Advertisement

Free q-deformed relativistic wave equations by representation theory

  • C. BlohmannEmail author
theoretical physics

Abstract.

In a representation theoretic approach a free q-relativistic wave equation must have the property that the space of solutions is an irreducible representation of the q-Poincaré algebra. It is shown how this requirement uniquely determines the q-wave equations. As examples, the q-Dirac equation (including q-gamma matrices which satisfy a q-Clifford algebra), the q-Weyl equations, and the q-Maxwell equations are computed explicitly.

Keywords

Wave Equation Theoretic Approach Irreducible Representation Representation Theory Relativistic Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M.R. Douglas, N.A. Nekrasov, Rev. Mod. Phys. 73, 977 (2001), hep-th/0106048CrossRefMathSciNetGoogle Scholar
  2. 2.
    R.J. Szabo, Phys. Rept. 378, 207 (2003), hep-th/0109162CrossRefzbMATHGoogle Scholar
  3. 3.
    N. Seiberg, E. Witten, JHEP 09, 032 (1999), hep-th/9908142zbMATHGoogle Scholar
  4. 4.
    J. Madore, S. Schraml, P. Schupp, J. Wess, Eur. Phys. J. C 16, 161 (2000), hep-th/0001203MathSciNetGoogle Scholar
  5. 5.
    B. Jurco, L. Moller, S. Schraml, P. Schupp, J. Wess, Eur. Phys. J. C 21, 383 (2001), hep-th/0104153CrossRefMathSciNetGoogle Scholar
  6. 6.
    X. Calmet, B. Jurco, P. Schupp, J. Wess, M. Wohlgenannt, Eur. Phys. J. C 23, 363 (2002), hep-ph/0111115MathSciNetGoogle Scholar
  7. 7.
    E.O. Iltan, JHEP 05, 065 (2003), hep-ph/0304097Google Scholar
  8. 8.
    P. Minkowski, P. Schupp, J. Trampetic, hep-th/0302175Google Scholar
  9. 9.
    P. Schupp, J. Trampetic, J. Wess, G. Raffelt, hep-ph/0212292Google Scholar
  10. 10.
    G. Abbiendi et al., OPAL Collaboration, hep-ex/0303035Google Scholar
  11. 11.
    I. Hinchliffe, N. Kersting, hep-ph/0205040Google Scholar
  12. 12.
    S. Minwalla, M. Van Raamsdonk, N. Seiberg, JHEP 02, 020 (2000), hep-th/9912072zbMATHGoogle Scholar
  13. 13.
    A. Matusis, L. Susskind, N. Toumbas, JHEP 12, 002 (2000), hep-th/0002075zbMATHGoogle Scholar
  14. 14.
    L. Alvarez-Gaume, M.A. Vazquez-Mozo, hep-th/0305093Google Scholar
  15. 15.
    D.J. Bird et al., Astrophys. J. 441, 144 (1995)CrossRefGoogle Scholar
  16. 16.
    G. Amelino-Camelia, Int. J. Mod. Phys. D 11, 35 (2002), gr-qc/0012051CrossRefMathSciNetGoogle Scholar
  17. 17.
    G. Amelino-Camelia, Int. J. Mod. Phys. D 11, 1643 (2002), gr-qc/0210063CrossRefGoogle Scholar
  18. 18.
    A. Agostini, G. Amelino-Camelia, F. D'Andrea, hep-th/0306013Google Scholar
  19. 19.
    H. Wachter, M. Wohlgenannt, Eur. Phys. J. C 23, 761 (2002), hep-th/0103120MathSciNetGoogle Scholar
  20. 20.
    C. Blohmann, math.qa/0209180, to be published in J. Math. PhysGoogle Scholar
  21. 21.
    L. Mesref, hep-th/0209005Google Scholar
  22. 22.
    E.P. Wigner, Annals Math. 40, 149 (1939)zbMATHGoogle Scholar
  23. 23.
    O. Ogievetskii, W.B. Schmidke, J. Wess, B. Zumino, Commun. Math. Phys. 150, 495 (1992)MathSciNetGoogle Scholar
  24. 24.
    V.K. Dobrev, Phys. Lett. B 341, 133 (1994)CrossRefMathSciNetGoogle Scholar
  25. 25.
    A. Schirrmacher, Talk given at NATO Advanced Research Workshop on Low Dimensional Topology and Quantum Field Theory, Cambridge, England, 6-13 September 1992Google Scholar
  26. 26.
    M. Pillin, J. Math. Phys. 35, 2804 (1994), hep-th/9310097CrossRefMathSciNetzbMATHGoogle Scholar
  27. 27.
    X.-C. Song, Z. Phys. C 55, 417 (1992)MathSciNetGoogle Scholar
  28. 28.
    U. Meyer, Commun. Math. Phys. 174, 457 (1995), hep-th/9404054zbMATHGoogle Scholar
  29. 29.
    P. Podles, Commun. Math. Phys. 181, 569 (1996), q-alg/9510019MathSciNetGoogle Scholar
  30. 30.
    A.O. Barut, R. Raczka, Theory of group representations and applications (PWN - Polish Scientific Publishers, 1977)Google Scholar
  31. 31.
    C. Blohmann, Spin Representations of the q-Poincaré Algebra, Ph.D. thesis, Ludwig-Maximilians-Universität München, 2001, math.qa/0110219Google Scholar
  32. 32.
    S. Majid, J. Math. Phys. 34, 2045 (1993), hep-th/9210141CrossRefMathSciNetzbMATHGoogle Scholar
  33. 33.
    S. Majid, Foundations of quantum group theory (Cambridge University Press, 1995)Google Scholar
  34. 34.
    C. Blohmann, math.qa/0111008, to be published in Comm. Math. PhysGoogle Scholar
  35. 35.
    S. Schraml, hep-th/0208173Google Scholar
  36. 36.
    M. Fichtmüller, A. Lorek, J. Wess, Z. Phys. C 71, 533 (1996), hep-th/9511106CrossRefGoogle Scholar
  37. 37.
    P. Podles, S.L. Woronowicz, Commun. Math. Phys. 130, 381 (1990)MathSciNetzbMATHGoogle Scholar
  38. 38.
    O. Ogievetskii, W.B. Schmidke, J. Wess, B. Zumino, Lett. Math. Phys. 23, 233 (1991)MathSciNetGoogle Scholar
  39. 39.
    A. Lorek, W. Weich, J. Wess, Z. Phys. C 76, 375 (1997)CrossRefMathSciNetGoogle Scholar
  40. 40.
    M. Rohregger, J. Wess, Eur. Phys. J. C 7, 177 (1999)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  1. 1.Sektion Physik, Lehrstuhl Prof. WessLudwig-Maximilians-Universität MünchenMünchenGermany
  2. 2.Max-Planck-Institut für PhysikMünchenGermany

Personalised recommendations