  In a previous paper we formulated axisymmetric general relativity in terms of
real Ashtekar--Barbero variables. Here we proceed to quantize the theory. We
are able to implement Thiemann's version of the Hamiltonian constraint. We
discuss its action including the matrix elements and its solutions. This
provides a 2+1 dimensional arena to test ideas for the dynamics of quantum
gravity and opens the possibility of quantum studies of rotating black hole
spacetimes.
