We quantise a Poisson structure on Hn+2g, where H is a semidirect product group of the form G ⋉ g. This Poisson structure arises in the combinatorial description of the phase space of Chern-Simons theory with gauge group G ⋉ g on R × Sg,n, where Sg,n is a surface of genus g with n punctures. The quantisation of this Poisson structure is a key step in the quantisation of Chern-Simons theory with...

This is an introduction to work on the generalisation to quantum groups of Mackey’s approach to quantisation on homogeneous spaces. We recall the bicrossproduct models of the author, which generalise the quantum double. We describe the general extension theory of Hopf algebras and the nonAbelian cohomology spaces H(H,A) which classify them. They form a new kind of topological quantum number in ...

We study the classical and quantum theory of spherically symmetric spacetimes with scalar field coupling in general relativity. We utilise the canonical formalism of geometrodynamics adapted to the Painleve-Gullstrand coordinates, and present a new quantisation of the resulting field theory. We give an explicit construction of operators that capture curvature properties of the spacetime and use...

We investigate a formulation of continuum 4d gravity in terms of a constrained topological (BF) theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum gravity. We identify both the continuum version of the linear simplicity constraints used in the quantum discrete context and a linear version of t...

A generalisation of the recently formulated nonlinear quantisation of a parameterised theory is presented in the context of quantum gravity. The parametric quantisation of a Friedmann universe with a massless scalar field is then considered in terms of the analytic solutions of the resulting evolution equations. PACS numbers: 04.20.Fy, 04.60.Ds, 04.60.Kz, 11.10.Lm In a recent paper [1] the quan...