Skip to main content
SpringerLink
Log in
Book cover

Geometric and Quantum Aspects of Integrable Systems pp 213–222Cite as

Some aspects of the q-deformed oscillator algebras as quantum groups

  • Conference paper
  • First Online:

  • 157 Accesses

Part of the book series: Lecture Notes in Physics ((LNP,volume 424))

Abstract

We study the q-deformation of the Clifford algebras that come out in a natural way for fermions and bosons in Fock space. An analysis of three particular cases; the transformation of fermion (bosons) among themselves, the linear combination of fermions (bosons) in order to get bosons (fermions) and a supersymmetric transformation, is carried out.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.B. Mc Guire, J. Math. Phys. 5, 622, 1964.

    Article  Google Scholar 

  2. C.N. Yang, Phys. Rev. Lett. 19, 1312, 1967.

    Article  Google Scholar 

  3. R.J. Baxter, Ann. Phys. 70, 193, 1972 and 76 1, 1973.

    Article  Google Scholar 

  4. L.D. Faddeev, E.K. Sklyanin and L.A. Takhtajan, Theor. Math. Phys. 40,194, 1979.

    Article  Google Scholar 

  5. M.F. Atiyah, R. Bott and A. Shapiro, Topology, vol. 3 suppl. 1, 3, 1964.

    Article  Google Scholar 

  6. C. Chevalley, The algebraic theory of spinors (Columbia University press, 1954).

    Google Scholar 

  7. A.Crumeyrolle, Clifford Algebras and their Applications in Mathematical Physics; J.S.R. Chisholm and A.K. Common editors, proceedings of the NATO and SERC Workshop in Canterbury U.K. (Reidel Dordrech, 1986).

    Google Scholar 

  8. L.D. Faddeev, Soviet Scientific Reviews (Harvard Academic, London) C1, 107, 1980.

    Google Scholar 

  9. L.D. Faddeev, Integrable models in (1+1) dimensional quantum field theory, Les Houches Session XXXIX (Elsevier, Amsterdam, 1982), 563.

    Google Scholar 

  10. L.D. Faddeev and N.Y. Reshetilkhin, Ann. Phys. 167, 227, 1986.

    Article  Google Scholar 

  11. V.G. Drinfeld, Sov. Math. Dokl. 27, 68, 1983.

    Google Scholar 

  12. V.G. Drinfeld, Sov. Math. Dokl. 32, 254, 1985.

    Google Scholar 

  13. V.G. Drinfeld, Quantum Groups, ICM Proceedings, Berkley, 798, 1986.

    Google Scholar 

  14. M. Jimbo, Lett. Math. Phys. 10, 63, 1985.

    Article  Google Scholar 

  15. M. Jimbo, Commun. Math. Phys., 102, 537, 1986.

    Article  Google Scholar 

  16. M. Jimbo, Lett. Math. Phys. 11, 247, 1986.

    Article  Google Scholar 

  17. S.L. Woronowicz, Commun. Math. Phys. 111, 613, 1987.

    Article  Google Scholar 

  18. Y.I. Manin, Ann. Inst. Fourier (Grenoble) 37, 4, 191, 1987.

    Google Scholar 

  19. Y.I. Manin, Commun. Math. Phys. 123, 163, 1989.

    Article  Google Scholar 

  20. Integrable Quantum Field Theories, proceedings. Lecture Notes in Physics, Springer Verlag, 1982.

    Google Scholar 

  21. S. Chaturvedi, A.K. Kapoor, R. Sandhya, V. Srinivasan and R. Simon, Phys. Rev. A, 43, 4555, 1991

    Article  PubMed  Google Scholar 

  22. Lüscher M., Nucl. Phys. B117, 475, 1976.

    Article  Google Scholar 

  23. U. Carow-Watamura, M. Schlieker, M. Scholl and S. Watamura, Int. Jour of Mod. Physics A, Vol. 6 N!17, 3081, 1991.

    Article  Google Scholar 

  24. K. Fredenhagen, Commun. Math. Phys. 79, 141, 1981.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Facultad de Estudios Superiores Cuautitlán, Universidad Nacional Autónoma de México, Cuautitlán lzcalli, Apdo 142, Estado de México, México

    Suemi Rodriguez-Romo

  2. Physics Department, University of Konstanz, Box 5560, D-7750, Konstanz, Germany

    Dieter W. Ebnere

Authors
  1. Suemi Rodriguez-Romo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dieter W. Ebnere
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

G. F. Helminck

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag

About this paper

Cite this paper

Rodriguez-Romo, S., Ebnere, D.W. (1993). Some aspects of the q-deformed oscillator algebras as quantum groups. In: Helminck, G.F. (eds) Geometric and Quantum Aspects of Integrable Systems. Lecture Notes in Physics, vol 424. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0021448

Download citation

  • DOI: https://doi.org/10.1007/BFb0021448

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57365-4

  • Online ISBN: 978-3-540-48090-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation