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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Heriot-Watt University
2010
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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 |
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510 Papageorgiou, Georgios Galilean quantum gravity in 2+1 dimensions |
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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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1718120829990993920 |