Curved-spacetime dynamics of spin-$\tfrac{1}{2}$ particles in superposed states from a WKB approximation of the Dirac equation

TL;DR

This paper uses a WKB approximation of the Dirac equation in curved spacetime to derive equations describing the motion and spin precession of spin-1/2 particles in superposed states, with implications for neutrino physics.

Contribution

It introduces a novel application of WKB approximation to derive dynamics of superposed spin-1/2 particles in curved spacetime, connecting quantum superposition with classical equations.

Findings

Derived Mathisson-Papapetrou-Dixon equations for superposed states

Analyzed spin precession in curved spacetime

Discussed implications for neutrino flavor oscillations

Abstract

We investigate the dynamics of spin-$\tfrac{1}{2}$ particles that are freely propagating in superposed states in curved spacetime. We first make use of a Wentzel-Kramers-Brillouin approximation of the Dirac equation in curved spacetime to extract the corresponding Mathisson-Papapetrou-Dixon equations that describe the deviation from geodesic motion as well as the spin precession of such particles. We then discuss, in light of our results, the case of flavour neutrinos which are, by nature, a superposition of mass eigenstates.