Holonomy Loops, Spectral Triples & Quantum Gravity
Abstract
We review the motivation, construction and physical interpretation of a semi-finite spectral triple obtained through a rearrangement of central elements of loop quantum gravity. The triple is based on a countable set of oriented graphs and the algebra consists of generalized holonomy loops in this set. The Dirac type operator resembles a global functional derivation operator and the interaction between the algebra of holonomy loops and the Dirac type operator reproduces the structure of a quantized Poisson bracket of general relativity. Finally we give a heuristic argument as to how a natural candidate for a quantized Hamiltonian might emerge from this spectral triple construction.
Cite
@article{arxiv.0902.4191,
title = {Holonomy Loops, Spectral Triples & Quantum Gravity},
author = {Johannes Aastrup and Jesper M. Grimstrup and Ryszard Nest},
journal= {arXiv preprint arXiv:0902.4191},
year = {2009}
}
Comments
24 pages, 7 figures, based on talk given by J.M.G. at the QG2 conference, Nottingham, juli 2008; at the QSTNG conference in Rome in sept/oct 2008; at the AONCG conference, Canberra, dec. 2008