The six dynamical variables gmn(x) are expressed in terms of three "coordinatelike" variables yA(x) and three invariant variables γα(k). The longitudinal constraints Rn0+Tn0=0 imply the vanishing of the momenta canonically conjugate to the yA(x), and the only remaining constraint can be written invariantly in terms of the γα(k), their conjugate momenta, and the matter variables. The quantization of this fourth constraint then leads to a Schwinger-Tomonaga equation iδΨδσ=H[σ]Ψ, whose solution yields a complete set of commuting observables for the gravitational field. For most applications, it is possible to select the initial hypersurface so as to get the much simpler equation i∂Ψ∂T=HΨ, where the dynamical variable T (which is a known functional of the metric and the matter variables at t=0) plays the role of an "invariant time."