Explicit solution for the zero signature (strong-coupling) limit of the propagation amplitude in quantum gravity

The quantum propagation amplitude between two gravitational field configurations may be represented by: (I) Giving the amplitude for a transition between two three-geometries for which one specifies their relative pointwise proper distance and relative spatial coordinate systems. (II) Integrating over all possible positive proper distances. (III) Averaging over all possible choices of the relative coordinate system. In this paper an explicit expression is found, in the limit of zero hamiltonian signature (strong coupling), for the amplitude obtained after steps (I) and (II) are taken. Step (III) is not dealt with. The analysis is carried out by relying on the notion of Fourier analysis over a symmetric space. (orig.)