Kappa-Minkowski space-time and the star product realizations

Abstract

We investigate a Lie algebra-type $\kappa$-deformed Minkowski space-time with undeformed Lorentz algebra and mutually commutative vector-like Dirac derivatives. There are infinitely many realizations of $\kappa$-Minkowski space. The coproduct and the star product corresponding to each of them are found. Utilizing the properties of the {\em{natural}} realization, we construct a scalar field theory on $\kappa$-deformed Minkowski space and show that it is equivalent to the scalar, nonlocal, relativistically invariant field theory on the ordinary Minkowski space.

23 pages, revtex4, no figures, typos corrected, references added; in v3 few references and some comments regarding kappa-Poincare symmetry are included; to appear in EPJC

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Cited by in corpus (130)

• Twisted Statistics in kappa-Minkowski Spacetime
• 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
• Scalar Field Theory on Non-commutative Snyder Space-Time
• Electrodynamics on $\kappa$-Minkowski space-time
• Classical basis for kappa-Poincare algebra and doubly special relativity theories
• Speed of particles and a relativity of locality in $\kappa$-Minkowski quantum spacetime
• 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
• Scalar field theory in Snyder space-time: alternatives
• 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
• $\kappa$-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
• Newton's Equation on the kappa space-time and the Kepler problem
• Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole
• A twisted look on kappa-Minkowski: U(1) gauge theory
• Noncommutative $R^d$ via closed star product
• $\kappa$-deformed Dirac Equation
• $\kappa$-Poincaré invariant quantum field theories with KMS weight
• On kappa-deformation and triangular quasibialgebra structure
• Noncommutative duality and fermionic quasinormal modes of the BTZ black hole
• Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Gauge theories on quantum spaces
• 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
• Effects of Noncommutativity on the Black Hole Entropy
• Maxwell's equations on the $\kappa$-Minkowski spacetime and Electric-Magnetic duality
• Noncommutative correction to the entropy of Schwarzschild black hole with GUP
• Unified description for kappa-deformations of orthogonal groups
• Differential algebras on kappa-Minkowski space and action of the Lorentz algebra
• Differential structure on the $\kappa$-Minkowski spacetime from twist
• Differential Structure on kappa-Minkowski Spacetime Realized as Module of Twisted Weyl Algebra
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• Kappa-deformed oscillators, the choice of star product and free kappa-deformed quantum fields
• $\kappa$-Poincaré invariant orientable field theories at 1-loop
• Nonassociative Snyder phi4 Quantum Field Theory
• Quantum statistics and noncommutative black holes
• $k$-Minkowski-deformation of $U(1)$ gauge theory
• The 2D $\kappa$-Dirac oscillator
• Uniformly accelerating observer in $\kappa$-deformed space-time
• Gauge Theories on Deformed Spaces
• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• Entanglement dynamics in $\kappa$-deformed spacetime
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Lie algebra type noncommutative phase spaces are Hopf algebroids
• $\kappa$-Minkowski star product in any dimension from symplectic realization
• Scalar Field theory in $\kappa$-Minkowski spacetime from twist
• Low-energy constraints on kappa-Minkowski extension of the Standard Model
• Planck-scale-deformed relativistic symmetries and diffeomorphisms in momentum space
• Different realizations of kappa-momentum space and relative-locality effect
• Kappa-deformation of phase space; generalized Poincare algebras and R-matrix
• UV/IR Mixing in Nonassociative Snyder phi^4 Theory
• Gauge Theory on Twisted $\kappa$-Minkowski: Old Problems and Possible Solutions
• Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity
• Poisson gauge models and Seiberg-Witten map
• Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry
• Differential forms and k-Minkowski spacetime from extended twist
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Spectral dimensions and dimension spectra of quantum spacetimes
• Observables in Quantum Mechanics and the Importance of Self-adjointness
• Hawking radiation in the kappa-spacetime
• Light-like $\kappa$-deformations and scalar field theory via Drinfeld twist
• Noncommutative fluid dynamics in the Snyder space-time
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• Hermitian realizations of kappa-Minkowski spacetime
• Vacuum energy and the cosmological constant problem in $\kappa$-Poincaré invariant field theories
• 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
• Extending general covariance: Moyal-type noncommutative manifolds
• Quantisation of Klein-Gordon field in $\kappa$ space-time: deformed oscillators and Unruh effect
• Compact stars in quantum spacetime
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• Quantum particles in non-commutative space-time: an identity crisis
• A short introduction to $\kappa$-deformation
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Noncommutativity and the Weak Cosmic Censorship
• Interpolations between Jordanian Twists Induced by Coboundary Twists
• The Weyl realizations of Lie algebras and left-right duality
• Kappa-deformed Dirac oscillator in an external magnetic field
• On the L${}_{\infty }$ structure of Poisson gauge theory
• Leibniz rules for enveloping algebras in symmetric ordering
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• Quantum space and quantum completeness
• Symmetries of $\kappa$ Minkowski space-time: A possibility of exotic momentum space geometry?
• Directly from $H$-flux to the family of three nonlocal $R$-flux theories
• Twist for Snyder space
• 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
• Conformal quantum mechanics and holography in noncommutative space-time
• Superdense star in a space-time with minimal length
• Phase structure of fuzzy black holes
• Newtonian cosmology and Evolution of kappa-deformed universe
• Conserved symmetries in noncommutative quantum mechanics
• Poisson electrodynamics on $\kappa$-Minkowski space-time
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Path integral action of a particle in $\kappa$-Minkowski spacetime
• Covariant formulation of Noether's Theorem for translations on kappa-Minkowski spacetime
• Plane waves in noncommutative fluids
• $\kappa$-General-Relativity I: a Non-Commutative GR Theory with the $\kappa$-Minkowski Spacetime as its Flat Limit
• Neutron Star in Quantized-space-time
• How does Casimir energy fall in $\kappa$-deformed space-time?
• Regularization of Kepler Problem in $\kappa$-spacetime
• $\kappa$-deformed power spectrum and modified Unruh temperature
• Superradiance scattering of scalar, electromagnetic, and gravitational fields and thin accretion disk around non-commutating Kerr black hole
• Noncommutative kappa-Minkowski phi4 theory: Construction, properties and propagation
• Some Features of Scattering Problem in a $\kappa$-Deformed Minkowski Spacetime
• The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime
• Influence of the cosmological constant on $\kappa$-deformed Neutron Star
• Quantisation of $\kappa$-deformed Dirac equation
• Twist deformations leading to kappa-Poincare Hopf algebra and their application to physics
• Centripetal force on Casimir energies in $\kappa$-deformed rotating frame
• Quantum spaces, central extensions of Lie groups and related quantum field theories
• $\kappa$-Poincaré phase space: speed of massless particles and relativity of spacetime locality
• A Poincaré Covariant Noncommutative Spacetime?
• Entropic force and bouncing behaviour in $\kappa$-Minkowski space-time
• Non-commutative correction of ideal gas thermodynamics
• The covariant and on-shell statistics in kappa-deformed spacetime
• Thermal Casimir effect in $\kappa$-Minkowski space-time
• Braided Statistics from Abelian Twist in $\kappa$-Minkowski Spacetime