Snyder-type spaces, twisted Poincaré algebra and addition of momenta

Abstract

We discuss a generalisation of the Snyder model that includes all the possible deformations of the Heisenberg algebra compatible with Lorentz invariance, in terms of realisations of the noncommutative geometry. The corresponding deformed addition of momenta, the twist and the $R$-matrix are calculated to first order in the deformation parameters for all models. In the particular case of the Snyder realisation, the exact formula for the twist is obtained.

11 pages

References in corpus (11)

• Twisted Statistics in kappa-Minkowski Spacetime
• Scalar field theory in Snyder space-time: alternatives
• Noncommutative Spaces and Poincaré Symmetry
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Deformed Covariant Quantum Phase Spaces as Hopf Algebroids
• Snyder dynamics in a Schwarzschild spacetime
• Quantum field theory in generalised Snyder spaces
• Nonassociative Snyder phi4 Quantum Field Theory
• Remarks on simple interpolation between Jordanian twists
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Spectrum of the hydrogen atom in Snyder space in a semiclassical approximation

Cited by in corpus (13)

• Worldline Formalism in Snyder Spaces
• Associative realizations of the extended Snyder model
• Generalizations of Snyder model to curved spaces
• UV/IR Mixing in Nonassociative Snyder phi^4 Theory
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• Noncommutative Yang model and its generalizations
• Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions
• Associative realizations of $\kappa$-deformed extended Snyder model
• Quantum perturbative solutions of extended Snyder and Yang models with spontaneous symmetry breaking
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Twist for Snyder space
• Interpolations between Jordanian twists, the Poincaré-Weyl algebra and dispersion relations
• On interpolations between Jordanian twists