Dynamics of charged spin-$\frac{1}{2}$ particles in superposed states minimally coupled to electromagnetism in curved spacetime within the WKB approximation

TL;DR

This paper explores the behavior of charged spin-1/2 particles in superposed states within curved spacetime, analyzing their spin dynamics and deviations from geodesic motion using a WKB approximation of the Dirac equation.

Contribution

It introduces a novel approach to study superposed mass states of charged particles in curved spacetime via a second-order differential equation derived from the Dirac equation.

Findings

Charged particles exhibit spin dynamics influenced by spacetime curvature.

Superposed mass states cause deviations from geodesic trajectories.

The method simplifies analysis of complex quantum-gravity interactions.

Abstract

We investigate the curved-spacetime dynamics of charged spin-$\frac{1}{2}$ particles minimally coupled to the electromagnetic field and propagating in superposed states of different masses. For that purpose, we make use of a Wentzel-Kramers-Brillouin approximation of the Dirac equation with a minimal coupling to the Maxwell field in curved spacetime. We obtain the spin dynamics as well as the deviation from geodesic motion of such particles. The problem of having the mass eigenstates experience different proper times, as opposed to the case of neutral particles, is here dealt with by first extracting the second-order differential equation obeyed by each superposition. This strategy proves to be not only powerful, but also very economical.