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) $\varphi$ and scale factor of 2-sphere part of the space time $\psi \mathrm{.}$ We obtained suitable duality transformations between $(\psi ,\varphi )$ and $(\rho ,S)$ where $\rho$ and $S$ is respectively amplitude and phase part of the corresponding de Broglie pilot wave function $\mathrm{\Psi }(\rho ,S)=\sqrt{\rho }{e}^{iS}\mathrm{.}$ Covariant conservation of mass-energy current density of particles ensemble $J_a=\rho {\mathrm{\partial }}_{a}S,$ is established by applying a particular dynamical conformal frame described by $(\rho ,S)\mathrm{.}$