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q-Deformed Poincaré algebra

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Abstract

Theq-differential calculus for theq-Minkowski space is developed. The algebra of theq-derivatives with theq-Lorentz generators is found giving theq-deformation of the Poincaré algebra. The reality structure of theq-Poincaré algebra is given. The reality structure of theq-differentials is also found. The real Laplacian is constructed. Finally the comultiplication, counit and antipode for theq-Poincaré algebra are obtained making it a Hopf algebra.

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Author notes

  1. O. Ogievetsky

    Present address: Theoretical Department, P.N. Lebedev Physical Institute, Leninsky prospect 53, 117924, Moscow, Russia

Authors and Affiliations

  1. Max-Planck-Institut für Physik und Astrophysik, Werner-Heisenberg-Institut für Physik, P.O. Box 40 12 12, W-8000, Munich 40, Germany

    O. Ogievetsky, W. B. Schmidke & J. Wess

  2. Sektion Physik, Universität München, Theresienstr. 37, W-8000, Munich 2, Germany

    J. Wess

  3. Department of Physics, University of California, 94720, Berkeley, California, USA

    B. Zumino

  4. Theoretical Physics Group, Physics Division, Lawrence Berkeley Laboratory, 1 Cyclotron Road, 94720, Berkeley, California, USA

    B. Zumino

Authors
  1. O. Ogievetsky
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  2. W. B. Schmidke
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  3. J. Wess
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  4. B. Zumino
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Communicated by N.Yu. Reshetikhin

This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY-90-21139

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Ogievetsky, O., Schmidke, W.B., Wess, J. et al. q-Deformed Poincaré algebra. Commun.Math. Phys. 150, 495–518 (1992). https://doi.org/10.1007/BF02096958

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  • DOI: https://doi.org/10.1007/BF02096958

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