Lessons from (2+1)-dimensional quantum gravity
arXiv:0710.5844
Abstract
Proposals that quantum gravity gives rise to non-commutative spacetime geometry and deformations of Poincare symmetry are examined in the context of (2+1)-dimensional quantum gravity. The results are expressed in five lessons, which summarise how the gravitational constant, Planck's constant and the cosmological constant enter the non-commutative and non-cocommutative structures arising in (2+1)-dimensional quantum gravity. It is emphasised that the much studied bicrossproduct kappa-Poincare algebra does not arise directly in (2+1)-dimensional quantum gravity.
17 pages, two figures, based on talk given at the conference ``From Quantum to Emergent Gravity: Theory and Phenomenology'',June 11-15 2007, Trieste, Italy
References in corpus (6)
- Introduction to Doubly Special Relativity
- Quantum symmetry, the cosmological constant and Planck scale phenomenology
- Symplectic structures associated to Lie-Poisson groups
- Symplectic structure of the moduli space of flat connections on a Riemann surface
- Hamiltonian Quantization of Chern-Simons theory with SL(2,C) Group
- Noncommutative geometry of angular momentum space U(su(2))
Cited by in corpus (10)
- Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra
- Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
- Effective particle kinematics from Quantum Gravity
- On limitations of the extent of inertial frames in non-commutative relativistic spacetimes
- Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity
- On the semiduals of local isometry groups in 3d gravity
- Snyder Momentum Space in Relative Locality
- q-Deformation and Semidualisation in 3d Quantum Gravity
- Quantum gravity and non-commutative spacetimes in three dimensions: a unified approach
- Classical r-matrices for the generalised Chern-Simons formulation of 3d gravity