2 research outputs found
On knottings in the physical Hilbert space of LQG as given by the EPRL model
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.Comment: 22 pages, 14 figure
Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
A covariant spin-foam formulation of quantum gravity has been recently
developed, characterized by a kinematics which appears to match well the one of
canonical loop quantum gravity. In this paper we reconsider the implementation
of the constraints that defines the model. We define in a simple way the
boundary Hilbert space of the theory, introducing a slight modification of the
embedding of the SU(2) representations into the SL(2,C) ones. We then show
directly that all constraints vanish on this space in a weak sense. The
vanishing is exact (and not just in the large quantum number limit.) We also
generalize the definition of the volume operator in the spinfoam model to the
Lorentzian signature, and show that it matches the one of loop quantum gravity,
as does in the Euclidean case.Comment: 11 page