General treatment of quantum and classical spinning particles in external fields

Abstract

We develop the general theory of spinning particles with electric and magnetic dipole moments moving in arbitrary electromagnetic, inertial and gravitational fields. Both the quantum-mechanical and classical dynamics is investigated. We start from the covariant Dirac equation extended to a spin-$\frac{1}{2}$ fermion with anomalous magnetic and electric dipole moments and then perform the relativistic Foldy-Wouthuysen transformation. This transformation allows us to obtain the quantum-mechanical equations of motion for the physical operators in the Schrödinger form and to establish the classical limit of relativistic quantum mechanics. The results obtained are then compared to the general classical description of the spinning particle interacting with electromagnetic, inertial and gravitational fields. The complete agreement between the quantum mechanics and the classical theory is proven in the general case. As an application of the results obtained, we consider the dynamics of a spinning particle in a gravitational wave and analyze the prospects of using the magnetic resonance setup to find possible manifestations of the gravitational wave on spin.

38 pages, Revtex, minor changes

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• Neutrino spin oscillations in conformally gravity coupling models and quintessence surrounding a black hole
• Neutrino scattering off a black hole surrounded by a magnetized accretion disk
• Spin oscillations of neutrinos scattered off a rotating black hole
• Gravitomagnetic Stern--Gerlach Force
• Polar solutions with tensorial connection of the spinor equation
• Spin and flavor oscillations of neutrinos in gravitational fields
• Dynamics of classical and quantum spin in external fields: A general formalism
• Geometric studies of the interplay between spin and gravity
• Neutrino spin oscillations in curved space-time under the influence of external fields