Curved-spacetime dynamics of spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> particles in superposed states from a WKB approximation of the Dirac eq

We investigate the dynamics of spin-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mfrac><a:mn>1</a:mn><a:mn>2</a:mn></a:mfrac></a:math> 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 flavor neutrinos which are, by nature, a superposition of mass eigenstates. Published by the American Physical Society 2024