assign to one of the coordinate axes. Thus, what we think about as time evolution of any physical system is just a gauge transformation, similar to that of QED induced by U(1) local gauge transformation where plays the role of local time. The role of a Hamiltonian is simply to restrict the space of the "kinematic" states of the Universe to that of "physical" states—the ones that follow gauge orbits. For this reason we call it a "Hamiltonian constraint." Upon quantization, physical states become wave functions that lie in the kernel of the Hamiltonian operator. In general, the Hamiltonian vanishes for a theory with general covariance or time-scaling invariance. See also ADM formalism Diffeomorphism constraint Euclidean quantum gravity Regge calculus Canonical quantum gravity Peres metric Loop quantum gravity References Quantum gravity Equations