# Discrete and Continuum Approaches to Three-Dimensional Quantum Gravity

@article{Ooguri1991DiscreteAC, title={Discrete and Continuum Approaches to Three-Dimensional Quantum Gravity}, author={Hirosi Ooguri and Naoki Sasakura}, journal={Modern Physics Letters A}, year={1991}, volume={06}, pages={3591-3600} }

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue… Expand

#### 57 Citations

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I argue that the complete partition function of 3D quantum gravity is given by a path integral over gauge-inequivalent manifolds times the Chern-Simons partition function. In a discrete version, it… Expand

Partition Functions and Topology-Changing Amplitudes in the 3D Lattice Gravity of Ponzano and Regge

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We define a physical Hilbert space for the three-dimensional lattice gravity of Ponzano and Regge and establish its isomorphism to the ones in the $ISO(3)$ Chern-Simons theory. It is shown that, for… Expand

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