Covariant realizations of kappa-deformed space

Abstract

We study a Lie algebra type $\kappa$-deformed space with undeformed rotation algebra and commutative vector-like Dirac derivatives in a covariant way. Space deformation depends on an arbitrary vector. Infinitely many covariant realizations in terms of commuting coordinates of undeformed space and their derivatives are constructed. The corresponding coproducts and star products are found and related in a new way. All covariant realizations are physically equivalent. Specially, a few simple realizations are found and discussed. The scalar fields, invariants and the notion of invariant integration is discussed in the natural realization.

31 pages, no figures, LaTeX

References in corpus (51)

• 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
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Testable scenario for Relativity with minimum-length
• 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
• Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
• The Effect of the Minimal Length Uncertainty Relation on the Density of States and the Cosmological Constant Problem
• 3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory
• Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• 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
• Deformed Boost Transformations That Saturate at the Planck Scale
• Symmetry, Gravity and Noncommutativity
• 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
• New realizations of Lie algebra kappa-deformed Euclidean space
• Local D=4 Field Theory on $\kappa$--Deformed Minkowski Space
• New Lie-Algebraic and Quadratic Deformations of Minkowski Space from Twisted Poincare Symmetries
• Noncommutative Differential Calculus on the Kappa-Minkowski Space
• Gauge theories on the kappa-Minkowski spacetime
• Harmonic oscillator with minimal length uncertainty relations and ladder operators
• A Lagrangian for DSR Particle and the Role of Noncommutativity
• Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics
• Unified View of Deformed Single - Mode Oscillator Algebras
• Local Field Theory ON $\kappa$-Minkowski Space, Star Products and Noncommutative Translations
• String theory and the mapping of gravity into gauge theory
• Representations of noncommutative quantum mechanics and symmetries
• $\kappa$-Minkowski Spacetime Through Exotic "Oscillator"
• Derivatives, forms and vector fields on the kappa-deformed Euclidean space
• 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
• Deformed Heisenberg algebras, a Fock-space representation and the Calogero model
• A symmetry invariant integral on kappa-deformed spacetime
• The $AdS$ particle
• Calogero model, deformed oscillators and the collapse
• $\kappa -$Minkowski spacetime and a uniformly accelerating observer
• Permutation Invariant Algebras, a Fock Space Realization and the Calogero Model
• The Energy Operator for a Model with a Multiparametric Infinite Statistics
• 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

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• Kappa-Minkowski space-time and the star product realizations
• Twisted Statistics in kappa-Minkowski Spacetime
• 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
• Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime
• Generalized kappa-deformed spaces, star-products, and their realizations
• Geodesic equation in $k$-Minkowski spacetime
• Kappa-deformed Snyder spacetime
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Noncommutative Differential Forms on the kappa-deformed Space
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
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• Noncommutative duality and fermionic quasinormal modes of the BTZ black hole
• Differential structure on kappa-Minkowski space, and kappa-Poincare algebra
• Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Effects of Noncommutativity on the Black Hole Entropy
• Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
• Maxwell's equations on the $\kappa$-Minkowski spacetime and Electric-Magnetic duality
• Unified description for kappa-deformations of orthogonal groups
• 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
• Uniformly accelerating observer in $\kappa$-deformed space-time
• Remarks on simple interpolation between Jordanian twists
• Entanglement dynamics in $\kappa$-deformed spacetime
• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Different realizations of kappa-momentum space and relative-locality effect
• Minimal and maximal lengths from position-dependent noncommutativity
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• Differential forms and k-Minkowski spacetime from extended twist
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Noncommutative fluid dynamics in the Snyder space-time
• Hermitian realizations of kappa-Minkowski spacetime
• Twisted statistics and the structure of Lie-deformed Minkowski spaces
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• 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
• Involutive representations of coordinate algebras and quantum spaces
• Quantisation of Klein-Gordon field in $\kappa$ space-time: deformed oscillators and Unruh effect
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Interpolations between Jordanian Twists Induced by Coboundary Twists
• Twisted conformal algebra related to $\kappa$-Minkowski space
• MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws
• The Weyl realizations of Lie algebras and left-right duality
• Generalized quantum phase spaces for the $\kappa$-deformed extended Snyder model
• Triangular quasi-Hopf algebra structures on certain non-semisimple quantum groups
• Heisenberg double versus deformed derivatives
• Symmetries of $\kappa$ Minkowski space-time: A possibility of exotic momentum space geometry?
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• 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
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
• Maximal acceleration in non-commutative space-time and its implications
• Superdense star in a space-time with minimal length
• Newtonian cosmology and Evolution of kappa-deformed universe
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• $\kappa$-deformed power spectrum and modified Unruh temperature
• Neutron Star in Quantized-space-time
• How does Casimir energy fall in $\kappa$-deformed space-time?
• Plane waves in noncommutative fluids
• Fate of $\kappa$-Minkowski space-time in non-relativistic (Galilean) and ultra-relativistic (Carrollian) regimes
• Regularization of Kepler Problem in $\kappa$-spacetime
• Spectral Dimension of kappa-deformed space-time
• Influence of the cosmological constant on $\kappa$-deformed Neutron Star
• Centripetal force on Casimir energies in $\kappa$-deformed rotating frame
• A Poincaré Covariant Noncommutative Spacetime?
• Some Features of Scattering Problem in a $\kappa$-Deformed Minkowski Spacetime
• Noncommutative kappa-Minkowski phi4 theory: Construction, properties and propagation
• Quantisation of $\kappa$-deformed Dirac equation
• Non-commutative correction of ideal gas thermodynamics
• Entropic force and bouncing behaviour in $\kappa$-Minkowski space-time
• Realizations of the Extended Snyder Model
• Thermal Casimir effect in $\kappa$-Minkowski space-time
• Unruh effect using Doppler shift method in DSR framework