Quantum $\kappa$-Poincare in Any Dimensions

Abstract

The $\kappa$-deformation of the D-dimensional Poincaré algebra $(D\ge 2)$ with any signature is given. Further the quadratic Poisson brackets, determined by the classical $r$-matrix are calculated, and the quantum Poincaré group "with noncommuting parameters" is obtained.

(PLAIN TeX, 10 pp. )

References in corpus (1)

• Braided Momentum Structure of the q-Poincare Group

Cited by in corpus (174)

• Quantum symmetry, the cosmological constant and Planck scale phenomenology
• Deformed Field Theory on kappa-spacetime
• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• Geometry and field theory in multi-fractional spacetime
• Twisted Statistics in kappa-Minkowski Spacetime
• Doubly Special Relativity versus $\kappa$-deformation of relativistic kinematics
• Covariant realizations of kappa-deformed space
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Noncommutative Differential Calculus on the Kappa-Minkowski Space
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Towards Quantum Noncommutative $\kappa$-deformed Field Theory
• Hamilton geometry: Phase space geometry from modified dispersion relations
• Realization of DSR-relativistic symmetries in Finsler geometries
• Electrodynamics on $\kappa$-Minkowski space-time
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Generalized Weyl systems and kappa-Minkowski space
• Deformed General Relativity
• Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime
• Generalized kappa-deformed spaces, star-products, and their realizations
• Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem
• Quantum deformations of the flat space superstring
• On the $\kappa$-Dirac Oscillator revisited
• Derivatives, forms and vector fields on the kappa-deformed Euclidean space
• Investigation on Finsler geometry as a generalization to curved spacetime of Planck-scale-deformed relativity in the de Sitter case
• Geodesic equation in $k$-Minkowski spacetime
• A non-commutative Minkowskian spacetime from a quantum AdS algebra
• Curved spacetimes with local $\kappa$-Poincaré dispersion relation
• Deformed relativity symmetries and the local structure of spacetime
• Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes
• $\kappa$-Deformed Statistics and Classical Fourmomentum Addition Law
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Noncommutative Differential Forms on the kappa-deformed Space
• Localization and Reference Frames in $\kappa$-Minkowski Spacetime
• Rainbow statistics
• Newton's Equation on the kappa space-time and the Kepler problem
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Pauli-Jordan Function and Scalar Field Quantization in $\kappa$-Minkowski Noncommutative Spacetime
• Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole
• $\kappa$-deformed Dirac Equation
• On kappa-deformation and triangular quasibialgebra structure
• The kappa-(A)dS quantum algebra in (3+1) dimensions
• 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
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Null-plane Quantum Universal $R$-matrix
• Deformed Covariant Quantum Phase Spaces as Hopf Algebroids
• Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
• Maxwell's equations on the $\kappa$-Minkowski spacetime and Electric-Magnetic duality
• Curved momentum spaces from quantum (Anti-)de Sitter groups in (3+1) dimensions
• Quantum gravity on a square graph
• Differential algebras on kappa-Minkowski space and action of the Lorentz algebra
• Planck-scale phenomenology with anti-de Sitter momentum space
• Relativistic and Newtonian kappa spacetimes
• Differential structure on the $\kappa$-Minkowski spacetime from twist
• Relative locality in a quantum spacetime and the pregeometry of $\kappa$-Minkowski
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• About Lorentz invariance in a discrete quantum setting
• Deformed and extended Galilei group Hopf algebras
• Representation Theory of Quantized Poincare Algebra. Tensor Operators and Their Application to One-Partical Systems
• Non-commutative relativistic spacetimes and worldlines from 2+1 quantum (anti-)de Sitter groups
• Canonical and Lie-algebraic twist deformations of Galilei algebra
• Quantum statistics and noncommutative black holes
• Kinematics of particles with quantum de Sitter symmetries
• Twisting and kappa-Poincare
• A (2+1) non-commutative Drinfel'd double spacetime with cosmological constant
• Uniformly accelerating observer in $\kappa$-deformed space-time
• The 2D $\kappa$-Dirac oscillator
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• A bound on Planck-scale deformations of CPT from muon lifetime
• Curved momentum spaces from quantum groups with cosmological constant
• Physical Constraints on Quantum Deformations of Spacetime Symmetries
• Noncommutativity and logarithmic correction to the black hole entropy
• Different realizations of kappa-momentum space and relative-locality effect
• Field theories on spaces with linear fuzziness
• Kappa-deformation of phase space; generalized Poincare algebras and R-matrix
• Effects of Planck-scale-modified dispersion relations on the thermodynamics of charged black holes
• Maximally extended sl(2|2), q-deformed d(2,1;epsilon) and 3D kappa-Poincaré
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• Twisted (2+1) $\kappa$-AdS Algebra, Drinfel'd Doubles and Non-Commutative Spacetimes
• Relativistic compatibility of the interacting $\kappa$-Poincaré model and implications for the relative locality framework
• Loop diagrams in space with SU(2) fuzziness
• Localization and observers in $\varrho$-Minkowski spacetime
• Differential forms and k-Minkowski spacetime from extended twist
• Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry
• Spectral dimensions and dimension spectra of quantum spacetimes
• Graded contractions and bicrossproduct structure of deformed inhomogeneous algebras
• Light-like $\kappa$-deformations and scalar field theory via Drinfeld twist
• Towards (3+1) gravity through Drinfel'd doubles with cosmological constant
• Effects of quantum deformation on the integer quantum Hall effect
• 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
• Coherent States for 3d Deformed Special Relativity: semi-classical points in a quantum flat spacetime
• Nonlinear and Quantum Origin of Doubly Infinite Family of Modified Addition Laws for Fourmomenta
• Coloured quantum universal enveloping algebras
• Vacuum energy and the cosmological constant problem in $\kappa$-Poincaré invariant field theories
• Metric perturbations in Noncommutative Gravity
• Associative realizations of $\kappa$-deformed extended Snyder model
• Poisson structure on a space with linear SU(2) fuzziness
• The Atick-Witten free energy, closed tachyon condensation and deformed Poincare' symmetry
• Noncommutative correction to the entropy of charged BTZ black hole
• A group theoretic description of the $\kappa$-Poincaré Hopf algebra
• Quantum mechanics on space with SU(2) fuzziness
• Blackbody radiation in κ-Minkowski spacetime
• Non-commutative Fourier transform for the Lorentz group via the Duflo map
• Effects of quantum deformation on the Jaynes-Cummings and anti-Jaynes-Cummings models
• Quantisation of Klein-Gordon field in $\kappa$ space-time: deformed oscillators and Unruh effect
• k-deformed Poincare algebras and quantum Clifford-Hopf algebras
• Quantum particles in non-commutative space-time: an identity crisis
• A short introduction to $\kappa$-deformation
• Quantum Algebras for Maximal Motion Groups of N-Dimensional Flat Spaces
• Accelerated horizons and Planck-scale kinematics
• Noncommutativity and the Weak Cosmic Censorship
• Bicrossproduct approach to the Connes-Moscovici Hopf algebra
• Kappa-deformed Dirac oscillator in an external magnetic field
• Statistical mechanics of free particles on space with Lie type noncommutativity
• The quantum 2-dimensional Poincare group from quantum group contraction
• Closedness of orbits in a space with SU(2) Poisson structure
• Photonic realization of the kappa-deformed Dirac equation
• $\kappa$-deformed BMS symmetry
• From Snyder space-times to doubly $\kappa$-dependent Yang quantum phase spaces and their generalizations
• Quantum space and quantum completeness
• Planck-scale deformation of CPT and particle lifetimes
• Triangular quasi-Hopf algebra structures on certain non-semisimple quantum groups
• Extended noncommutative Minkowski spacetimes and hybrid gauge symmetries
• The quantum Poincare group from quantum group contraction
• Effect of Non-commutativity of space-time on Thermodynamics of Photon gas
• Gravitational probe of quantum spacetime
• TeV-photon paradox and space with SU(2) fuzziness
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Dirac theory on a space with linear Lie type fuzziness
• Conformal quantum mechanics and holography in noncommutative space-time
• Maximal acceleration in non-commutative space-time and its implications
• Gauge theory on a space with linear Lie type fuzziness
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• BMS algebras in 4 and 3 dimensions, their quantum deformations and duals
• Central force problem in space with SU(2) Poisson structure
• Neutrinos as possible probes for quantum gravity
• Non-Commutative space-time and Hausdorff dimension
• The bicovariant differential calculus on the kappa-Poincare group and on the kappa-Minkowski space
• On the spectral and homological dimension of k-Minkowski space
• $\kappa$-deformed power spectrum and modified Unruh temperature
• Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries
• Path integral action of a particle in $\kappa$-Minkowski spacetime
• Quantisation of $\kappa$-deformed Dirac equation
• Reproducing the effects of quantum deformation in the undeformed Jaynes-Cummings model
• Some considerations on duality concerning kappa-Minkowski spacetime theories
• Yang-Baxter deformations of the flat space string
• Some Features of Scattering Problem in a $\kappa$-Deformed Minkowski Spacetime
• T-Minkowski noncommutative spacetimes I: Poincaré groups, differential calculi and braiding
• Projective representation of k-Galilei group
• Twist deformations leading to kappa-Poincare Hopf algebra and their application to physics
• A general approach to noncommutative spaces from Poisson homogeneous spaces: Applications to (A)dS and Poincaré
• Eigenvalue problem for radial potentials in space with SU(2) fuzziness
• Braided algebras and the kappa-deformed oscillators
• Vulcanized Vortex
• Maxwell's equations and Lorentz force in doubly special relativity
• Parity at the Planck scale
• Symplectic realization of generalized Snyder-Poisson algebra
• Testing the universality of quantum gravity theories with cosmic messengers in the context of DSR theories
• Spacetime defects and group momentum space
• Entropic force and bouncing behaviour in $\kappa$-Minkowski space-time
• Entropy of black holes, charged probes and noncommutative generalization
• Revisiting the algebraic structure of the generalized uncertainty principle
• Coherence and Entanglement in a Non-commutative Spacetime
• Braided Statistics from Abelian Twist in $\kappa$-Minkowski Spacetime
• Three-dimensional gravity and deformations of relativistic symmetries
• Unruh effect using Doppler shift method in DSR framework
• Towards constructing one-particle representations of the deformed Poincaré algebra