Generalizations of Snyder model to curved spaces

Abstract

We consider generalizations of the Snyder algebra to a curved spacetime background with de Sitter symmetry. As special cases, we obtain the algebras of the Yang model and of triply special relativity. We discuss the realizations of these algebras in terms of canonical phase space coordinates, up to fourth order in the deformation parameters. In the case of triply special relativity we also find exact realization, exploiting its algebraic relation with the Snyder model.

arXiv comment8 pages, plain TeX, some typos corrected

References in corpus (18)

• Lorentz invariance with an invariant energy scale
• Testable scenario for Relativity with minimum-length
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• The β-function in duality-covariant noncommutative ϕ^4-theory
• Triply Special Relativity
• Planck-scale-modified dispersion relations in FRW spacetime
• Noncommutative Spaces and Poincaré Symmetry
• Yang's Model as Triply Special Relativity and the Snyder's Model--de Sitter Special Relativity Duality
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Doubly special relativity in de Sitter spacetime
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Classical dynamics on curved Snyder space
• Quantum field theory in generalised Snyder spaces
• Asymptotic freedom for $\lambda {\varphi }_{\star }^4$ QFT in Snyder-de Sitter space
• Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach
• Snyder-de Sitter model from two-time physics
• Snyder-type spaces, twisted Poincaré algebra and addition of momenta
• Twist for Snyder space

Cited by in corpus (8)

• Noncommutative Yang model and its generalizations
• Generalized Extended Uncertainty Principles, Liouville theorem and density of states: Snyder-de Sitter and Yang models
• Quantum perturbative solutions of extended Snyder and Yang models with spontaneous symmetry breaking
• Generalized quantum phase spaces for the $\kappa$-deformed extended Snyder model
• From Snyder space-times to doubly $\kappa$-dependent Yang quantum phase spaces and their generalizations
• Towards new relativistic doubly $\kappa$-deformed D=4 quantum phase spaces
• Yang model revisited
• Realizations of the Extended Snyder Model