The Configuration Space of Conformal Connection-Dynamics
General Relativity and Quantum Cosmology
2012-08-21 v3 Differential Geometry
Abstract
The configuration space of the reduced Hamiltonian formulation of quantum gravity has been shown, for non-Ricci flat metrics, to be a higher-dimensional analogue of the Teichm\"{u}ller space of conformal structures on a Riemann surface. In this article we show that the configuration space of conformal connection-dynamics is naturally a higher-dimensional Teichm\"{u}ller space, subject to the same condition. An immediate consequence of this result is that the Barbero-Immirzi parameter of loop quantum gravity naturally assumes a dilatonic character in all conformal canonical gravity theories.
Cite
@article{arxiv.1102.5560,
title = {The Configuration Space of Conformal Connection-Dynamics},
author = {James A. Reid and Charles H. -T. Wang},
journal= {arXiv preprint arXiv:1102.5560},
year = {2012}
}