Generalized quantum phase spaces for the $\kappa$-deformed extended Snyder model

Abstract

We describe, in an algebraic way, the $\kappa$-deformed extended Snyder models, that depend on three parameters $\beta ,\kappa$ and $\lambda$, which in a suitable algebra basis are described by the de Sitter algebras $o(1,N)$. The commutation relations of the algebra contain a parameter $\lambda$, which is used for the calculations of perturbative expansions. For such $\kappa$-deformed extended Snyder models we consider the Heisenberg double with dual generalized momenta sector, and provide the respective generalized quantum phase space depending on three parameters mentioned above. Further, we study for these models an alternative Heisenberg double, with the algebra of functions on de Sitter group. In both cases we calculate the formulae for the cross commutation relations between generalized coordinate and momenta sectors, at linear order in $\lambda$. We demonstrate that in the commutators of quantum space-time coordinates and momenta of the quantum-deformed Heisenberg algebra the terms generated by $\kappa$-deformation are dominating over $\beta$-dependent ones for small values of $\lambda$.

11 pages, no figures, accepted version

References in corpus (9)

• Covariant realizations of kappa-deformed space
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• The $\kappa$-(A)dS noncommutative spacetime
• Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach
• Heisenberg doubles for Snyder type models
• Generalizations of Snyder model to curved spaces
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• Associative realizations of $\kappa$-deformed extended Snyder model

Cited by in corpus (4)

• 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
• Realizations of the Extended Snyder Model