# Wheeler-Dewitt equation and canonical quantum gravity

1. Nov 24, 2005

### ylping

In the canonical quantum gravity, Hamiltonian equal zero, why? Since the split is space, the time is a constant? or the space-time is Ricci-flat?

In other words, if the space-time is Ricci-flat whether time supersurface, Hamiltonian equal zero?

2. Nov 25, 2005

### hellfire

The hamiltonian is equal to zero in any system which is invariant under reparametrizations. This is always the case for the gravitational field in general relativity. Another example is a relativistic point particle in geodesic motion.