A symmetric scalar constraint for loop quantum gravity

Understand

In the framework of loop quantum gravity, we define a new Hilbert space of states which are solutions of a large number of components of the diffeomorphism constraint.

• On this Hilbert space, using the methods of Thiemann, we obtain a family of gravitational scalar constraints.
• They preserve the Hilbert space for every choice of lapse function.
• Thus adjointness and commutator properties of the constraint can be investigated in a straightforward manner.