Integrability for Relativistic Spin Networks

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.

The ins and outs of biosecurity: bird 'flu in East Anglia and the spatial representation of risk

Avian influenza, or 'bird 'flu' arrived in Norfolk in April 2006 in the form of the low pathogenic strain H7N3. In February 2007 a highly pathogenic strain, H5N1, which can pose a risk to humans, was discovered in Suffolk. We examine how a local newspaper reported the outbreaks, focusing on the linguistic framing of biosecurity. Consistent with the growing concern with securitisation among policymakers, issues were discussed in terms of space (indoor–outdoor; local–global; national–international) and flows (movement, barriers and vectors) between spaces (farms, sheds and countries). The apportioning of blame along the lines of 'them and us'– Hungary and England – was tempered by the reporting on the Hungarian operations of the British poultry company. Explanations focused on indoor and outdoor farming and alleged breaches of biosecurity by the companies involved. As predicted by the idea of securitisation, risks were formulated as coming from outside the supposedly secure enclaves of poultry production.