Abstract
By using the remarkable properties of the (non-compact) quantum dilogarithm it is shown that the Dehn twist operator in quantum Teichmüller 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 expected spectrum of conformal weights in continuous quantum Liouville theory at c > 1.
Supported in part by grants CRDF RM1-2244, INTAS 99-01705, and RFBR 99-01-00101
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© 2001 Springer Science+Business Media Dordrecht
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Kashaev, R. (2001). The Quantum Dilogarithm and Dehn Twists in Quantum TeichmÜller Theory. In: Pakuliak, S., von Gehlen, G. (eds) Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory. NATO Science Series, vol 35. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0670-5_13
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DOI: https://doi.org/10.1007/978-94-010-0670-5_13
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