# New quantum Poincaré algebra and κ-deformed field theory

@article{Lukierski1992NewQP,
title={New quantum Poincar{\'e} algebra and $\kappa$-deformed field theory},
author={Jerzy Lukierski and Anatol Nowicki and Henri Ruegg},
journal={Physics Letters B},
year={1992},
volume={293},
pages={344-352}
}
• Published 29 October 1992
• Mathematics, Physics
• Physics Letters B
517 Citations
• Physics, Mathematics
• 1993
The κ-deformed D = 4 Poincare algebra is obtained by a special contraction of the real quantum Lie algebra U q (0(3,2)). We describe this contraction and study the consequences of the κ-deformation
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• 2009
Several issues concerning the quantum κ-Poincaré algebra are discussed and reconsidered here. We propose two different formulations of the κ-Poincaré quantum algebra. Firstly we present a complete
• Mathematics
Physics Letters B
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• Mathematics
• 1996
We consider new class of classicalr-matrices forD=4 conformal Lie algebra. These r-matrices do satisfy the classical Yang-Baxter equation and as two-tensors belong to the tensor product of Borel
• Mathematics
• 2008
The Minkowski spacetime quantum Clifford algebra structure associated with the conformal group and the Clifford-Hopf alternative k-deformed quantum Poincare algebra is investigated in the
I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-∗
• Mathematics
• 1993
The kappa -deformation of D=4 Poincare algebra is extended to the N=1 D=4 Poincare superalgebra. By the contraction of real Hopf superalgebra Uq(OSp(1 mod 4)) (q real) we obtain real Hopf algebra
The classical r-matrix implied by the quantum kappa -Poincare algebra of Lukierski, Nowicki and Ruegg is used to generate a Poisson structure on the Poincare group. A quantum deformation of the

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The structure of the quantum Heisenberg group is studied in the two different frameworks of the Lie algebra deformations and of the quantum matrix pseudogroups. The R‐matrix connecting the two
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A contraction procedure starting from SO(4)q is used to determine the quantum analog E(3)q of the three‐dimensional Euclidean group and the structure of its representations. A detailed analysis of
To SU(2) q , the quantum deformation of SU(2), the van der Waerden method for calculating the Clebsch–Gordan (CG) coefficients is genaralized. The polynomial basis for irreducible representations of
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References: [1] S. Tomonaga, Prog. Theor. Phys. 1 pp 27– (1946) · Zbl 0038.13101 · doi:10.1143/PTP.1.27 [2] S. Tomonaga, Prog. Theor. Phys. 2 pp 101– (1947) · Zbl 0038.13102 · doi:10.1143/ptp/2.3.101
An introduction to field quantization , An introduction to field quantization , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی