Geometric post-Newtonian description of spin-half particles in curved spacetime

Einstein Equivalence Principle (EEP) requires all matter components to universally couple to gravity via a single common geometry: that of spacetime. This relates quantum theory with geometry as soon as interactions with gravity are considered. In this work, I study the geometric theory of coupling a spin-1/2 particle to gravity in a twofold expansion scheme: First with respect to the distance based on Fermi normal coordinates around a preferred worldline (e.g., that of a clock in the laboratory), second with respect to 1/c (post-Newtonian expansion). I consider the one-particle sector of a massive spinor field in QFT, here described effectively by a classical field. The formal expansion in powers of 1/c yields a systematic and complete generation of GR corrections for quantum systems. I find new terms that were overlooked in the literature at order 1/c^2 and extended the level of approximation to the next order. These findings are significant for a consistent inclusion of gravity corrections in the description of quantum experiments of corresponding sensitivities, and also for testing aspects of GR, like the EEP, in the quantum realm.