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Integrability for Relativistic Spin Networks

Barrett, John W.; Baez, John C.

Authors

John W. Barrett

John C. Baez



Abstract

The evaluation of relativistic spin networks plays a fundamental role in the Barrett-Crane state sum model of Lorentzian quantum gravity in 4 dimensions. A relativistic spin network is a graph labelled by unitary irreducible representations of the Lorentz group appearing in the direct integral decomposition of the space of L^2 functions on three-dimensional hyperbolic space. To `evaluate' such a spin network we must do an integral; if this integral converges we say the spin network is `integrable'. Here we show that a large class of relativistic spin networks are integrable, including any whose underlying graph is the 4-simplex (the complete graph on 5 vertices). This proves a conjecture of Barrett and Crane, whose validity is required for the convergence of their state sum model.

Journal Article Type Article
Publication Date Jan 1, 2001
Journal Classical and Quantum Gravity
Print ISSN 0264-9381
Publisher IOP Publishing
Peer Reviewed Not Peer Reviewed
Volume 18
Issue 4683-4
APA6 Citation Barrett, J. W., & Baez, J. C. (2001). Integrability for Relativistic Spin Networks. Classical and Quantum Gravity, 18(4683-4),
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf


0101107.pdf (210 Kb)
PDF

Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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