In a LQG book of all places:
"$H = 0$... More precisely, the hamiltonian is proportional to the constraint $H \approx C$. This should not be a real surprise, since the hamiltonian generates evolution in the evolution parameter in the action, namely in $\tau$, but a change in $\tau$ is pure gauge, and in the hamiltonian formalism the generator of a gauge transformation vanishes (weakly).
This does not mean in any sense that the dynamics is "frozen", or other similar absurdities that one sometimes reads. The dynamics of this system is the one described by the Newton equation above. The vanish…