Quantisation of Paths in Space-Time and Non-Perturbative Quantum Gravity

TL;DR

This paper develops a mathematically coherent approach to non-perturbative quantum gravity using discrete spacetime, revealing emergent supersymmetry, noncommutative geometry, and predicting a massless graviton and gravitino.

Contribution

It introduces a new quantization framework for paths in spacetime that addresses open questions in Loop Quantum Gravity and demonstrates the emergence of supersymmetry and noncommutative spacetime.

Findings

Discrete spacetime as a renormalization limit

Invariant quantum states under diffeomorphisms or Lie group actions

Emergence of supersymmetry and noncommutative geometry

Abstract

In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a discrete spacetime and shows that macroscopic spacetime 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 spacetime 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 supersymmetry and noncommutative spacetime naturally emerges, which predicts a massless graviton and its companion gravitino.