Intrinsic Time Quantum Gravity

TL;DR

This paper proposes a self-consistent quantum gravity theory based on 3D spatial diffeomorphism invariance, intrinsic time, and a new set of fundamental, non-canonical commutation relations involving unimodular dreibein components and SU(3) generators.

Contribution

It introduces a novel gauge symmetry identification, intrinsic time, and a new algebra of fundamental variables with well-defined group theoretical meanings for quantum gravity.

Findings

Consistent quantum gravity framework using unimodular dreibein and SU(3) variables.

New non-canonical commutation relations with clear group theoretical interpretation.

Wave functionals are naturally represented in dreibein variables.

Abstract

Correct identification of the true gauge symmetry of General Relativity being 3d spatial diffeomorphism invariant(3dDI) (not the conventional infinite tensor product group with principle fibre bundle structure), together with intrinsic time extracted from clean decomposition of the canonical structure yields a self-consistent theory of quantum gravity. A new set of fundamental commutation relations is also presented. The basic variables are the eight components of the unimodular part of the spatial dreibein and eight SU(3) generators which correspond to Klauder's momentric variables that characterize a free theory of quantum gravity. The commutation relations are not canonical, but have well defined group theoretical meanings. All fundamental entities are dimensionless; and the quantum wave functionals are preferentially in the dreibein representation. The successful quantum theory of gravity involves only broad spectrum of knowledge and deep insights but no exotic idea.