Associative realizations of $\kappa$-deformed extended Snyder model

Abstract

Usually, the realizations of the noncommutative Snyder model lead to a nonassociative star product. However, it has been shown that this problem can be avoided by adding to the spacetime coordinates new tensorial degrees of freedom. The model so obtained, called extended Snyder model, can be subject to a $\kappa$-deformation, giving rise to a unification of the Snyder and the $\kappa$-Poincaré algebras in the formalism of extended spacetime. In this paper we review this construction and consider the generic realizations of the $\kappa$-deformed extended Snyder model, calculating the associated star product, coproduct and twist in a perturbative setting. We also introduce a representation of the Lorentz algebra in the extended space and speculate on possible interpretations of the tensorial degrees of freedom.

arXiv comment11 pages; version accepted for publication on Phys. Rev. D

References in corpus (21)

• The quantum structure of spacetime at the Planck scale and quantum fields
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Quantum mechanics on the noncommutative plane and sphere
• Quantum $\kappa$-Poincare in Any Dimensions
• 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 Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Toward the classification of differential calculi on $\kappa$-Minkowski space and related field theories
• Unified description for kappa-deformations of orthogonal groups
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• Associative realizations of the extended Snyder model
• Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach
• Remarks on simple interpolation between Jordanian twists
• Heisenberg doubles for Snyder type models
• Snyder-type spaces, twisted Poincaré algebra and addition of momenta
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• Light-like $\kappa$-deformations and scalar field theory via Drinfeld twist
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Interpolations between Jordanian twists, the Poincaré-Weyl algebra and dispersion relations

Cited by in corpus (7)

• 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
• Realizations of the Extended Snyder Model