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.

arXiv comment30 pages, Latex, accepted for publication in Eur.Phys.J.C, some typos corrected

References in corpus (32)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Quantum Field Theory on Noncommutative Spaces
• The quantum structure of spacetime at the Planck scale and quantum fields
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• A Gravity Theory on Noncommutative Spaces
• Quantum mechanics on the noncommutative plane and sphere
• The Effect of the Minimal Length Uncertainty Relation on the Density of States and the Cosmological Constant Problem
• Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
• New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications
• Non-commutative superspace from string theory
• Quantum $\kappa$-Poincare in Any Dimensions
• Coproduct and star product in field theories on Lie-algebra non-commutative space-times
• Deformed Field Theory on kappa-spacetime
• Non-Commutative GUTs, Standard Model and C,P,T
• Local D=4 Field Theory on $\kappa$--Deformed Minkowski Space
• New Lie-Algebraic and Quadratic Deformations of Minkowski Space from Twisted Poincare Symmetries
• Gauge theories on the kappa-Minkowski spacetime
• Harmonic oscillator with minimal length uncertainty relations and ladder operators
• Local Field Theory ON $\kappa$-Minkowski Space, Star Products and Noncommutative Translations
• Noncommutative Model with Spontaneous Time Generation and Planckian bound
• Generalized Quon Statistics
• Group velocity in noncommutative spacetime
• Unified view of multimode algebras with Fock-like representations
• Bosonic realization of algebras in the Calogero model
• A symmetry invariant integral on kappa-deformed spacetime
• Deformed Heisenberg algebras, a Fock-space representation and the Calogero model
• Permutation Invariant Algebras, a Fock Space Realization and the Calogero Model
• Harmonic oscillator on noncommutative spaces
• Determinants and Inversion of Gram Matrices in Fock Representation of $\{q_{kl}\}$- Canonical Commutation Relations and Applications to Hyperplane Arrangements and Quantum Groups. Proof of an Extension of Zagier's Conjecture

Cited by in corpus (115)

• 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
• Topics in Noncommutative Geometry Inspired Physics
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Scalar Field Theory on Non-commutative Snyder Space-Time
• Modification of Heisenberg uncertainty relations in non-commutative Snyder space-time geometry
• Electrodynamics on $\kappa$-Minkowski space-time
• Classical basis for kappa-Poincare algebra and doubly special relativity theories
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Constraints on the quantum gravity scale from kappa - Minkowski spacetime
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime
• Generalized kappa-deformed spaces, star-products, and their realizations
• On the $\kappa$-Dirac Oscillator revisited
• Scalar field propagation in the phi^4 kappa-Minkowski model
• Geodesic equation in $k$-Minkowski spacetime
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Kappa-deformed Snyder spacetime
• Star products made (somewhat) easier
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Noncommutative Differential Forms on the kappa-deformed Space
• Newton's Equation on the kappa space-time and the Kepler problem
• Localization and Reference Frames in $\kappa$-Minkowski Spacetime
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole
• $\kappa$-deformed Dirac Equation
• Noncommutative $R^d$ via closed star product
• On kappa-deformation and triangular quasibialgebra structure
• Differential structure on kappa-Minkowski space, and kappa-Poincare algebra
• Noncommutative duality and fermionic quasinormal modes of the BTZ black hole
• Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
• Toward the classification of differential calculi on $\kappa$-Minkowski space and related field theories
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Effects of Noncommutativity on the Black Hole Entropy
• Noncommutative correction to the entropy of Schwarzschild black hole with GUP
• Maxwell's equations on the $\kappa$-Minkowski spacetime and Electric-Magnetic duality
• Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
• Differential algebras on kappa-Minkowski space and action of the Lorentz algebra
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• Quantum statistics and noncommutative black holes
• The 2D $\kappa$-Dirac oscillator
• Uniformly accelerating observer in $\kappa$-deformed space-time
• Remarks on simple interpolation between Jordanian twists
• Entanglement dynamics in $\kappa$-deformed spacetime
• Nonassociative Weyl star products
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Different realizations of kappa-momentum space and relative-locality effect
• Kappa-deformation of phase space; generalized Poincare algebras and R-matrix
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• Differential forms and k-Minkowski spacetime from extended twist
• Noncommutative fluid dynamics in the Snyder space-time
• Hawking radiation in the kappa-spacetime
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Twisted statistics and the structure of Lie-deformed Minkowski spaces
• Hermitian realizations of kappa-Minkowski spacetime
• Star Product and Invariant Integration for Lie type Noncommutative Spacetimes
• Exponential Formulas and Lie Algebra Type Star Products
• Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions
• Double Quantization
• Involutive representations of coordinate algebras and quantum spaces
• Time-space noncommutativity and Casimir effect
• Compact stars in quantum spacetime
• Quantisation of Klein-Gordon field in $\kappa$ space-time: deformed oscillators and Unruh effect
• MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Interpolations between Jordanian Twists Induced by Coboundary Twists
• The Weyl realizations of Lie algebras and left-right duality
• Leibniz rules for enveloping algebras in symmetric ordering
• On the L${}_{\infty }$ structure of Poisson gauge theory
• Photonic realization of the kappa-deformed Dirac equation
• Dimensional flow in the kappa-deformed space-time
• Heisenberg double versus deformed derivatives
• Twist for Snyder space
• Effect of Non-commutativity of space-time on Thermodynamics of Photon gas
• Lie algebraic deformations of Minkowski space with Poincare algebra
• Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
• Conformal quantum mechanics and holography in noncommutative space-time
• Phase structure of fuzzy black holes
• Maximal acceleration in a Lorentz invariant non-commutative space-time
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• Superdense star in a space-time with minimal length
• Maximal acceleration in non-commutative space-time and its implications
• 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
• Non-Commutative space-time and Hausdorff dimension
• $\kappa$-deformed power spectrum and modified Unruh temperature
• Path integral action of a particle in $\kappa$-Minkowski spacetime
• Plane waves in noncommutative fluids
• One Parameter Family of Jordanian Twists
• Neutron Star in Quantized-space-time
• How does Casimir energy fall in $\kappa$-deformed space-time?
• Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries
• Spectral Dimension of kappa-deformed space-time
• A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra
• Noncommutative kappa-Minkowski phi4 theory: Construction, properties and propagation
• A Poincaré Covariant Noncommutative Spacetime?
• Quantisation of $\kappa$-deformed Dirac equation
• Some Features of Scattering Problem in a $\kappa$-Deformed Minkowski Spacetime
• Quantisation of Lorentz invariant scalar field theory in non-commutative space-time and its consequence
• Centripetal force on Casimir energies in $\kappa$-deformed rotating frame
• The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime
• Influence of the cosmological constant on $\kappa$-deformed Neutron Star
• Wormhole Solutions in deformed space-time
• Non-commutative correction of ideal gas thermodynamics
• Entropic force and bouncing behaviour in $\kappa$-Minkowski space-time
• Interpolations between Jordanian twists, the Poincaré-Weyl algebra and dispersion relations
• Unruh effect using Doppler shift method in DSR framework
• Thermal Casimir effect in $\kappa$-Minkowski space-time