouthuysen transformation for the most general case of a fermion in arbitrary configurations of the gravitational, inertial and electromagnetic fields is derived. We demonstrate the complete consistency of the quantum and classical dynamics. As physical applications, we discuss prospects of probing spacetime structure and using spin effects for gravitational wave detection