Noncommutative Yang model and its generalizations

Abstract

Long time ago, C.N. Yang proposed a model of noncommutative spacetime that generalized the Snyder model to a curved background. In this paper we review his proposal and the generalizations that have been suggested during the years. In particular, we discuss the most general algebras that contain as subalgebras both de Sitter and Snyder algebras, preserving Lorentz invariance, and are generated by a two-parameter deformation of the canonical Heisenberg algebra. We also define their realizations on quantum phase space, giving explicit examples, both exact and in terms of a perturbative expansion in the deformation parameters.

11 pages; version published on Journal of Mathematical Physics

References in corpus (13)

• de Sitter special relativity
• Special Relativity in the 21${}^{\mathrm{st}}$ century
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• Noncommutative Spaces and Poincaré Symmetry
• Yang's Model as Triply Special Relativity and the Snyder's Model--de Sitter Special Relativity Duality
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• Generalizations of Snyder model to curved spaces
• Casimir effect in Snyder Space
• Physics of Quantum Relativity through a Linear Realization
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists

Cited by in corpus (5)

• 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
• Towards new relativistic doubly $\kappa$-deformed D=4 quantum phase spaces
• Yang model revisited
• Realizations of the Extended Snyder Model