The Gauss Linking Number in Quantum Gravity

Details The Gauss Linking Number in Quantum Gravity The Gauss Linking Number in Quantum Gravity

1993-10-19

arxiv.org/abs/gr-qc/9310025v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13pp, 3 figures (included) Latex/Multi, to appear in ``Knots and quantum gravity'', J. Baez editor, Oxford UP, CGPG-93/10-1

Scientific paper

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.

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