Topological quantum field theory and quantum gravity

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Kerr, Steven (2014) Topological quantum field theory and quantum gravity. PhD thesis, University of Nottingham.

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Abstract

This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a 1-manifold. The models are independent of the triangulation and give the same result as the continuum partition functions evaluated using zeta-function regularisation. Some implications for more physical models are discussed.

In the second part, the gauge gravity action is written using a particularly simple matrix technique. The coupling to scalar, fermion and Yang-Mills fields is reviewed, with some small additions. A sum over histories quantisation of the gauge gravity theory in 2+1 dimensions is then carried out for a particular class of triangulations of the three-sphere. The preliminary stage of the Hamiltonian analysis for the (3+1)-dimensional gauge gravity theory is undertaken.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Barrett, J.W.
Louko, J.M.T.
Subjects: Q Science > QA Mathematics > QA611 Topology
Q Science > QC Physics > QC170 Atomic physics. Constitution and properties of matter
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 14094
Depositing User: EP, Services
Date Deposited: 19 Jan 2015 09:31
Last Modified: 15 Dec 2017 08:51
URI: https://eprints.nottingham.ac.uk/id/eprint/14094

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