Generalized kappa-deformed spaces, star-products, and their realizations

Abstract

In this work we investigate generalized kappa-deformed spaces. We develop a systematic method for constructing realizations of noncommutative (NC) coordinates as formal power series in the Weyl algebra. All realizations are related by a group of similarity transformations, and to each realization we associate a unique ordering prescription. Generalized derivatives, the Leibniz rule and coproduct, as well as the star-product are found in all realizations. The star-product and Drinfel'd twist operator are given in terms of the coproduct, and the twist operator is derived explicitly in special realizations. The theory is applied to a Nappi-Witten type of NC space.

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Cited by in corpus (42)

• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Electrodynamics on $\kappa$-Minkowski space-time
• Classical basis for kappa-Poincare algebra and doubly special relativity theories
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Geodesic equation in $k$-Minkowski spacetime
• Kappa-deformed Snyder spacetime
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Star products made (somewhat) easier
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Quantized Nambu-Poisson Manifolds and n-Lie Algebras
• Noncommutative Differential Forms on the kappa-deformed Space
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Newton's Equation on the kappa space-time and the Kepler problem
• Localization and Reference Frames in $\kappa$-Minkowski Spacetime
• $\kappa$-deformed Dirac Equation
• Differential structure on kappa-Minkowski space, and kappa-Poincare algebra
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Maxwell's equations on the $\kappa$-Minkowski spacetime and Electric-Magnetic duality
• Differential structure on the $\kappa$-Minkowski spacetime from twist
• Differential Structure on kappa-Minkowski Spacetime Realized as Module of Twisted Weyl Algebra
• Uniformly accelerating observer in $\kappa$-deformed space-time
• Classical Mechanics on Noncommutative Space with Lie-algebraic Structure
• Entanglement dynamics in $\kappa$-deformed spacetime
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Scalar Field theory in $\kappa$-Minkowski spacetime from twist
• Differential forms and k-Minkowski spacetime from extended twist
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions
• MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• The Weyl realizations of Lie algebras and left-right duality
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• Effect of Non-commutativity of space-time on Thermodynamics of Photon gas
• Lie algebraic deformations of Minkowski space with Poincare algebra
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• Maximal acceleration in non-commutative space-time and its implications
• Superdense star in a space-time with minimal length
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Quantisation of $\kappa$-deformed Dirac equation
• Braided algebras and the kappa-deformed oscillators
• Quantum speed limit as a sensitive probe of Planck-scale effects
• Braided Statistics from Abelian Twist in $\kappa$-Minkowski Spacetime