Abstract
We study a type of geometric theory with a non-dynamical 1-form field. Its dynamical variables are an su(2) gauge field and a triad of su(2) valued 1-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.
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