Spin, gravity, and inertia

TL;DR

This paper investigates gravitational effects in relativistic quantum mechanics, deriving a Hamiltonian that includes spin-gravity interactions, and confirms that these effects do not violate the equivalence principle for Dirac fermions.

Contribution

The paper constructs an exact Foldy-Wouthuysen transformation for Dirac particles in static spacetimes and analyzes the non-relativistic limit including spin-gravity interactions.

Findings

Identifies a new spin-gravity interaction term in the Hamiltonian.

Shows that spin effects do not violate the equivalence principle.

Provides a detailed non-relativistic limit analysis.

Abstract

The gravitational effects in the relativistic quantum mechanics are investigated. The exact Foldy-Wouthuysen transformation is constructed for the Dirac particle coupled to the static spacetime metric. As a direct application, we analyze the non-relativistic limit of the theory. The new term describing the specific spin (gravitational moment) interaction effect is recovered in the Hamiltonian. The comparison of the true gravitational coupling with the purely inertial case demonstrates that the spin relativistic effects do not violate the equivalence principle for the Dirac fermions.