The application of canonical methods to gravity has a long history [De-Witt 1967]. In [Dirac 1950] a general Hamiltonian approach was presented, which allowed for the presence of constraints in a theory, due to the momenta not being independent functions of the velocities. In particular, this occurs in general relativity, because of the underlying coordinate invariance of gravity. The general approach above was applied to general relativity in [Dirac 1958a,b, 1959] and further described in [Dirac 1965]. It was seen that there are four constraints, usually written ℋi(i = 1,2,3) and ℋ⊥, associated with the freedom to make coordinate transformations in the spatial and normal directions relative to a hypersurface t = const. in the Hamiltonian decomposition. Classically, these four constraints must vanish for allowed initial data. In the quantum theory, as will be seen in chapter 2, these constraints become operators on physically allowed states Ψ, which must obey ℋiΨ = 0, ℋ⊥Ψ = 0. Here, in the simplest representation, Ψ is a functional of the spatial metric hij(x). It was shown in [Higgs 1958, 1959] that the constraints ℋiΨ = 0 precisely describe the invariance of the wave function under spatial coordinate transformations. The Hamiltonian formulation of gravity was also studied by [Arnowitt et al. 1962], who provided the standard definition of the mass or energy M of a spacetime, as measured at spatial infinity.