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U(N) Coherent States for Loop Quantum Gravity

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arxiv 1005.2090 v1 pith:QR2ZV6GR submitted 2010-05-12 gr-qc math-phmath.MP

classification gr-qcmath-phmath.MP
keywords coherentstatesintertwinersspaceactingcovariantdirectelements
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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 U(N) transformations. These states are labeled by elements of the Grassmannian Gr(N,2), they possess a direct geometrical interpretation in terms of framed polyhedra and are shown to be related to the well-known coherent intertwiners.

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  1. Homothetic expansion of polyhedra in the two-vertex model: emergence of FLRW

    gr-qc 2025-07 conditional novelty 6.0 of 10

    In the U(N)-symmetric sector of the two-vertex loop-quantum-gravity model, the face frames of the twisted-geometry polyhedra evolve by a common scaling plus rotation, so all planar angles stay constant and the polyhed...

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