JOHN BARRETT john.barrett@nottingham.ac.uk
Professor of Mathematical Physics
Integrability for Relativistic Spin Networks
Barrett, John W.; Baez, John C.
Authors
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.
Citation
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Peer Reviewed | Not Peer Reviewed |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 | http://eprints.nottingham.ac.uk/id/eprint/7 |
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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