Quantum Theory of Fermions in a Weak Gravitational Field.

The interaction between electrons and a weak gravitational field in a quantum theory is investigated. Specifically, a generalized Gordon decomposition is applied to the electron's energy-current density in order to obtain the form of the interaction between an electron and the gravitational field of a rotating mass, in the nonrelativistic limit. This is analogous to the interaction between the magnetic dipole moment of an electron and an external magnetic field (due to a rotating charge). Using a weak-field approximation to the exact coupled gravitational, electromagnetic, and electron system, quantum corrections (electromagnetic and gravitational) to this interaction are then obtained.