Geometrization of Scalar and Spinor Electrodynamics via Bohmian Quantum Gravity

Quantum theory is formulated as a probabilistic theory on a flat Minkowski space-time, while general theory of relativity is formulated on a curved manifold as a geometric theory. Bohmian Quantum Gravity approach indicates that one need to convert a probabilistic theory to a geometric form to merge it with general theory of relativity. We explore the differential geometric formulation of Scalar Electrodynamics and Spinor Electrodynamics and its coupling to the gravitational field equation. Using Feynman-Gell-Mann equation (second order Dirac equation), the fermionic matter field is nicely incorporated into general theory of relativity with the help of scalar-vector-tensor theory of gravity. Gravitationally coupled spin-field equations and generalized Feynman-Gell-Mann equation are derived from the action proposed here in the article. It is also shown that spin-electromagnetic interaction and spin-spin interaction can curve the space-time