On the Pauli–Schrödinger coupling to the Galilean gravity

This paper deals with the coupling between spinor fields and nonrelativistic gravity in the context of Galilean covariance. By formulating nonrelativistic physics in a five-dimensional manifold, gravitational interaction is described geometrically through the teleparallel version of Galilean gravity. This covariant framework allows the Pauli–Schrödinger field to be consistently coupled to Newtonian gravitation, following a procedure analogous to minimal coupling in relativistic theories. The result is a geometrically motivated and unified description of spinor fields under nonrelativistic gravitational interaction.