The Gauss Linking Number in Quantum Gravity
General Relativity and Quantum Cosmology
2007-05-23 v1
Abstract
We show that the exponential of the Gauss (self) linking number of a knot is a solution of the Wheeler-DeWitt equation in loop space with a cosmological constant. Using this fact, it is straightforward to prove that the second coefficient of the Jones Polynomial is a solution of the Wheeler-DeWitt equation in loop space with no cosmological constant. We perform calculations from scratch, starting from the connection representation and give details of the proof. Implications for the possibility of generation of other solutions are also discussed.
Cite
@article{arxiv.gr-qc/9310025,
title = {The Gauss Linking Number in Quantum Gravity},
author = {R. Gambini and J. Pullin},
journal= {arXiv preprint arXiv:gr-qc/9310025},
year = {2007}
}
Comments
13pp, 3 figures (included) Latex/Multi, to appear in ``Knots and quantum gravity'', J. Baez editor, Oxford UP, CGPG-93/10-1