Quantum Deformation of the Poincare Supergroup and $\kappa$-deformed Superspace

Abstract

The classical $r$-matrix for $N=1$ superPoincar{é} algebra, given by Lukierski, Nowicki and Sobczyk is used to describe the graded Poisson structure on the $N=1$ Poincar{é} supergroup. The standard correspondence principle between the even (odd) Poisson brackets and (anti)commutators leads to the consistent quantum deformation of the superPoincar{é} group with the deformation parameter $q$ described by fundamental mass parameter $\kappa ({\kappa }^{-1}=\ln q)$. The $\kappa$-deformation of $N=1$ superspace as dual to the $\kappa$-deformed supersymmetry algebra is discussed.

Wroclaw University preprint IFTUWr 868 /94, March 1994, 12 pages

References in corpus (2)

• The Quantum Deformed Dirac Equation from the k-Poincare` Algebra
• The Lagrangian of q-Poincare' Gravity

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• Deformed Covariant Quantum Phase Spaces as Hopf Algebroids
• Classification of Low Dimensional Lie Super-Bialgebras
• Field Theory on Nonanticommutative Superspace
• A Path Integral Approach To Noncommutative Superspace
• $\kappa$-Deformation of Poincaré Superalgebra with Classical Lorentz Subalgebra and its Graded Bicrossproduct Structure
• Classical r-matrices of two and three dimensional Lie super-bialgebras and their Poisson-Lie supergroups
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• D-deformed Wess-Zumino model and its renormalizability properties
• $C{P}^{(N-1)}$ model in aether-superspace
• (Non)renormalizability of the D-deformed Wess-Zumino model
• Noncommutative Parameters of Quantum Symmetries and Star Products
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• On Hopf algebroid structure of kappa-deformed Heisenberg algebra
• Twisted SUSY: twisted symmetry versus renormalizability
• q-Deformed Superalgebras
• N=1/2 Global SUSY: R-Matrix Approach
• The universe is not a Lie, but actually an Hopf, algebra
• Quantum Deformations of Space-Time Symmetries with Mass-Like Deformation Parameter