Semiclassical limit for Dirac particles interacting with a gravitational field

TL;DR

This paper analyzes the semiclassical behavior of spin-1/2 particles in weak gravitational fields, deriving operator equations for momentum and spin, and confirming the quantum-classical correspondence while clarifying previous misconceptions.

Contribution

It provides the first derivation of operator equations for momentum and spin motion in a gravitational field and clarifies the non-observability of spin-gravity coupling effects.

Findings

Operator equations for momentum and spin motion are derived.

Quantum and classical analyses are shown to agree.

Gravitational Stern-Gerlach force expression is obtained.

Abstract

The behavior of spin-1/2 particle in a weak static gravitational field is considered. The Dirac Hamiltonian is diagonalized by the Foldy-Wouthuysen transformation providing also the simple form for the momentum and spin polarization operators. The operator equations of momentum and spin motion are derived for a first time. Their semiclassical limit is analyzed. The dipole spin-gravity coupling in the previously found (another) Hamiltonian does not lead to any observable effects. The general agreement between the quantum and classical analysis is established, contrary to several recent claims. The expression for gravitational Stern-Gerlach force is derived. The helicity evolution in the gravitational field and corresponding accelerated frame coincides, being the manifestation of the equivalence principle.