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Integrability for Relativistic Spin Networks

Barrett, John W.; Baez, John C.


Professor of Mathematical Physics

John C. Baez


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.


Barrett, J. W., & Baez, J. C. (2001). Integrability for Relativistic Spin Networks. Classical and Quantum Gravity, 18(4683-4),

Journal Article Type Article
Publication Date Jan 1, 2001
Deposit Date Jul 30, 2001
Publicly Available Date Oct 9, 2007
Journal Classical and Quantum Gravity
Print ISSN 0264-9381
Publisher IOP Publishing
Peer Reviewed Not Peer Reviewed
Volume 18
Issue 4683-4
Public URL
Copyright Statement Copyright information regarding this work can be found at the following address:


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