Nonrelativistic limit of scalar and Dirac fields in curved spacetime

We give from first principles the non-relativistic limit of scalar and Dirac fields in curved spacetime. aim to find general relativistic corrections quantum theory particles affected by Newtonian gravity, a regime nowadays experimentally accessible. believe that ever-improving measurement accuracy theoretical interest finding effects systems require introduction Schr\"{o}dinger-Newtonian theory. rigorously determine these fully theories For static spacetimes, we show how non-inertial observer (equivalently, an presence gravitational field) can distinguish field particle-gravity interaction. study Rindler spacetime discuss difference between resulting Hamiltonians. for sufficiently large acceleration, gravity-spin coupling dominates over fields, promoting as best candidates observing non-Newtonian gravity particle phenomenology.