  We study a type of geometric theory with a non-dynamical one-form field. Its
dynamical variables are an $su(2)$ gauge field and a triad of $su(2)$ valued
one-forms. Hamiltonian decomposition reveals that the theory has a true
Hamiltonian, together with spatial diffeomorphism and Gauss law constraints,
which generate the only local symmetries. Although perturbatively
non-renormalizable, the model provides a test bed for the non-perturbative
quantization techniques of loop quantum gravity.
