Quantum Gravity and Non-commutative Space-times in Three Dimensions: A Unified Approach

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12 Citations (Scopus)

Abstract

These notes summarise a talk surveying the combinatorial or Hamiltonian quantisation of three dimensional gravity in the Chern-Simons formulation, with an emphasis on the role of quantum groups and on the way the various physical constants (c, G, A, h) enter as deformation parameters. The classical situation is summarised, where solutions can be characterised in terms of model space-times (which depend on c and A) together with global identifications via elements of the corresponding isometry groups. The quantum theory may be viewed as a deformation of this picture, with quantum groups replacing the local isometry groups, and non-commutative space-times replacing the classical model space-times. This point of view is explained, and open issues are sketched.

Original languageEnglish
Title of host publicationGeometry and Physics in Cracow
EditorsM Praszalowicz, P Bizon, W Broniowski, M Kutschera, W Slominski
Pages379-402
Number of pages24
Volume4
DOIs
Publication statusPublished - 2011
EventConference on Geometry and Physics in Cracow - Krakow, Poland
Duration: 21 Sep 201025 Sep 2010

Publication series

NameActa Physica Polonica B Proceedings Supplement
PublisherJagellonian University
Number3
Volume4
ISSN (Print)1899-2358

Conference

ConferenceConference on Geometry and Physics in Cracow
CountryPoland
CityKrakow
Period21/09/1025/09/10

Keywords

  • CHERN-SIMONS THEORY
  • (2+1)-DIMENSIONAL GRAVITY
  • COMBINATORIAL QUANTIZATION
  • SYMPLECTIC STRUCTURE
  • POINCARE ALGEBRA
  • EINSTEIN GRAVITY
  • FIELD-THEORY
  • SCATTERING
  • SYMMETRY
  • DEFORMATION

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