kappa-Minkowski representations on Hilbert spaces

Abstract

The algebra of functions on kappa-Minkowski noncommutative spacetime is studied as algebra of operators on Hilbert spaces. The representations of this algebra are constructed and classified. This new approach leads to a natural construction of integration in kappa-Minkowski spacetime in terms of the usual trace of operators.

23 pag. Latex, correction of a couple of typos, reference added, title slightly changed

References in corpus (23)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• The quantum structure of spacetime at the Planck scale and quantum fields
• Quantum gravity and minimum length
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Noncommutative Perturbative Dynamics
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Gauge Theory on Noncommutative Spaces
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Doubly Special Relativity
• Non-commutative space-time of Doubly Special Relativity theories
• Deformed Field Theory on kappa-spacetime
• Physical Instances of Noncommuting Coordinates
• Gauge theories on the kappa-Minkowski spacetime
• Quantum Groups and Noncommutative Geometry
• Hopf-algebra description of noncommutative-spacetime symmetries
• Infinitely many star products to play with
• Generalized Weyl systems and kappa-Minkowski space
• Dirac spinors for Doubly Special Relativity and $\kappa$-Minkowski noncommutative spacetime
• Local Field Theory ON $\kappa$-Minkowski Space, Star Products and Noncommutative Translations
• A non-commutative Minkowskian spacetime from a quantum AdS algebra
• Distance Measurement and $\kappa$-Deformed Propagation of Light and Heavy Probes
• Lochlainn O'Raifeartaigh, Fluids, and Noncommuting Fields

Cited by in corpus (15)

• Groupoids, Loop Spaces and Quantization of 2-Plectic Manifolds
• Localization and Reference Frames in $\kappa$-Minkowski Spacetime
• The $\kappa$-(A)dS noncommutative spacetime
• Relative locality in a quantum spacetime and the pregeometry of $\kappa$-Minkowski
• The Momentum Spaces of $\kappa$-Minkowski noncommutative spacetime
• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Cayley-Klein Lie bialgebras: Noncommutative spaces, Drinfel'd doubles and kinematical applications
• Canonical k-Minkowski Spacetime
• Compact $\kappa$-deformation and spectral triples
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis
• The k-Minkowski Spacetime: Trace, Classical Limit and uncertainty Relations
• Covariant formulation of Noether's Theorem for translations on kappa-Minkowski spacetime
• The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime