Integrability for Relativistic Spin Networks
Data(s) |
2001
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Resumo |
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. |
Formato |
application/postscript application/pdf |
Identificador |
http://eprints.nottingham.ac.uk/7/3/0101107.ps http://eprints.nottingham.ac.uk/7/1/0101107.pdf Barrett, John W. and Baez, John C. (2001) Integrability for Relativistic Spin Networks. Classical and Quantum Gravity, 18 (4683-4). |
Relação |
http://eprints.nottingham.ac.uk/7/ |
Tipo |
Article NonPeerReviewed |