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.
This is based on lectures given at the Quantum Hyperbolic Geometry Workshop, Albert-Einstein-Institute June 2004, and the Workshop on Quantum Gravity and Noncommutative Geometry, Universidade Lusófona July 2004. Copyright © John W. Barrett 2004 2005.
