Quantum Gravity and the Emergence of Matter

TL;DR

This paper establishes a non-perturbative quantum gravity theory called quantum holonomy theory, demonstrating a Hilbert space representation of the QHD(M) algebra and its classical limit, with implications for singularities and quantum field theories.

Contribution

It constructs a Hilbert space representation of the QHD(M) algebra and shows the emergence of classical gravity and matter structures in the quantum gravity framework.

Findings

Existence of a Hilbert space representation of the QHD(M) algebra.

Emergence of classical gravity and matter in the classical limit.

Non-local structure potentially resolving singularities.

Abstract

In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which is an algebra generated by holonomy-diffeomorphisms and by translation operators on an underlying configuration space of Ashtekar connections, exist. We construct operators, which correspond to the Hamiltonian of general relativity and the Dirac Hamiltonian, and show that they give rise to their classical counterparts in a classical limit. We also find that the structure of an almost-commutative spectral triple emerge in the same limit. The Hilbert space representation, that we find, is inherently non-local, which appears to rule out spacial singularities such as the big bang and black hole singularities. Finally, the framework also permits an interpretation in terms of non-perturbative Yang-Mills theory as well as other non-perturbative quantum field theories. This paper is the first of two, where the second paper contains mathematical details and proofs.