Yang model revisited

Abstract

A long time ago C.N. Yang proposed a generalization of the Snyder model to the case of a curved background spacetime, based on an algebra isomorphic to $so(1,5)$, which includes as subalgebras both the Snyder and the de Sitter algebras. His proposal can therefore be interpreted as a model of noncommutative curved spacetime, and could be useful for relating physics at very small and very large scales. We review this model and some recent progress concerning its generalizations and its interpretation in the framework of Hopf algebras. We also report some possibilities to relate it to more phenomenological aspects.

9 pages

References in corpus (14)

• The quantum structure of spacetime at the Planck scale and quantum fields
• Quantum gravity and minimum length
• Minimal Length Scale Scenarios for Quantum Gravity
• Triply Special Relativity
• Planck-scale-modified dispersion relations in FRW spacetime
• Yang's Model as Triply Special Relativity and the Snyder's Model--de Sitter Special Relativity Duality
• Linear Form of 3-scale Relativity Algebra and the Relevance of Stability
• Symmetries of Snyder--de Sitter space and relativistic particle dynamics
• Generalizations of Snyder model to curved spaces
• Physics of Quantum Relativity through a Linear Realization
• Noncommutative Yang model and its generalizations
• Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions
• Quantum perturbative solutions of extended Snyder and Yang models with spontaneous symmetry breaking
• From Snyder space-times to doubly $\kappa$-dependent Yang quantum phase spaces and their generalizations