Combinatorial quantization of Euclidean gravity in three dimensions
Jun, 2000Citations per year
Abstract:
In the Chern-Simons formulation of Einstein gravity in 2+1 dimensions the phase space of gravity is the moduli space of flat G-connections, where G is a typically non-compact Lie group which depends on the signature of space-time and the cosmological constant. For Euclidean signature and vanishing cosmological constant, G is the three-dimensional Euclidean group. For this case the Poisson structure of the moduli space is given explicitly in terms of a classical r-matrix. It is shown that the quantum R-matrix of the quantum double D(SU(2)) provides a quantisation of that Poisson structure.Note:
- cosmetic change Report-no: MS-00-007 Subj-class: Quantum Algebra; Mathematical Physics MSC-class: 81R50 (Primary) 83C45 (Secondary)
- gravitation
- field theory: Euclidean
- dimension: 3
- gauge field theory: SO(3)
- gauge field theory: SO(2,1)
- Chern-Simons term
- quantization
- group theory: deformation
- algebra: Lie
- moduli space: symplectic
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