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LQG vertex with finite Immirzi parameter
Abstract We extend the definition of the “flipped” loop-quantum-gravity vertex to the case of a finite Immirzi parameter γ . We cover both the Euclidean and Lorentzian cases. We show that theExpand
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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, theExpand
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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 $U({2}^{n})$ onExpand
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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 modelExpand
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Solving the simplicity constraints for spinfoam quantum gravity
General relativity can be written as topological BF theory plus a set of second-class constraints. Classically the constraints provide the geometric interpretation of the B variables and reduce BF toExpand
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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 underExpand
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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 asExpand
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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 aExpand
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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 spinExpand
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Lifting SU(2) spin networks to projected spin networks
Projected spin network states are the canonical basis of quantum states of geometry for the recent EPRL-FK spinfoam models for quantum gravity introduced by Engle-Pereira-Rovelli-Livine andExpand
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