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A q-deformed Lorentz algebra |
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| Authors: | W. B. Schmidke J. Wess B. Zumino |
| Affiliation: | 1. Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, P.O. Box 401212, W-8000, Munich, Federal Republic of Germany 2. Sektion Physik, Universit?t München, Theresienstrasse 37, W-8000, Munich 2, Federal Republic of Germany 3. Department of Physics, University of California, 94720, Berkeley, CA, USA 4. Theoretical Physics Group, Physics Division, Lawrence Berkeley Laboratory, 1 Cyclotron Road, 94720, Berkeley, CA, USA |
| Abstract: | We derive a q-deformed version of the Lorentz algebra by deforming the algebraSL(2,C). The method is based on linear representations of the algebra on the complex quantum spinor space. We find that the generators usually identified withSL q(2,C) generateSU q (2) only. Four additional generators are added which generate Lorentz boosts. The full algebra of all seven generators and their coproduct is presented. We show that in the limitq→1 the generators are those of the classical Lorentz algebra plus an additionalU(1). Thus we have a deformation ofSL(2,C)×U(1). |
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