Discrete and Continuum Approaches to Three-Dimensional Quantum Gravity

  title={Discrete and Continuum Approaches to Three-Dimensional Quantum Gravity},
  author={Hirosi Ooguri and Naoki Sasakura},
  journal={Modern Physics Letters A},
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
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Nucl. Phys
  • Nucl. Phys
  • 1990
Phys. Rev. Lett
  • Phys. Rev. Lett
  • 1990
Yahikozawa, preprint IC-90-44
  • 1990
Commun. Math. Phys
  • Commun. Math. Phys
  • 1989
Moore and N. Reshetikhin, Nucl. Phys
  • Moore and N. Reshetikhin, Nucl. Phys
  • 1989