Galilean quantum gravity in 2+1 dimensions

In this thesis, we study the Galilean limit of gravity in 2+1 dimensions and give the necessary ingredients for its quantisation. We study two groups that play fundamental role in this thesis, the two-fold central extension of the Galilei and Newton-Hooke groups in 2+1 dimensions and their correspon...

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Main Author: Papageorgiou, Georgios
Other Authors: Schroers, Bernd
Published: Heriot-Watt University 2010
Subjects:
510
Online Access:http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.547663
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spelling ndltd-bl.uk-oai-ethos.bl.uk-5476632015-11-03T03:45:35ZGalilean quantum gravity in 2+1 dimensionsPapageorgiou, GeorgiosSchroers, Bernd2010In this thesis, we study the Galilean limit of gravity in 2+1 dimensions and give the necessary ingredients for its quantisation. We study two groups that play fundamental role in this thesis, the two-fold central extension of the Galilei and Newton-Hooke groups in 2+1 dimensions and their corresponding Lie algebras. We construct what we call \Galilean gravity in 2+1 dimensions" as the Chern-Simons theory of the Galilei group and generalise this construction to include a cosmological constant which, in the present setting corresponds to the Chern-Simons theory of the Newton-Hooke group. Finally, we apply the combinatorial quantisation program in detail to the Galilei group: we give the irreducible, unitary representation of the relevant quantum double and fully explore Galilean quantum gravity in this setting. We highlight the associated structures for the Newton-Hooke group and provide an outline for a similar quantisation. In doing so, we provide the link between Newton-Hooke gravity, and a deformation of an extension of the Heisenberg algebra that is well-studied.510Heriot-Watt Universityhttp://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.547663http://hdl.handle.net/10399/2403Electronic Thesis or Dissertation
collection NDLTD
sources NDLTD
topic 510
spellingShingle 510
Papageorgiou, Georgios
Galilean quantum gravity in 2+1 dimensions
description In this thesis, we study the Galilean limit of gravity in 2+1 dimensions and give the necessary ingredients for its quantisation. We study two groups that play fundamental role in this thesis, the two-fold central extension of the Galilei and Newton-Hooke groups in 2+1 dimensions and their corresponding Lie algebras. We construct what we call \Galilean gravity in 2+1 dimensions" as the Chern-Simons theory of the Galilei group and generalise this construction to include a cosmological constant which, in the present setting corresponds to the Chern-Simons theory of the Newton-Hooke group. Finally, we apply the combinatorial quantisation program in detail to the Galilei group: we give the irreducible, unitary representation of the relevant quantum double and fully explore Galilean quantum gravity in this setting. We highlight the associated structures for the Newton-Hooke group and provide an outline for a similar quantisation. In doing so, we provide the link between Newton-Hooke gravity, and a deformation of an extension of the Heisenberg algebra that is well-studied.
author2 Schroers, Bernd
author_facet Schroers, Bernd
Papageorgiou, Georgios
author Papageorgiou, Georgios
author_sort Papageorgiou, Georgios
title Galilean quantum gravity in 2+1 dimensions
title_short Galilean quantum gravity in 2+1 dimensions
title_full Galilean quantum gravity in 2+1 dimensions
title_fullStr Galilean quantum gravity in 2+1 dimensions
title_full_unstemmed Galilean quantum gravity in 2+1 dimensions
title_sort galilean quantum gravity in 2+1 dimensions
publisher Heriot-Watt University
publishDate 2010
url http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.547663
work_keys_str_mv AT papageorgiougeorgios galileanquantumgravityin21dimensions
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