Intersecting Connes Noncommutative Geometry with Quantum Gravity
High Energy Physics - Theory
2010-10-27 v1 General Relativity and Quantum Cosmology
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.
Cite
@article{arxiv.hep-th/0601127,
title = {Intersecting Connes Noncommutative Geometry with Quantum Gravity},
author = {Johannes Aastrup and Jesper M. Grimstrup},
journal= {arXiv preprint arXiv:hep-th/0601127},
year = {2010}
}
Comments
19 pages, 4 figures