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.


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  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

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