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arXiv · gr-qc/0412107

Feynman loops and three-dimensional quantum gravity

John W. Barrett
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Abstract

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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John W. Barrett. 2005-02-11. Feynman loops and three-dimensional quantum gravity. https://doi.org/10.1142/s0217732305017743

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