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Holomorphic simplicity constraints for 4D spinfoam models

Identifieur interne : 006265 ( Main/Exploration ); précédent : 006264; suivant : 006266

Holomorphic simplicity constraints for 4D spinfoam models

Auteurs : Mat Dupuis [France, Australie] ; Etera R. Livine [France]

Source :

RBID : ISTEX:14817C24849700947628577DAB0E25000260A8C0

Descripteurs français

English descriptors

Abstract

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 networks in terms of spinors, which has come out from both the recently developed U(N) framework for SU(2) intertwiners and the twisted geometry approach to spin networks and spinfoam boundary states. Using these tools, we are able to perform a holomorphic/anti-holomorphic splitting of the simplicity constraints and define a new set of holomorphic simplicity constraints, which are equivalent to the standard ones at the classical level and which can be imposed strongly on intertwiners at the quantum level. We then show how to solve these new holomorphic simplicity constraints using coherent intertwiner states. We further define the corresponding coherent spin network functionals and introduce a new spinfoam model for 4D Riemannian gravity based on these holomorphic simplicity constraints and whose amplitudes are defined from the evaluation of the new coherent spin networks.

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DOI: 10.1088/0264-9381/28/21/215022


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Le document en format XML

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<div type="abstract">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 networks in terms of spinors, which has come out from both the recently developed U(N) framework for SU(2) intertwiners and the twisted geometry approach to spin networks and spinfoam boundary states. Using these tools, we are able to perform a holomorphic/anti-holomorphic splitting of the simplicity constraints and define a new set of holomorphic simplicity constraints, which are equivalent to the standard ones at the classical level and which can be imposed strongly on intertwiners at the quantum level. We then show how to solve these new holomorphic simplicity constraints using coherent intertwiner states. We further define the corresponding coherent spin network functionals and introduce a new spinfoam model for 4D Riemannian gravity based on these holomorphic simplicity constraints and whose amplitudes are defined from the evaluation of the new coherent spin networks.</div>
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