Mathématiques physiques

Towards a Non-Perturbative Quantum Gravity

Abstract

James Moffat and Charles Wang

We have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a discrete space-time and shows that macroscopic space-time is a renormalization limiting form. Weaving together a number of our previous results we then prove that quantum states invariant under either an external group of local diffeomorphisms of space-time or, by contrast, quantum states invariant under the internal action of a compact Lie group are ‘common’, in a well-defined sense. These form the building blocks of invariant fields and Lagrangians. A form of N=1 Supersymmetry and noncumulative space – time naturally emerges, which predicts a spin-2 massless graviton and its companion graviton.