Communications in Mathematical Physics

, Volume 174, Issue 3, pp 457–475 | Cite as

Wave equations onq-Minkowski space

  • U. Meyer


We give a systematic account of a “component approach” to the algebra of forms onq-Minkowski space, introducing the corresponding exterior derivative, Hodge star operator, coderivative, Laplace-Beltrami operator and Lie-derivative. Using this (braided) differential geometry, we then give a detailed exposition of theq-d'Alembert andq-Maxwell equation and discuss some of their non-trivial properties, such as for instance, plane wave solutions. For theq-Maxwell field, we also give aq-spinor analysis of theq-field strength tensor.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Plane 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Carow-Watamura, U., Schlieker, M., Scholl, M., Watamura, S.: A quantum Lorentz group. Int. J. Mod. Phys.A(17), 3081–3108 (1991)Google Scholar
  2. 2.
    Carow-Watamura, U., Schlieker, M., Scholl, W., Watamura, S.: Tensor representations of the quantum groupSL q(2,C) and quantum Minkowski space. Z. Phys.C(48), 159–165 (1990)Google Scholar
  3. 3.
    Majid, S.: Examples of braided groups and braided matrices. J. Math. Phys.32, 3246–3253 (1991)Google Scholar
  4. 4.
    Majid, S.: Beyond supersymmetry and quantum symmetry. In: Ge, M.-L., de Vega, H.J., (eds.), Proc. 5th Nankai Workshop, Tianjin, China. Singapore: World Scientific, June 1992Google Scholar
  5. 5.
    Majid, S.: Braided groups. J. Pure Applied Algebra.86, 187–221 (1993)Google Scholar
  6. 6.
    Majid, S.: Braided momentum in theq-Poincaré group. J. Math. Phys.34, 2045–2058 (1993)Google Scholar
  7. 7.
    Majid, S.: Free braided differential calculus, braided binomial theorem, and the braided exponential map. J. Math. Phys.34(10), 4843–4856 (1993)Google Scholar
  8. 8.
    Majid, S.: Quantum and braided linear algebra. J. Math. Phys.34, 1176–1196 (1993)Google Scholar
  9. 9.
    Majid, S.: *-Structures on braided spaces. Preprint DAMTP/94-66, August 1994Google Scholar
  10. 10.
    Majid, S., Meyer, U.: Braided matrix structure ofq-Minkowski space andq-Poincaré gorup. Z. Phys. C63, (2) 357–362 (1994)Google Scholar
  11. 11.
    Meyer, U.:q-Lorentz group and braided coaddition onq-Minkowski space. Commun. Math. Phys.Google Scholar
  12. 12.
    Ogievetsky, O., Schmidke, W.B., Wess, J., Zumino, B.:q-Deformed Poincaré algebra. Commun. Math. Phys.150, 495–518 (1992)Google Scholar
  13. 13.
    Pillin, M.:q-deformed relativistic wave equations. J. Math. Phys.35 (6), 2804–2817 (1994)Google Scholar
  14. 14.
    Schirrmacher, A.: The algebra ofq-deformed γ-matrices. In: del Olmo, M.A. et al., (ed.) Group Theoretical Methods in Physics, 1992Google Scholar
  15. 15.
    Schlieker, M., Scholl, M.: Spinor calculus for quantum groups. Z. Phys. C47, 625–628 (1990)Google Scholar
  16. 16.
    Schlieker, M., Weich, W., Weixler, R.: Inhomogeneous quantum groups. Z. Phys. C53, 79–82 (1992)Google Scholar
  17. 17.
    Wess, J., Zuminó, B.: Covariant differential calculus on the quantum hyperpane. In: Recent Advances in Field Theory, Nucl. Phys. B (Proc. Suppl)18B, 302–312 (1990)Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • U. Meyer
    • 1
  1. 1.D.A.M.T.P.University of CambridgeCambridgeUK

Personalised recommendations