Lorentzian Connes Distance, Spectral Graph Distance and Loop Gravity
General Relativity and Quantum Cosmology
2014-09-10 v4 Mathematical Physics
math.MP
Abstract
Connes' formula defines a distance in loop quantum gravity, via the spinfoam Dirac operator. A simple notion of spectral distance on a graph can be extended do the discrete Lorentzian context, providing a physically natural example of Lorentzian spectral geometry, with a neat space of Dirac operators. The Hilbert structure of the fermion space is Lorentz covariant rather than invariant.
Cite
@article{arxiv.1408.3260,
title = {Lorentzian Connes Distance, Spectral Graph Distance and Loop Gravity},
author = {Carlo Rovelli},
journal= {arXiv preprint arXiv:1408.3260},
year = {2014}
}
Comments
4 pages