New realizations of Lie algebra kappa-deformed Euclidean space

Abstract

We study Lie algebra $\kappa$-deformed Euclidean space with undeformed rotation algebra $S{O}_a(n)$ and commuting vectorlike derivatives. Infinitely many realizations in terms of commuting coordinates are constructed and a corresponding star product is found for each of them. The $\kappa$-deformed noncommutative space of the Lie algebra type with undeformed Poincar{é} algebra and with the corresponding deformed coalgebra is constructed in a unified way.

30 pages, Latex, accepted for publication in Eur.Phys.J.C, some typos corrected

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Cited by in corpus (46)

• Kappa-Minkowski space-time and the star product realizations
• Twisted Statistics in kappa-Minkowski Spacetime
• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Covariant realizations of kappa-deformed space
• The shadows and observational appearance of a noncommutative black hole surrounded by various profiles of accretions
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• 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
• Newton's Equation on the kappa space-time and the Kepler problem
• On kappa-deformation and triangular quasibialgebra structure
• Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
• Noncommutative correction to the entropy of Schwarzschild black hole with GUP
• The 2D $\kappa$-Dirac oscillator
• Entanglement dynamics in $\kappa$-deformed spacetime
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Star Product and Invariant Integration for Lie type Noncommutative Spacetimes
• Double Quantization
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Photonic realization of the kappa-deformed Dirac equation
• On the L${}_{\infty }$ structure of Poisson gauge theory
• Lie algebraic deformations of Minkowski space with Poincare algebra
• Maximal acceleration in a Lorentz invariant non-commutative space-time
• Superdense star in a space-time with minimal length
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Poisson electrodynamics on $\kappa$-Minkowski space-time
• Newtonian cosmology and Evolution of kappa-deformed universe
• $\kappa$-deformed power spectrum and modified Unruh temperature
• How does Casimir energy fall in $\kappa$-deformed space-time?
• Neutron Star in Quantized-space-time
• Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries
• Spectral Dimension of kappa-deformed space-time
• Influence of the cosmological constant on $\kappa$-deformed Neutron Star
• The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime
• Quantisation of Lorentz invariant scalar field theory in non-commutative space-time and its consequence
• A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra
• Wormhole Solutions in deformed space-time
• Centripetal force on Casimir energies in $\kappa$-deformed rotating frame
• Non-commutative correction of ideal gas thermodynamics
• Entropic force and bouncing behaviour in $\kappa$-Minkowski space-time
• Unruh effect using Doppler shift method in DSR framework
• Thermal Casimir effect in $\kappa$-Minkowski space-time