The Quantum Dilogarithm and Dehn Twists in Quantum TeichmÜller Theory

@inproceedings{Kashaev2001TheQD,
  title={The Quantum Dilogarithm and Dehn Twists in Quantum Teichm{\"U}ller Theory},
  author={Rinat Kashaev},
  year={2001}
}
By using the remarkable properties of the (non-compact) quantum dilogarithm it is shown that the Dehn twist operator in quantum Teichmuller theory has a complete continuous spectrum, the eigenvectors in certain basis being given as a ratio of two quantum dilogarithms. The completeness condition of the eigenvectors includes the integration measure which appeared in the representation theoretic approach to quantum Liouville theory by Ponsot and Teschner. The obtained spectrum is consistent with… CONTINUE READING