Associative realizations of the extended Snyder model

Abstract

The star product usually associated to the Snyder model of noncommutative geometry is nonassociative, and this property prevents the construction of a proper Hopf algebra. It is however possible to introduce a well-defined Hopf algebra by including the Lorentz generators and their conjugate momenta into the algebra. In this paper, we study the realizations of this extended Snyder spacetime, and obtain the coproduct and twist and the associative star product in a Weyl-ordered realization, to first order in the noncommutativity parameter. We then extend our results to the most general realizations of the extended Snyder spacetime, always up to first order.

arXiv comment10 pages; version accepted for publication on Phys. Rev. D

References in corpus (26)

• The quantum structure of spacetime at the Planck scale and quantum fields
• Quantum gravity and minimum length
• Coproduct and star product in field theories on Lie-algebra non-commutative space-times
• Triply Special Relativity
• 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
• 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
• Kappa-deformed Snyder spacetime
• Snyder dynamics in a Schwarzschild spacetime
• Quantum field theory in generalised Snyder spaces
• Worldline Formalism in Snyder Spaces
• Nonassociative Snyder phi4 Quantum Field Theory
• Remarks on simple interpolation between Jordanian twists
• Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach
• Symmetries of Snyder--de Sitter space and relativistic particle dynamics
• UV/IR Mixing in Nonassociative Snyder phi^4 Theory
• Snyder-type spaces, twisted Poincaré algebra and addition of momenta
• Relative-locality effects in Snyder 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
• Quantum Twist-Deformed D=4 Phase Spaces with Spin Sector and Hopf Algebroid Structures
• Relative-locality phenomenology on Snyder spacetime
• Twist for Snyder space

Cited by in corpus (12)

• Heisenberg doubles for Snyder type models
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• Associative realizations of $\kappa$-deformed extended Snyder model
• 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
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• Generalized Heisenberg algebra, realizations of the $\mathfrak{gl}(n)$ algebra and applications
• 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