  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.
