Kappa-deformation of phase space; generalized Poincare algebras and R-matrix

Abstract

We deform Heisenberg algebra and corresponding coalgebra by twist. We present undeformed and deformed tensor identities. Coalgebras for the generalized Poincaré algebras have been constructed. The exact universal $R$-matrix for the deformed Heisenberg (co)algebra is found. We show, up to the third order in the deformation parameter, that in the case of $\kappa$-Poincaré Hopf algebra this $R$-matrix can be expressed in terms of Poincaré generators only. This implies that the states of any number of identical particles can be defined in a $\kappa$-covariant way.

10 pages, revtex4; discussion enlarged, references added

References in corpus (10)

• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime
• Scalar field propagation in the phi^4 kappa-Minkowski model
• $\kappa$-Deformed Statistics and Classical Fourmomentum Addition Law
• On kappa-deformation and triangular quasibialgebra structure
• Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
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Cited by in corpus (15)

• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• Twisting and kappa-Poincare
• Different realizations of kappa-momentum space and relative-locality effect
• Snyder-type spaces, twisted Poincaré algebra and addition of momenta
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Light-like $\kappa$-deformations and scalar field theory via Drinfeld twist
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Hermitian realizations of kappa-Minkowski spacetime
• Twisted bialgebroids versus bialgebroids from a Drinfeld twist
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• On Hopf algebroid structure of kappa-deformed Heisenberg algebra
• Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries
• Dirac Operators on Noncommutative Curved Spacetimes