The Gauss Linking Number in Quantum Gravity

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.