Canonical General Relativity: the Diffeomorphism constraints and Spatial Frame Transformations

The constraint algebra derived in Class. Quantum Grav. 14 (1997), 1851--1864 is generated explicitly from a formulation of general relativity in which both the metric and vielbein are independent degrees of freedom. The standard form of the Hamiltonian is composed of the Hamiltonian and momentum constraints, as well as constraints that generate spatial frame transformations; all appearing as primary, first class constraints on phase space. From these results, the conditions that must be satisfied by the generators of any diffeomorphism invariant, non-derivatively coupled, classical field are derived.