General covariance, new variables, and dynamics without dynamics

We give an example of a generally covariant geometric field theory which leads to the standard Gaussian and supermomentum constraints but which lacks the super-Hamiltonian constraint. This theory is closely linked to Ashtekar’s canonical formulation of general relativity. We discuss the Dirac constraint quantization of our model and comment on the issues which it raises regarding the quantization of generally covariant systems.