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Abstract: In this work we give an explicit isomorphism between the usual spin networkbasis and the direct quantization of the reduced phase space of tetrahedra. Themain outcome is a formula that describes the space of SU2 invariant states byan integral over coherent states satisfying the closure constraint exactly, orequivalently, as an integral over the space of classical tetrahedra. Thisprovides an explicit realization of theorems by Guillemin-Sternberg and Hallthat describe the commutation of quantization and reduction. In the final partof the paper, we use our result to express the FK spin foam model as anintegral over classical tetrahedra and the asymptotics of the vertex amplitudeis determined.



Author: Florian Conrady, Laurent Freidel Perimeter Inst. Theor. Phys.

Source: https://arxiv.org/







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