A Renormalizable Model of Quantized Gravitational and Matter Fields

A Lagrange multiplier field can be used to restrict radiative corrections to the Einstein-Hilbert action to one-loop order. This result is employed to show that it is possible to couple a scalar field to the metric (graviton) field in such a way that the model is both renormalizable and unitary. The usual Einstein equations of motion for the gravitational field are recovered, perturbatively, in the classical limit. By evaluating the generating functional of proper Green’s functions in closed form, one obtains a novel analytic contribution to the effective action.