Heisenberg doubles for Snyder type models

Abstract

A Snyder model generated by the noncommutative coordinates and Lorentz generators close a Lie algebra. The application of the Heisenberg double construction is investigated for the Snyder coordinates and momenta generators. It leads to the phase space of the Snyder model. Further, the extended Snyder algebra is constructed by using the Lorentz algebra, in one dimension higher. The dual pair of extended Snyder algebra and extended Snyder group is then formulated. Two Heisenberg doubles are considered, one with the conjugate tensorial momenta and another with the Lorentz matrices. Explicit formulae for all Heisenberg doubles are given.

arXiv comment19 pages, no figures, 1 Appendix; version accepted for publication

References in corpus (19)

• A Generalized Uncertainty Principle in Quantum Gravity
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• Lorentz-covariant deformed algebra with minimal length and application to the 1+1-dimensional Dirac oscillator
• Scalar Field Theory on Non-commutative Snyder Space-Time
• Modification of Heisenberg uncertainty relations in non-commutative Snyder space-time geometry
• Scalar field theory in Snyder space-time: alternatives
• Kappa-deformed Snyder spacetime
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Snyder dynamics in a Schwarzschild spacetime
• Nonassociative Snyder phi4 Quantum Field Theory
• Associative realizations of the extended Snyder model
• Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach
• Lorentzian Snyder spacetimes and their Galilei and Carroll limits from projective geometry
• Relative-locality effects in Snyder spacetime
• Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions
• Quantum Twist-Deformed D=4 Phase Spaces with Spin Sector and Hopf Algebroid Structures
• Relative-locality phenomenology on Snyder spacetime
• Heisenberg double versus deformed derivatives
• Generalized noncommutative Snyder spaces and projective geometry

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• Quantum perturbative solutions of extended Snyder and Yang models with spontaneous symmetry breaking
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• 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
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• Towards new relativistic doubly $\kappa$-deformed D=4 quantum phase spaces
• Spinorial Snyder and Yang Models From Superalgebras And Noncommutative Quantum Superspaces
• $\hslash$-perturbative solutions of quantum Snyder and Yang models with parameters describing spontaneous symmetry breaking
• Realizations of the Extended Snyder Model
• Refining Bounds for Snyder and GUP Models through Seismic Wave Analysis