@inproceedings{9bf48b516dbf48419a20d4544f52d5c3,

title = "Quantum Gravity and Non-commutative Space-times in Three Dimensions: A Unified Approach",

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.",

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

author = "Schroers, {Bernd Johannes}",

year = "2011",

doi = "10.5506/APhysPolBSupp.4.379",

language = "English",

volume = "4",

series = "Acta Physica Polonica B Proceedings Supplement",

publisher = "Jagellonian University",

number = "3",

pages = "379--402",

editor = "M Praszalowicz and P Bizon and W Broniowski and M Kutschera and W Slominski",

booktitle = "Geometry and Physics in Cracow",

note = "Conference on Geometry and Physics in Cracow ; Conference date: 21-09-2010 Through 25-09-2010",

}