Spherically Symmetric Jordan-Brans-Dicke Quantum Gravity with de Broglie Bohm Pilot Wave Perspective

We obtain two dimensional analogue of the Jordan-Brans-Dicke (JBD) gravity action described in four dimensional spherically symmetric curved space time metric. There will be two scalar fields, namely, the Brans Dicke (BD) I center dot and scale factor of 2-sphere part of the space time psi. We obtained suitable duality transformations between (psi, I center dot) and (rho, S) where rho and S is respectively amplitude and phase part of the corresponding de Broglie pilot wave function Covariant conservation of mass-energy current density of particles ensemble J (a) = rho a, (a) S, is established by applying a particular dynamical conformal frame described by (rho, S).