Skip to main content
SpringerLink
Log in

Vertex Operators for Boundary Algebras

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

We construct embeddings of boundary algebras \(\mathcal{B}\) into ZF algebras \(\mathcal{A}\). Since it is known that these algebras are the relevant ones for the study of quantum integrable systems (with boundaries for \(\mathcal{B}\) and without for \(\mathcal{A}\)), this connection allows to make the link between different approaches of the systems with boundaries. The construction uses the well-bred vertex operators built recently, and is classified by reflection matrices. It relies only on the existence of an R-matrix obeying a unitarity condition, and as such can be applied to any infinite dimensional quantum group.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cherednik, V. I.: Theor. Math. Phys. 61 (1984), 977.

    Google Scholar 

  2. Sklyanin, E. K.: J. Phys. A: Math. Gen. 21 (1988), 2375.

    Google Scholar 

  3. Ghoshal, S. and Zamolodchikov, A. B.: Internat. J. Modern Phys. A 9 (1994), 3841.

    Google Scholar 

  4. Bowcock, P., Corrigan, E., Dorey, P. E. and Rietdijk, R. H.: Nuclear Phys. B 455 (1995), 469; Corrigan, E.: Internat. J. Modern Phys. A 13 (1998), 2709; Boundary bound states in integrable quantum celd theory, Proc. Non-Perturbative Quantum Effects 2000, hep-th/0010094.

    Google Scholar 

  5. Liguori, A. and Mintchev, M.: Nuclear Phys. B 522 (1998), 345; Gattobigio, M., Liguori, A. and Mintchev, M.: Phys. Lett. B 428 (1998), 143; J. Math. Phys. 40 (1999), 2949.

    Google Scholar 

  6. Liguori, A., Mintchev, M. and Zhao, L.: Comm. Math. Phys. 194 (1998), 569.

    Google Scholar 

  7. Mintchev, M., Ragoucy, E. and Sorba, P.: Spontaneous symmetry breaking in the g;(N)-NLS algebra, Preprint LAPTH-844/2001, IFUP-TH 15/2001, hep-th/0104079.

  8. Zamolodchikov, A. B. and Zamolodchikov, A. B.: Ann. Phys. 120 (1979), 253; Faddeev, L. D.: Soviet Sci. Rev. C 1 (1980), 107.

    Google Scholar 

  9. Ragoucy, E.: Vertex operators for quantum groups and application to integrable systems, Preprint LAPTH-859/01, math.QA/0108207.

  10. Freidel, L. and Maillet, J. M.: Phys. Lett. B 262 (1991), 278.

    Google Scholar 

  11. Molev, A. and Ragoucy, E.: Representations of boundary algebras, Preprint LAPTH-863/01, Rev. Math. Phys. to appear.

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Physique Théorique, LAPTH, LAPP, BP 110, F-74941, Annecy-le-Vieux Cedex, France

    E. Ragoucy

Authors
  1. E. Ragoucy
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ragoucy, E. Vertex Operators for Boundary Algebras. Letters in Mathematical Physics 58, 249–260 (2001). https://doi.org/10.1023/A:1014551218947

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1014551218947

Search

Navigation