Quantum gravity and non-commutative spacetimes in three dimensions: a unified approach

Understand

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,\Lambda,\hbar) enter as deformation parameters.

• The classical situation is summarised, where solutions can be characterised in terms of model spacetimes (which depend on c and \Lambda), 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 spacetimes replacing the classical model spacetimes.
• This point of view is explained, and open issues are sketched.