Quantum GraviElectro Dynamics

Abstract This report presents a possible attempt at renormalizable quantum gravity based on the standard BRST quantization used for Yang–Mills theory. The BRST invariant Lagrangian of the gravitationally interacting gauge theory is provided, namely the Quantum GraviElectro Dynamics (QGED), including the gauge fixing and the ghost Lagrangian. A set of Feynman rules is extracted in the local inertial frame where gravity locally vanishes from this Lagrangian. Using the Feynman rules of the QGED constructed here, all the renormalization constants are build and it is showed that the theory is perturbatively renormalizable, 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 parameters, it is showed that the gravitational coupling constant can be experimentally measured. A running effect of the gravitational coupling constant and the perturbative estimation of the Hawking radiation as examples of perturbative QGED is also discussed. The difference between this theory and the widely known un‐renormalizable quantum general relativity is clarified.