Intersecting Connes Noncommutative Geometry with Quantum Gravity

TL;DR

This paper explores integrating Alain Connes' Noncommutative Geometry with Loop Quantum Gravity, proposing a framework that unifies the Standard Model and gravity, and discusses potential quantization approaches.

Contribution

It introduces a novel approach combining Noncommutative Geometry with Loop Quantum Gravity through a spectral triple construction.

Findings

Proposes a noncommutative algebra of holonomy loops

Outlines a spectral triple construction

Discusses interpretation and classical limit

Abstract

An intersection of Noncommutative Geometry and Loop Quantum Gravity is proposed. Alain Connes' Noncommutative Geometry provides a framework in which the Standard Model of particle physics coupled to general relativity is formulated as a unified, gravitational theory. However, to this day no quantization procedure compatible with this framework is known. In this paper we consider the noncommutative algebra of holonomy loops on a functional space of certain spin-connections. The construction of a spectral triple is outlined and ideas on interpretation and classical limit are presented.