Quantum GraviElectro Dynamics

TL;DR

This paper introduces Quantum GraviElectro Dynamics (QGED), a renormalisable quantum gravity theory based on BRST quantisation, demonstrating its perturbative renormalisability and potential for experimental measurement of gravitational coupling.

Contribution

It presents a BRST invariant Lagrangian for QGED, establishing its one-loop renormalisability and differentiating it from unrenormalisable quantum gravity theories.

Findings

QGED is perturbatively renormalisable at one-loop order.

The gravitational coupling constant can be experimentally measured.

Discussion of the running of the gravitational coupling and Hawking radiation estimates.

Abstract

This report presents a possible attempt at renormalisable quantum gravity based on the standard BRST quantisation used for Yang-Mills theory. We have provided the BRST invariant Lagrangian of the gravitationally interacting U(1) gauge theory, namely the Quantum GraviElectro Dynamics (QGED), including the gauge fixing and the ghost Lagrangian. We have extracted a set of Feynman rules in the local inertial frame where gravity locally vanishes from this Lagrangian. Using the Feynman rules of the QGED constructed here, we have built all the renormalisation constants and show that the theory is perturbatively renormalisable, at least in the one-loop order. All infinite naked objects in the naked Lagrangian can replace experimentally measured ones. In addition to the standard QED parameters, we have shown that the gravitational coupling constant can be experimentally measured. We have also discussed a running effect of the gravitational coupling constant and the perturbative estimation of the Hawking radiation as examples of perturbative QGED. The difference between our theory and the widely known un-renormalisable quantum general relativity is clarified.