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Large Quantum Poincare Subgroup of q-Conformal Group and q-Minkowski Geometry

M. Chaichian·A. P. Demichev
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Abstract

We construct quantum deformation of Poincaré group using as a starting point $SU(2,2)$ conformal group and twistor-like definition of the Minkowski space. We obtain quantum deformation of $SU(2,2)$ as a real form of multiparametric $GL(4,C)_{q_{ij},r}$. It is shown that Poincaré subgroup exists for special nonstandard one-parametric deformation only, the deformation parameter $r$ being equal to unity. This leads to commuting affine structure of the corresponding Minkowski space and simple structure of the corresponding Lie algebra, the deformation of the group being non-trivial.

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M. Chaichian, A. P. Demichev. 1993-11-10. Large Quantum Poincare Subgroup of q-Conformal Group and q-Minkowski Geometry. https://arxiv.org/abs/hep-th/9311061

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