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Perelomov-type coherent states of SO(D+1) in all-dimensional loop quantum gravity

Long, Gaoping ; Bodendorfer, Norbert


A comprehensive study of the application of SO(D + 1) coherent states of Perelomov type to loop quantum gravity in general spacetime dimensions 1 + D >= 3 is given in this paper. We focus on so-called simple representations of SO(D + 1) which solve the simplicity constraint acting on edges and the associated homogeneous harmonic function spaces. With the harmonic function formulation, we study ...


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