QG4 - Loop Quantum gravity, Quantum Geometry, Spin Foams |
Speaker_ |
Sahlmann, Hanno |
Talk _ |
Exploring the diffeomorphism invariant Hilbert space of LQG |
Abstract _ |
For the simple toy model of a scalar field/abelian sigma model we investigate the Hilbert space of states that are invariant under spatial diffeomorphisms: We explicitly compute the scalar product, show that there is a natural Fock-space structure associated to it, and quantize a certain class of observables. We also explain that the precise form of the symmetry factors that show up in the scalar product seems to be important, not merely a technicality. |