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q-Integration on quantum spaces

  • theoretical physics
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Abstract.

In this article we present explicit formulae for q-integration on quantum spaces which could be of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three or four dimensions. Furthermore, our formulae can be regarded as a generalization of Jackson’s q-integral to three or four dimensions and provide a new possibility for an integration over the whole space being invariant under translations and rotations.

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References

  1. N.Yu. Reshetikhin, L.A. Takhtadzhyan, L.D. Faddeev, Leningrad Math. J. 1, 193 (1990)

    MathSciNet  MATH  Google Scholar 

  2. J. Wess, q-deformed Heisenberg Algebras, in Proceedings of the 38. Internationale Universitätswochen für Kern- und Teilchen physik, no. 543, edited by H. Gausterer, H. Grosse, L. Pittner, in Lecture Notes in Physics (Springer-Verlag, Schladming 2000), math-phy/9910013

  3. S. Majid, Braided geometry: A new approach to q-deformations,in First Caribbean Spring School of Mathematics and Theoretical Physics, edited by R. Coquereaux (World Scientific, Guadeloupe 1993)

  4. J.E. Moyal, Proceedings Camb. Phil. Soc. 45, 99 (1949)

    MathSciNet  MATH  Google Scholar 

  5. J. Madore, S. Schraml, P. Schupp, J. Wess, Eur. Phys. J. C 16, 161 (2000), hep-th/0103120

    MathSciNet  Google Scholar 

  6. H. Wachter, M. Wohlgenannt, Eur. Phys. J. C 23, 761 (2002), hep-th/0103120

    MathSciNet  Google Scholar 

  7. V.G. Drinfeld, Soviet Math. Dokl. 32, 254 (1985)

    Google Scholar 

  8. M. Jimbo, Lett. Math. Phys. 10, 63 (1985)

    MathSciNet  MATH  Google Scholar 

  9. J. Wess, B. Zumino, Nucl. Phys. B Suppl. 18, 302 (1991)

    Article  Google Scholar 

  10. C. Bauer, H. Wachter, Eur. Phys. J. C (2003), Digital Object Identifier (DOI) 10.1140/epjc/s2003-01324-0 [math-ph/0201023]

  11. F.H. Jackson, q-Integration, Proceedings Durham Phil. Soc. 7, 182 (1927)

    Google Scholar 

  12. A. Lorek, W. Weich, J. Wess, Z. Phys. C 76, 375 (1997), q-alg/9702025

    Article  MathSciNet  Google Scholar 

  13. A. Klimyk, K. Schmüdgen, Quantum groups and their representations (Springer Verlag, Berlin 1997)

  14. S. Majid, Foundations of quantum group theory (University Press, Cambridge 1995)

  15. H. Ocambo, Z. Phys. C 70, 525 (1996)

    Article  Google Scholar 

  16. U. Carow-Watamura, M. Schlieker, M. Scholl, S. Watamura, Z. Phys. C 48, 159 (1990)

    MathSciNet  Google Scholar 

  17. W.B. Schmidke, J. Wess, B. Zumino, Z. Phys. C 52, 471 (1991)

    MathSciNet  MATH  Google Scholar 

  18. S. Majid, J. Math. Phys. 32, 3246 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  19. V.K. Dobrev, Phys. Lett. B 341, 133 (1994)

    Article  MathSciNet  Google Scholar 

  20. O. Ogievetsky, W.B. Schmidke, J. Wess, B. Zumino, Commun. Math. Phys. 150, 495 (1992)

    MathSciNet  Google Scholar 

  21. M. Rohregger, J. Wess, Eur. Phys. J. 7, 177 (1999)

    Article  MathSciNet  Google Scholar 

  22. H. Steinacker, J. Math. Phys. 37, 4738 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  23. C. Chryssomalakos, B. Zumino, Translations integrals and Fourier transforms in the quantum plane,preprint LBL-34803, UCCB-PTH-93/30, in Salamfestschrift, edited by A. Ali, J. Ellis, S. Randjbar-Daemi (World Scientific, Singapore 1993)

  24. G. Fiore, Int. J. Mod. Phys. A 8, 4679 (1993)

    MathSciNet  MATH  Google Scholar 

  25. A. Hebecker, W. Weich, Lett. Math. Phys. 26, 245 (1992)

    MathSciNet  MATH  Google Scholar 

  26. M.A. Dietz, Symmetrische Formen auf Quantenalgebren,diploma-thesis, Universität Hamburg, Fakultät für Physik (2001)

  27. A. Kempf, S. Majid, J. Math. Phys. 35, 6802 (1994)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Sektion Physik, Ludwig-Maximilians-Universität, Theresienstr. 37, 80333, München, Germany

    H. Wachter

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  1. H. Wachter
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Correspondence to H. Wachter.

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Received: 9 September 2003, Published online: 26 November 2003

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Wachter, H. q-Integration on quantum spaces. Eur. Phys. J. C 32, 281–297 (2004). https://doi.org/10.1140/epjc/s2003-01397-7

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  • DOI: https://doi.org/10.1140/epjc/s2003-01397-7

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