Merging higher derivative gravity and quantum mechanics (Q702985)

The Klein-Gordon equation \((\square+ m^2)\varphi= 0\) for a scalar field \(\varphi\) can be recast in Schrödinger form \(i\partial_t\Phi= H\Phi\). The authors extend the well-known procedure to the partial differential equation \((\square+ m^2+\lambda R)\varphi= 0\) with a coupling constant \(\lambda\) on a spherically symmetric static spacetime. They apply then to their Schrödinger-type equation a Foldy-Wouthuysen transformation, and they specialize to a metric found by Teyssandier 1989 as a kind of Newtonian limit of fourth-order gravity. The back-reaction of the scalar field \(\varphi\) on the spacetime metric is not considered so that the merging announced in the title does not take place.