Covariant factor ordering of gauge systems

Gauge systems described in the preceding paper are canonically quantized in a way which is manifestly covariant under all transformations relevant in the classical theory. Special observables are represented by scalar differential operators acting on the space scrF of $C^{\infty }$(scrM,C ) functions on the ‘‘big’’ configuration manifold scrM. Physical states Ψ∈${\mathrm{scrF}}_0$ are annihilated by all operators υ^ representing the elements υ of the gauge algebra scrV. The inner product in ${\mathrm{scrF}}_0$ is based on the measure provided by the physical metric induced by the Hamiltonian. Special quantum observables are self-adjoint on the resulting Hilbert space ${\mathrm{scrH}}_0$. Factor ordering of such observables, based on their split into standard physical and gauge parts, is self-consistent. In particular, all special quantum observables commute with the constraints υ^ on the physical space ${\mathrm{scrF}}_0$ and hence can be considered as operators on ${\mathrm{scrF}}_0$. The Hamilton operator does not evolve the states out of the physical Hilbert space. These results are corroborated by an explicit evaluation of all commutators among special observables on the big function space scrF. Both the factor ordering and the construction of the inner product are ultimately cast into language which does not require the splitting of observables.