In loop quantum gravity, dynamics such as time-evolutions of fields are controlled by the Hamiltonian constraint. The identity of the Hamiltonian constraint is a major open question in quantum gravity, as is extracting of physical observables from any such specific constraint.

The Thiemann operator has been proposed as such a constraint. Although this operator defines a complete and consistent quantum theory, doubts have been raised as to the physical reality of this theory due to inconsistencies with classical general relativity, and so variants have been proposed.

External links

• Overview by Carlo Rovelli
• Thiemann's paper in Physics Letters