q-deformed conformal and Poincaré algebras on quantum 4-spinors |
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Authors: | Tatsuo Kobayashi Tsuneo Uematsu |
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Institution: | 1. Department of Fundamental Sciences, FIHS, Kyoto University, 606, Kyoto, Japan
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Abstract: | We investigate quantum deformation of conformal algebras by constructing the quantum space forsl
q
(4). The differential calculus on the quantum space and the action of the quantum generators are studied. We derive deformedsu(2,2) algebra from the deformedsl(4) algebra using the quantum 4-spinor and its conjugate spinor. The quantum 6-vector inso
q
(4,2) is constructed as a tensor product of two sets of 4-spinors. We obtain theq-deformed conformal algebra with the suitable assignment of the generators which satisfy the reality condition. The deformed Poincaré algebra is derived through a contraction procedure.Work partially supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture (#030083) |
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