Kappa-deformed Snyder spacetime

Abstract

We present Lie-algebraic deformations of Minkowski space with undeformed Poincare algebra. These deformations interpolate between Snyder and kappa-Minkowski space. We find realizations of noncommutative coordinates in terms of commutative coordinates and derivatives. Deformed Leibniz rule, the coproduct structure and star product are found. Special cases, particularly Snyder and kappa-Minkowski in Maggiore-type realizations are discussed. Our construction leads to a new class of deformed special relativity theories.

12 pages, no figures, LaTeX2e class file, accepted for publication in Modern Physics Letters A

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Cited by in corpus (34)

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• 30 years in: Quo vadis generalized uncertainty principle?
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• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Classical dynamics on curved Snyder space
• Quantum field theory in generalised Snyder spaces
• Associative realizations of the extended Snyder model
• Remarks on simple interpolation between Jordanian twists
• Heisenberg doubles for Snyder type models
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Snyder-type spaces, twisted Poincaré algebra and addition of momenta
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Noncommutative fluid dynamics in the Snyder space-time
• Hermitian realizations of kappa-Minkowski spacetime
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions
• Interpolations between Jordanian Twists Induced by Coboundary Twists
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Snyder Space-Time: K-Loop and Lie Triple System
• Snyder-de Sitter meets the Grosse-Wulkenhaar model
• From Snyder space-times to doubly $\kappa$-dependent Yang quantum phase spaces and their generalizations
• Generalized relativistic kinematics in Poincaré-invariant models
• Twist for Snyder space
• Superdense star in a space-time with minimal length
• Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra
• Plane waves in noncommutative fluids
• Towards new relativistic doubly $\kappa$-deformed D=4 quantum phase spaces
• One Parameter Family of Jordanian Twists
• Interpolations between Jordanian twists, the Poincaré-Weyl algebra and dispersion relations
• On interpolations between Jordanian twists
• Realizations of the Extended Snyder Model