A Renormalizable Model of Quantized Gravitational and Matter Fields

TL;DR

This paper introduces a renormalizable and unitary model coupling scalar and gravitational fields using a Lagrange multiplier, ensuring Einstein equations are recovered classically and providing a new analytic form for the effective action.

Contribution

It presents a novel approach to couple matter and gravity fields that maintains renormalizability and unitarity, with explicit analytic expressions for the effective action.

Findings

Coupling scalar fields to gravity can be made renormalizable and unitary.

The model reproduces Einstein's equations in the classical limit.

A new analytic form of the effective action is derived.

Abstract

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.