Relativistic generalization of the Schrodinger-Newton model for the wavefunction reduction

We consider the model of the self-gravity driven spontaneous wavefunction reduction proposed by L. Diosi, R. Penrose et al. and based on a self-consistent system of Schrodinger and Poisson equations. An analogous system of coupled Dirac and Maxwell-like equations is proposed as a relativization. Regular solutions to the latter form a discrete spectrum in which all the "active" gravitational masses are always positive, and approximately equal to inertial masses and to the mass In of the quanta of Dirac field up to the corrections of order alpha(2) . Here alpha = (m/M-p(l))(2) is the gravitational analogue of the fine structure constant negligibly small for nucleons. In the limit alpha = 0 the model reduces back to the nonrelativistic Schrodinger-Newton one. The equivalence principle is fulfilled with an extremely high precision. The above solutions correspond to various states of the same (free) particle rather than to different particles. These states possess a negligibly small difference in characteristics but essentially differ in the widths of the wavefunctions. For the ground state the latter is a times larger the Compton length, so that a nucleon cannot be sufficiently localized to model the reduction process.