Skip to main content
Log in

Zero modes for the quantum Liouville model

  • Published:
Functional Analysis and Its Applications Aims and scope

Abstract

The problem of identification of zero modes for the quantum Liouville model is discussed and the corresponding Hilbert space representation is constructed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J.-L. Gervais and J. Schnittger, “The many faces of the quantum Liouville exponentials,” Nuclear Phys. B, 413 (1994), 433–457; http://arxiv.org/abs/hep-th/9308134.

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Teschner, “A lecture on the Liouville vertex operators,” Internat. J. Modern. Phys. A, 19 (2004), May, suppl., 436–458; http://arxiv.org/abs/hep-th/0303150.

    Article  MathSciNet  MATH  Google Scholar 

  3. O. Babelon, “Universal exchange algebra for Bloch waves and Liouville theory,” Comm. Math. Phys., 139:3 (1991), 619–643.

    Article  MathSciNet  MATH  Google Scholar 

  4. L. D. Faddeev and A. Y. Volkov, “Discrete evolution for the zero-modes of the quantum Liouville model,” J. Phys. A, 41 (2008), no. 19, 194008; http://arxiv.org/abs/0803.0230.

    Article  MathSciNet  Google Scholar 

  5. L. D. Faddeev and L. A. Takhtajan, “Liouville model on the lattice,” in: Lecture Notes in Phys., vol. 246, Springer-Verlag, Berlin, 1986, 166–179.

    Google Scholar 

  6. V. G. Drinfeld, “Hopf algebras and the quantum Yang-Baxter equation,” Dokl. Akad. Nauk SSSR, 283:5 (1985), 1060–1064; English transl.: Soviet Math. Dokl., 32: 1 (1985), 254–258.

    MathSciNet  Google Scholar 

  7. L. D. Faddeev, N. Y. Reshetikhin, and L. A. Takhtajan, “Quantization of Lie groups and Lie algebras,” Algebra Analiz, 1:1 (1989), 178–206; English transl.: Leningrad Math. J., 1:1 (1990), 193–225.

    MathSciNet  Google Scholar 

  8. R. M. Kashaev, On the Spectrum of Dehn Twists in Quantum Teichmuller Theory, http://arxiv.org/abs/math/0008148.

  9. V. V. Fock and L. Chekhov, “A quantum Teichmüller space,” Teoret. Mat. Fiz., 120:3 (1999), 511–528; English transl.: Theoret. Math. Phys., 120:3 (1999), 1245–1259; http://arxiv.org/abs/math/9908165.

    Article  MathSciNet  Google Scholar 

  10. S. E. Derkachov and L. D. Faddeev, 3j-Symbol for the Modular Double of SL q(2,R) Revisited, http://arxiv.org/abs/1302.5400.

  11. R. M. Kashaev, “The quantum dilogarithm and Dehn twists in quantum Teichmuller theory,” in: Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory (Kiev, 2000), NATO Sci. Ser. II Math. Phys. Chem., vol. 35, Kluwer Acad. Publ., Dordrecht, 2001, 211–221.

    Chapter  Google Scholar 

  12. L. D. Faddeev, “Discrete Heisenberg-Weyl group and modular group,” Lett. Math. Phys., 34:3 (1995), 249–254; http://arxiv.org/abs/hep-th/9504111.

    Article  MathSciNet  MATH  Google Scholar 

  13. A. Y. Volkov, “Noncommutative hypergeometry,” Comm. Math. Phys., 258:2 (2005), 257–273; http://arxiv.org/abs/math/0312084.

    Article  MathSciNet  MATH  Google Scholar 

  14. A. B. Zamolodchikov and A. B. Zamolodchikov, “Conformal bootstrap in Liouville field theory,” Nuclear Phys. B, 477:2 (1996), 577–605; http://arxiv.org/abs/hep-th/9506136.

    Article  MathSciNet  MATH  Google Scholar 

  15. G. Jorjadze and G. Weigt, Zero Mode Problem of Liouville Field Theory, http://arxiv.org/abs/hep-th/0207041.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to L. D. Faddeev.

Additional information

__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 48, No. 3, pp. 14–23, 2014

Original Russian Text Copyright © by L. D. Faddeev

To the centenary of Israel Moiseevich Gelfand

The work was partially supported by RFBR grants 14-01-00341 and 13-01-12405-ofi_m and by the program “Mathematical problems of nonlinear dynamics” of Russian Academy of Science.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Faddeev, L.D. Zero modes for the quantum Liouville model. Funct Anal Its Appl 48, 166–174 (2014). https://doi.org/10.1007/s10688-014-0058-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10688-014-0058-8

Key words

Navigation