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

Abstract

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.

22 pages, 14 figures

References in corpus (7)

• LQG vertex with finite Immirzi parameter
• A new spinfoam vertex for quantum gravity
• A New Spin Foam Model for 4d Gravity
• Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
• The Ponzano-Regge model
• Face amplitude of spinfoam quantum gravity
• Exploring the diffeomorphism invariant Hilbert space of a scalar field

Cited by in corpus (7)

• Perfect discretization of reparametrization invariant path integrals
• Holonomy Spin Foam Models: Definition and Coarse Graining
• Operator Spin Foam Models
• Coarse graining flow of spin foam intertwiners
• Discretization independence implies non-locality in 4D discrete quantum gravity
• Radiation from quantum weakly dynamical horizons in LQG
• The new spin foam models and quantum gravity