Nonrelativistic field theoretic setting for gravitational self-interactions

It is shown that a recently proposed model for the gravitational interaction in non relativistic quantum mechanics is the instantaneous action at a distance limit of a field theoretic model containing a negative energy field. It reduces to the Schroedinger-Newton theory in a suitable mean field approximation. While both the exact model and its approximation lead to estimates for localization lengths, only the former gives rise to an explicit non unitary dynamics accounting for the emergence of the classical behavior of macroscopic bodies.