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

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

2010-06-03

arxiv.org/abs/1006.0700v1

Class.Quant.Grav.28:045002,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, 14 figures

Scientific paper

10.1088/0264-9381/28/4/045002

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.

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