Feynman loops and three-dimensional quantum gravity

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.

approx 14 pages. v2: minor descriptive changes and added refs. v3: minor corrections

References in corpus (3)

• Ponzano-Regge model revisited II: Equivalence with Chern-Simons
• Observables in the Turaev-Viro and Crane-Yetter models
• Some limits of the colored Jones polynomials of the figure-eight knot

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• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Holonomy observables in Ponzano-Regge type state sum models
• Invariants of Spin Networks Embedded in Three-Manifolds