Skip to main content

q-differential calculus and deformed light-cone

  • Quantum Symmetries And q-Deformed Groups
  • Conference paper
  • First Online:
  • 505 Accesses

Part of the book series: Lecture Notes in Physics ((LNP,volume 509))

Abstract

We propose a “short” version of q-deformed differential calculus on the light-cone using twistor representation. The commutation relations between coordinates and momenta are obtained. The quasi-classical limit introduced gives an exact shape of the off-shell shifting.

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

  • Akulov, V. P. and Gerschun, V. D. (1995): Matched reduction of differential calculus on quantum groups GL q(2, c), SL q(2, C) and E q(2)., preprint q-alg/9509030.

    Google Scholar 

  • Azcarraga, J. A., Kulish, P. P., and Rodenas, F. (1994): Quantum groups and deformed special relativity, preprint FTUV 94-21, hep-th/9405161.

    Google Scholar 

  • Clifford, A. H. and Preston, G. B. (1961): The Algebraic Theory of Semigroups, Vol. 1, Amer. Math. Soc., Providence.

    MATH  Google Scholar 

  • Demidov, E. E. (1993): Some aspects of the theory of quantum groups, Russian Math. Surv. 48, 41–79.

    Article  MathSciNet  ADS  Google Scholar 

  • Duplij, S. (1996): On an alternative supermatrix reduction, Lett. Math. Phys. 37, 385–396.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Duplij, S. (1997): Some abstract properties of semigroups appearing in superconformal theories, Semigroup Forum 54, 253–260.

    Article  MATH  MathSciNet  Google Scholar 

  • Faddeev, L. D. and Pyatov, P. N. (1984): The differential calculus on linear quantum groups, preprint hep-th/9402070.

    Google Scholar 

  • Faddeev, L. D., Reshetikhin, N. Y., and Takhtajan, I. A. (1990): Quantum lie groups and lie algebras, Leningrad Math. J. 1, 193–236.

    MATH  MathSciNet  Google Scholar 

  • Green, M. B., Schwarz, J. H., and Witten, E. (1987): Superstring Theory, Vol. 1,2, Cambridge Univ. Press, Cambridge, 1987.

    MATH  Google Scholar 

  • Schirrmacher, A., Wess, J., and Zumino, B. (1991): The two parameter deformation of GL(2) its differential calculus, and Lie algebra, Z. Phys. 49, 317–321.

    Article  MathSciNet  Google Scholar 

  • Wess, J. and Zumino, B. (1990): Covariant differential calculus on the quantum hyperplane, Nucl. Phys. (Proc. Suppl.) B18, 302–312.

    ADS  MathSciNet  Google Scholar 

  • Zupnik, B. M. (1993): Minimal deformations of the commutative algebra and the linear group GL(n), Theor. Math. Phys. 95, 403–415.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. Duplij .

Editor information

Julius Wess Vladimir P. Akulov

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag

About this paper

Cite this paper

Akulov, V.P., Chitov, V.V., Duplij, S. (1998). q-differential calculus and deformed light-cone. In: Wess, J., Akulov, V.P. (eds) Supersymmetry and Quantum Field Theory. Lecture Notes in Physics, vol 509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105262

Download citation

  • DOI: https://doi.org/10.1007/BFb0105262

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64623-5

  • Online ISBN: 978-3-540-69217-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics