General treatment of quantum and classical spinning particles in external fields

TL;DR

This paper develops a comprehensive theory for the dynamics of spinning particles with electric and magnetic dipole moments in various external fields, bridging quantum and classical descriptions and exploring potential gravitational wave effects on spin.

Contribution

It provides a unified framework for quantum and classical spinning particle dynamics in external fields, including gravitational effects, and demonstrates their equivalence.

Findings

Quantum and classical equations of motion are in complete agreement.

The theory applies to particles in gravitational waves and magnetic resonance setups.

Potential detection of gravitational wave effects on spin is discussed.

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-${\frac 12}$ 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 Schr\"odinger 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.