Noncommutative Spaces and Poincaré Symmetry

Abstract

We present a framework which unifies a large class of non-commutative spacetimes that can be described in terms of a deformed Heisenberg algebra. The commutation relations between spacetime coordinates are up to linear order in the coordinates, with structure constants depending on the momenta plus terms depending only on the momenta. The possible implementations of the action of Lorentz transformations on these deformed phase spaces are considered, together with the consistency requirements they introduce. It is found that Lorentz transformations in general act nontrivially on tensor products of momenta. In particular the Lorentz group element which acts on the left and on the right of a composition of two momenta is different, and depends on the momenta involved in the process. We conclude with two representative examples, which illustrate the mentioned effect.

arXiv comment7 pages, to be published in Phys. Lett. B

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Cited by in corpus (35)

• Localization and Reference Frames in $\kappa$-Minkowski Spacetime
• Pauli-Jordan Function and Scalar Field Quantization in $\kappa$-Minkowski Noncommutative Spacetime
• Quantum field theory in generalised Snyder spaces
• Nonassociative Snyder phi4 Quantum Field Theory
• Associative realizations of the extended Snyder model
• Remarks on simple interpolation between Jordanian twists
• $k$-Minkowski-deformation of $U(1)$ gauge theory
• Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach
• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Generalizations of Snyder model to curved spaces
• Snyder-type spaces, twisted Poincaré algebra and addition of momenta
• UV/IR Mixing in Nonassociative Snyder phi^4 Theory
• Does a deformation of special relativity imply energy dependent photon time delays?
• Vector-like deformations of relativistic quantum phase-space and relativistic kinematics
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Noncommutative Yang model and its generalizations
• Twisted statistics and the structure of Lie-deformed Minkowski spaces
• Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions
• Spacetime from locality of interactions in deformations of special relativity: the example of $\kappa$-Poincaré Hopf algebra
• Probing Noncommutativities of Phase Space by Using Persistent Charged Current and Its Asymmetry
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Constrains of Charge-to-Mass Ratios on Noncommutative Phase Space
• Interpolations between Jordanian Twists Induced by Coboundary Twists
• Twist for Snyder space
• Influences of the coordinate dependent noncommutative space on charged and spin currents
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
• One Parameter Family of Jordanian Twists
• Generalization of Weyl realization to a class of Lie superalgebras
• Noncommutative spacetime symmetries from covariant quantum mechanics
• The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime
• On interpolations between Jordanian twists
• Interpolations between Jordanian twists, the Poincaré-Weyl algebra and dispersion relations