A Renormalizable Theory of Quantum Gravity: Renormalization Proof of the Gauge Theory of Volume Preserving Diffeomorphisms

TL;DR

This paper proves the spacetime renormalizability of a gauge theory of volume-preserving diffeomorphisms, establishing a consistent quantum gravity framework that handles divergences via symmetry-preserving regularization.

Contribution

It introduces a renormalizable quantum gravity model based on gauge theory of volume-preserving diffeomorphisms and demonstrates its renormalizability through BRST symmetry and effective action analysis.

Findings

Proves the spacetime renormalizability of the gauge theory.

Shows divergence regularization consistent with symmetries.

Extends gauge theory framework beyond finite-dimensional groups.

Abstract

Inertial and gravitational mass or energy-momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The gauge-fixed action and the path integral measure occurring in the generating functional for the quantum Green functions of the theory are shown to obey a BRST-type symmetry. The related Zinn-Justin-type equation restricting the corresponding quantum effective action is established. This equation limits the infinite parts of the quantum effective action to have the same form as the gauge-fixed Lagrangian of the theory proving its spacetime renormalizability. The inner space integrals occurring in the quantum effective action which are divergent due to the gauge group's infinite volume are shown to be regularizable in a way consistent with the symmetries of the theory demonstrating as a byproduct that viable quantum gauge field theories are not limited to finite-dimensional compact gauge groups as is commonly assumed.