The Journey to Affine Histories

• Main Author: Kessari, Smaragda
• Published: Lancaster University 2006
• Subjects: 520
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.485229

Two problems are tackled in this thesis, both involving modern approaches to the 'problem of time' in canonical quantum. gravity. The first task involves applying the recently introduced 'parametric theory' of Charles Wang to the Bianchi IX. cosmological model. The second task involves showing how consistent histories quantum cosmology can be realised in the context of Chris Isham's Histories Projection Operator (HPO) consistent histories scheme. This involves using an 'affine histories' approach in which, in or:der to better reflect the positivity proper- ..... ties of a classical spatial metric, I use an affine algebra instead of a canonical one. In particular, this algebra is discussed for the case of a Friedmann Robertson-Walker (FRW) universe coupled to a scalar field. I then study the properties of some appropriate cocycle representations of this algebra that are ·obtained using old ideas of Gel'fand. Because of the use of a continuous time variable, certain divergences arise in quantities of physical interest, and these need to be removed. I do this by introducing a regularisation scheme that is closely adapted to the representations in use, and I then show how this leads to a well-defined history Hamiltonian that exists as a genuine, positive, self-adjoint operator. The role of the choice of cocycle is discussed and it is shown how it is related to a type of ground-state energy.