On knottings in the physical Hilbert space of LQG as given by the EPRL model

Benjamin Bahr (1, 2)

1 DAMTP - Department of Applied Mathematics and Theoretical Physics
2 AEI - Max Planck Institute for Gravitational Physics (Albert Einstein Institute)

We consider the EPRL spin foam amplitude for arbitrary embedded two-complexes. Choosing a definition of the face- and edge amplitudes which lead to spin foam amplitudes invariant under trivial subdivisions, we investigate invariance properties of the amplitude under consistent deformations, which are deformations of the embedded two-complex where faces are allowed to pass through each other in a controlled way. Using this surprising invariance, we are able to show that the physical Hilbert space, as defined by the sum over all spin foams, contains no information about knotting classes of graphs anymore.

Mots clés: Physical Sciences

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Benjamin Bahr. On knottings in the physical Hilbert space of LQG as given by the EPRL model. Classical and Quantum Gravity, 2011, 28 (4), pp.45002. ⟨10.1088/0264-9381/28/4/045002⟩. ⟨hal-00672300⟩