Unification of $\kappa$-Minkowski and extended Snyder spaces

Abstract

In a recent paper, we have studied associative realizations of the noncommutative extended Snyder model, obtained by including the Lorentz generators (tensorial coordinates) and their conjugated momenta. In this paper, we extend this result to also incorporate a covariant realization of the $\kappa$-Poincaré spacetime. We obtain the coproduct, the associative star product and the twist in a Weyl-ordered realization, to first order in the noncommutativity parameters. This could help the construction of a quantum field theory based on this geometry.

8 pages

References in corpus (6)

• New realizations of Lie algebra kappa-deformed Euclidean space
• Covariant realizations of kappa-deformed space
• Noncommutative Spaces and Poincaré Symmetry
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations

Cited by in corpus (8)

• 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
• 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