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q-Exponentials on quantum spaces

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Abstract.

We present explicit formulae for q-exponentials on quantum spaces which could be of particular importance in physics, i.e. the q-deformed Minkowski space and the q-deformed Euclidean space with two, three or four dimensions. Furthermore, these formulae can be viewed as 2-, 3- or 4-dimensional analogues of the well-known q-exponential function.

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References

  1. H. Grosse, C. Klim cik, P. Pre snajder, Int. J. Theor. Phys. 35, 231 (1996) [hep-th/9505175]

    MathSciNet  MATH  Google Scholar 

  2. R. Oeckl, Commun. Math. Phys. 217, 451 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. C. Blohmann, Eur. Phys. J. C 30, 435 (2003) [hep-th/0111172]

    Article  MathSciNet  Google Scholar 

  4. M. Chaichian, A.P. Demichev, Phys. Lett. B 320, 273 (1994) [hep-th/9310001]

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  6. C. Bauer, H. Wachter, Eur. Phys. J. C 31, 261 (2003) [math-ph/0201023]

    Article  MATH  Google Scholar 

  7. H. Wachter, Eur. Phys. J. C 32, 281 (2004) [hep-th/0206083]

    Article  Google Scholar 

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

  9. S. Majid, Introduction to Braided Geometry and q-Minkowski Space, preprint (1994) [hep-th/9410241]

  10. J. Wess, q-deformed Heisenberg Algebras, in Proceedings of the 38. Internationale Universitätswochen für Kern- und Teilchenphysik, Schladming, 1999, edited by H. Gausterer, H. Grosse, L. Pittner (no. 543 Lect. Notes in Phys., Springer 2000) [math-phy/9910013]

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

    MathSciNet  MATH  Google Scholar 

  12. J.E. Moyal, Proc. Camb. Phil. Soc. 45, 99 (1949)

    MathSciNet  MATH  Google Scholar 

  13. J. Madore, S. Schraml, P. Schupp, J. Wess, Eur. Phys. J C 16, 161 (2000) [hep-th/0001203]

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  17. S. Majid, Suppl. Rend. Circ. Mat. Palermo, Ser. II, 26, 197 (1991)

  18. S. Majid, Lec. Notes Pure Appl. Math. 158, 55 (1994)

    MATH  Google Scholar 

  19. S. Mac Lane, Categories for the working mathematician (Springer, Berlin 1974)

  20. M. Chaichian, A.P. Demichev, Introduction to quantum groups (World Scientific, Singapore 1996)

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

  22. S. Majid, J. Math. Phys. 34, 4843 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  23. L.C. Biedenharn, M.A. Lohe, Quantum group symmetry and q-tensor algebras (World Scientific, Singapore 1995)

  24. T.H. Koornwinder, Special functions and q-commuting variables, preprint (1996) [q-alg/9608008]

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

    Article  MathSciNet  Google Scholar 

  26. U. Carow-Watamura, M. Schlieker, S. Watamura, Z. Phys. C 49, 439 (1991)

    MathSciNet  Google Scholar 

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

  28. S. Majid, J. Geom. Phys. 22, 14 (1997)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  33. V.K. Dobrev, Phys. Lett. B 341 133 (1994); B 346, 427 (1995)

    Google Scholar 

  34. M. Chaichian, A.P. Demichev, J. Math. Phys. 36, 398 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  35. A. Lorek, W.B. Schmidke, J. Wess, Lett. Math. Phys. 31, 279 (1994)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  38. S. Majid, J. Math. Phys. 36, 4436 (1995)

    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: 21 January 2004, Revised: 19 May 2004, Published online: 7 September 2004

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Wachter, H. q-Exponentials on quantum spaces. Eur. Phys. J. C 37, 379–389 (2004). https://doi.org/10.1140/epjc/s2004-01999-5

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  • DOI: https://doi.org/10.1140/epjc/s2004-01999-5

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