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Journal Article

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


Bahr,  Benjamin
Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Bahr, B. (2011). On knottings in the physical Hilbert space of LQG as given by the EPRL model. Classical and quantum gravity, 28(4): 045002. doi:10.1088/0264-9381/28/4/045002.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-105A-7
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 in the physical Hilbert space as defined by the sum over all spin foams contains no knotting classes of graphs anymore.