We study the Schrödinger-Newton system of equations with the addition of gravitational field energy sourcing -such additional nonlinearity is to be expected from a theory of gravity (like general relativity), and its appearance in this simplified scalar setting (one of Einstein's precursors to general relativity) leads to significant changes in the spectrum of the self-gravitating theory.Using an iterative technique, we compare the mass dependence of the ground state energies of both Schrödinger-Newton and the new, self-sourced system and find that they are dramatically different. The Bohr method approach from old quantization provides a qualitative description of the difference, which comes from the additional nonlinearity introduced in the self-sourced case.In addition to comparison of ground state energies, we calculate the transition energy between the ground state and first excited state to compare emission frequencies between Schrödinger-Newton and the self-coupled scalar case. * jfrankli@reed.edu 1 arXiv:1501.07537v1 [gr-qc]

We probe the dynamics of a modified form of the Schrödinger-Newton system of gravity coupled to single particle quantum mechanics. At the masses of interest here, the ones associated with the onset of "collapse" (where the gravitational attraction is competitive with the quantum mechanical dissipation), we show that the Schrödinger ground state energies match the Dirac ones with an error of ∼ 10%. At the Planck mass scale, we predict the critical mass at which a potential collapse could occur for the self-coupled gravitational case, m ≈ 3.3 Planck mass, and show that gravitational attraction opposes Gaussian spreading at around this value, which is a factor of two higher than the one predicted (and verified) for the Schrödinger-Newton system. Unlike the Schrödinger-Newton dynamics, we do not find that the self-coupled case tends to decay towards its ground state; there is no collapse in this case. * jfrankli@reed.edu 1 arXiv:1603.03380v1 [gr-qc]

In this paper, we have proposed the theory of ( ) 1 U gravity gauge, and the gravity theory has been introduced into quantum field theory. We have further given the tensor equation of gravity field in the flat space, and found the gravity field equation is the Lorentz covariant and gauge invariant. The gravity theory can be quantized and can be unified with the electroweak and strong interaction at a new gauge group