Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-12-21
Mod.Phys.Lett. A20 (2005) 1271
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
approx 14 pages. v2: minor descriptive changes and added refs. v3: minor corrections
Scientific paper
This paper explores the idea that within the framework of three-dimensional quantum gravity one can extend the notion of Feynman diagram to include the coupling of the particles in the diagram with quantum gravity. The paper concentrates on the non-trivial part of the gravitational response, which is to the large momenta propagating around a closed loop. By taking a limiting case one can give a simple geometric description of this gravitational response. This is calculated in detail for the example of a closed Feynman loop in the form of a trefoil knot. The results show that when the magnitude of the momentum passes a certain threshold value, non-trivial gravitational configurations of the knot play an important role. The calculations also provide some new information about a limit of the coloured Jones polynomial which may be of independent mathematical interest.
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