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By using the Weil-Gel'fand-Zak transform of Faddeev's quantum dilogarithm, we propose a new state-integral model for the Teichm\"uller TQFT, where the circle valued state variables live on the edges of oriented leveled shaped triangulations.
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André Weil · 1941
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Expansion in characteristic functions of an equation with periodic coefficients
I. M. Gel ′ · 1950
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Finite translations in solid state physics
J. Zak · 1967
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The decorated Teichmüller space of punctured surfaces
R. C. Penner · 1987
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Topological quantum field theories
Michael Atiyah · 1988
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G. B. Segal · 1988
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Edward Witten · 1988
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State sum invariants of 3 3 -manifolds and quantum 6 j 6j -symbols
V. G. Turaev and O. Ya. Viro · 1992
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Topological quantum field theories derived from the Kauffman bracket
C. Blanchet, N. Habegger, G. Masbaum, and P. Vogel · 1995
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Discrete Heisenberg–Weyl group and modular group
L. D. Faddeev · 1995
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Quantization of Teichmüller spaces and the quantum dilogarithm
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V. V. Fock and L. O. Chekhov · 1999
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L. D. Faddeev, R. M. Kashaev, and A. Yu. Volkov · 2001
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Kazuhiro Hikami · 2001
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Tudor Dimofte, Sergei Gukov, Jonatan Lenells, and Don Zagier · 2009
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A TQFT from quantum Teichmüller theory
Jørgen Ellegaard Andersen and Rinat Kashaev · 2011
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The volume conjecture, perturbative knot invariants, and recursion relations for topological strings
Robbert Dijkgraaf, Hiroyuki Fuji, and Masahide Manabe · 2011
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Quantum Riemann surfaces in Chern–Simons theory
Tudor Dimofte · 2011
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Yurii A. Neretin · 2011
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