Advertisement

Particle Physics on Noncommutative Space-Time

  • Peter Schupp
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 616)

Abstract

This is a concise overview of the construction of Yang-Mills theories with realistic gauge groups on noncommutative generalizations of space-time and of the construction of the noncommutative standard model. We discuss the relevant mathematical tools including tensor products, indicate some exciting physical consequences and conclude with a short-list of challenging open problems.

Keywords

Gauge Theory Gauge Group Gauge Transformation Gauge Boson Star Product 
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.
    H. S. Snyder, “Quantized Space-Time,” Phys. Rev. 71, 38 (1947).zbMATHCrossRefADSMathSciNetGoogle Scholar
  2. 2.
    H. Arfaei and M. H. Yavartanoo, arXiv:hep-th/0010244.Google Scholar
  3. 3.
    J. L. Hewett, F. J. Petriello and T. G. Rizzo, Phys. Rev. D 64, 075012 (2001).CrossRefADSGoogle Scholar
  4. 4.
    I. Hinchliffe and N. Kersting, Phys. Rev. D 64, 116007 (2001).CrossRefADSGoogle Scholar
  5. 5.
    W. Behr, N. G. Deshpande, G. Duplancic, P. Schupp, J. Trampetic and J. Wess, arXiv:hep-ph/0202121.Google Scholar
  6. 6.
    C. E. Carlson, C. D. Carone and R. F. Lebed, Phys. Lett. B 518, 201 (2001).zbMATHCrossRefADSGoogle Scholar
  7. 7.
    I. Hinchliffe and N. Kersting, arXiv:hep-ph/0205040.Google Scholar
  8. 8.
    A. Connes, Non-commutative geometry (Academic Press, London 1994).Google Scholar
  9. 9.
    J. Madore, An Introduction to Noncommutative Differential Geometry and its Physical Applications, 2nd edn. (Cambridge University Press 1999).Google Scholar
  10. 10.
    J. Madore, S. Schraml, P. Schupp and J. Wess, Eur. Phys. J. C 16, 161 (2000).CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    B. Jurco, S. Schraml, P. Schupp and J. Wess, Eur. Phys. J. C 17, 521 (2000).zbMATHCrossRefADSMathSciNetGoogle Scholar
  12. 12.
    B. Jurco, P. Schupp and J. Wess, Nucl. Phys. B 604, 148 (2001).zbMATHCrossRefADSMathSciNetGoogle Scholar
  13. 13.
    B. Jurco, L. Moller, S. Schraml, P. Schupp and J. Wess, Eur. Phys. J. C 21, 383 (2001).zbMATHCrossRefADSMathSciNetGoogle Scholar
  14. 14.
    P. Schupp, hep-th/0111038.Google Scholar
  15. 15.
    J. Madore, Class. and Quant. Grav. 9, 69 (1992).zbMATHCrossRefADSMathSciNetGoogle Scholar
  16. 16.
    B. L. Cerchiai and J. Wess, Eur. Phys. J. C 5, 553 (1998).ADSMathSciNetGoogle Scholar
  17. 17.
    F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, D. Sternheimer, Ann. Phys. 111, 61 (1978).zbMATHCrossRefADSMathSciNetGoogle Scholar
  18. 18.
    N. Seiberg and E. Witten, J. High Energy Phys. 9909, 032 (1999).CrossRefADSMathSciNetGoogle Scholar
  19. 19.
    R. Stora, privat communication.Google Scholar
  20. 20.
    D. Brace, B. L. Cerchiai, A. F. Pasqua, U. Varadarajan and B. Zumino, J. High Energy Phys. 0106, 047 (2001); D. Brace, B. L. Cerchiai and B. Zumino, hepth/0107225.CrossRefADSMathSciNetGoogle Scholar
  21. 21.
    G. Barnich, F. Brandt and M. Grigoriev, hep-th/0206003.Google Scholar
  22. 22.
    B. Jurco, P. Schupp and J. Wess, Lett. Math. Phys. (to appear), hep-th/0106110.Google Scholar
  23. 23.
    A. A. Bichl, J. M. Grimstrup, L. Popp, M. Schweda and R. Wulkenhaar, hepth/0102103.Google Scholar
  24. 24.
    H. Dorn and C. Sieg, hep-th/0205286.Google Scholar
  25. 25.
    M. Hayakawa, hep-th/9912167.Google Scholar
  26. 26.
    X. Calmet, B. Jurco, P. Schupp, J. Wess and M. Wohlgenannt, Eur. Phys. J. C 23, 363 (2002).zbMATHCrossRefADSMathSciNetGoogle Scholar
  27. 27.
    P. Aschieri, B. Jurco, P. Schupp and J. Wess, hep-th/0205214.Google Scholar
  28. 28.
    N. G. Deshpande and X. G. He, Phys. Lett. B 533, 116 (2002).CrossRefADSGoogle Scholar
  29. 29.
    D. Bahns, S. Doplicher, K. Fredenhagen and G. Piacitelli, Phys. Lett. B 533, 178 (2002).zbMATHCrossRefADSMathSciNetGoogle Scholar
  30. 30.
    A. Bichl, J. Grimstrup, H. Grosse, L. Popp, M. Schweda and R. Wulkenhaar, J. High Energy Phys. 0106, 013 (2001); R. Wulkenhaar, J. High Energy Phys. 0203, 024 (2002).CrossRefADSMathSciNetGoogle Scholar
  31. 31.
    J. M. Grimstrup and R. Wulkenhaar, hep-th/0205153.Google Scholar
  32. 32.
    E. O. Iltan, hep-ph/0204332; hep-ph/0204129.Google Scholar
  33. 33.
    Z. Chang and Z. z. Xing, hep-ph/0204255.Google Scholar
  34. 34.
    M. Chaichian, P. Presnajder, M. M. Sheikh-Jabbari and A. Tureanu, hepth/0107055.Google Scholar

Copyright information

© Springer-VerlagBerlin Heidelber 2003

Authors and Affiliations

  • Peter Schupp
    • 1
  1. 1.Theoretical PhysicsUniversity of MunichMünchenGermany

Personalised recommendations