General covariance and dynamics with a Gauss law

Abstract

We present a 4-dimensional generally covariant gauge theory which leads to the Gauss constraint but lacks both the Hamiltonian and spatial diffeomorphism constraints. The canonical theory therefore resembles Yang-Mills theory without the Hamiltonian. We describe its observables, quantization, and some generalizations.

8 pages; explanation of missing constraints added; version to appear in Phys. Rev. D