Generalized Weyl systems and kappa-Minkowski space

Abstract

We introduce the notion of generalized Weyl system, and use it to define *-products which generalize the commutation relations of Lie algebras. In particular we study in a comparative way various *-products which generalize the k-Minkowski commutation relations.

21 pages, minor corrections and references added

References in corpus (2)

• The quantum structure of spacetime at the Planck scale and quantum fields
• Algebras of distributions suitable for phase-space quantum mechanics. I

Cited by in corpus (45)

• Kappa-Minkowski space-time and the star product realizations
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Towards Quantum Noncommutative $\kappa$-deformed Field Theory
• Hopf-algebra description of noncommutative-spacetime symmetries
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Fractional and noncommutative spacetimes
• Dirac spinors for Doubly Special Relativity and $\kappa$-Minkowski noncommutative spacetime
• Generalized kappa-deformed spaces, star-products, and their realizations
• Symplectic geometry and Noether charges for Hopf algebra space-time symmetries
• Derivatives, forms and vector fields on the kappa-deformed Euclidean space
• Noncommutative field theory from angular twist
• Duality symmetry for star products
• $\kappa$-Deformed Statistics and Classical Fourmomentum Addition Law
• Noncommutative Differential Forms on the kappa-deformed Space
• Pauli-Jordan Function and Scalar Field Quantization in $\kappa$-Minkowski Noncommutative Spacetime
• Localization and Reference Frames in $\kappa$-Minkowski Spacetime
• A twisted look on kappa-Minkowski: U(1) gauge theory
• kappa-Minkowski representations on Hilbert spaces
• Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
• Differential structure on the $\kappa$-Minkowski spacetime from twist
• Kappa-deformed oscillators, the choice of star product and free kappa-deformed quantum fields
• Quantum statistics and noncommutative black holes
• The Momentum Spaces of $\kappa$-Minkowski noncommutative spacetime
• $k$-Minkowski-deformation of $U(1)$ gauge theory
• Noncommutative Field Theory on Homogeneous Gravitational Waves
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• $\kappa$-Minkowski star product in any dimension from symplectic realization
• Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity
• Lorentz Covariant k-Minkowski Spacetime
• Blackbody radiation in κ-Minkowski spacetime
• Canonical k-Minkowski Spacetime
• Hopf-algebra description of noncommutative-spacetime symmetries
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• The k-Minkowski Spacetime: Trace, Classical Limit and uncertainty Relations
• kappa-Deformed Oscillators: Deformed Multiplication Versus Deformed Flip Operator and Multiparticle Clusters
• Covariant formulation of Noether's Theorem for translations on kappa-Minkowski spacetime
• T-Minkowski noncommutative spacetimes II: classical field theory
• Total momentum and other Noether charges for particles interacting in a quantum spacetime
• The Structure of Spacetime and Noncommutative Geometry
• From quantum deformations of relativistic symmetries to modified kinematics and dynamics
• Braided algebras and the kappa-deformed oscillators
• Gauge Theories on Open Lie Algebra Non-Commutative Spaces
• Asymmetry in momentum space: restoring $\mathcal{C}\mathcal{P}\mathcal{T}$ invariance of $\kappa$-field theory