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New spinfoam vertex for quantum gravity
We introduce a new spinfoam vertex to be used in models of 4d quantum gravity based on SU(2) and SO(4) BF theory plus constraints. It can be seen as the conventional vertex of SU(2) BF theory, the
Exact and approximate unitary 2-designs and their application to fidelity estimation
We develop the concept of a unitary $t$-design as a means of expressing operationally useful subsets of the stochastic properties of the uniform (Haar) measure on the unitary group $U({2}^{n})$ on
Projected spin networks for Lorentz connection: linking spin foams and loop gravity
In the search for a covariant formulation for loop quantum gravity, spin foams have arisen as the corresponding discrete spacetime structure and, among the different models, the Barrett–Crane model
U(N) coherent states for loop quantum gravity
We investigate the geometry of the space of N-valent SU(2) intertwiners. We propose a new set of holomorphic operators acting on this space and a new set of coherent states which are covariant under
Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
We give an independent derivation of the Engle-Pereira-Rovelli spinfoam model for quantum gravity which recently appeared in [arXiv:0705.2388]. Using the coherent state techniques introduced earlier
Ponzano-Regge model revisited: III. Feynman diagrams and effective field theory
We study the no-gravity limit GN → 0 of the Ponzano–Regge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with the Hadamard propagator) expressed as
Spin networks for noncompact groups
Spin networks are a natural generalization of Wilson loop functionals. They have been extensively studied in the case where the gauge group is compact and it has been shown that they naturally form a
Holomorphic simplicity constraints for 4D spinfoam models
Within the framework of spinfoam models, we revisit the simplicity constraints reducing topological BF theory to 4D Riemannian gravity. We use the reformulation of SU(2) intertwiners and spin
Spectra of length and area in (2 + 1) Lorentzian loop quantum gravity
We study the spectrum of the length and area operators in Lorentzian loop quantum gravity, in 2 + 1 spacetime dimensions. We find that the spectrum of spacelike intervals is continuous, whereas the
The fine structure of SU(2) intertwiners from U(N) representations
In this work, we study the Hilbert space space of N-valent SU(2) intertwiners with fixed total spin, which can be identified, at the classical level, with a space of convex polyhedra with N faces and