Generalized quantum phase spaces for the κ-deformed extended Snyder model

Lukierski, Jerzy; Meljanac, Stjepan; Mignemi, Salvatore; Pachoł, Anna (2023) Generalized quantum phase spaces for the κ-deformed extended Snyder model. Physics Letters B, 838 . ISSN 03702693

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Abstract

We describe, in an algebraic way, the κ-deformed extended Snyder models, that depend on three parameters and λ, which in a suitable algebra basis are described by the de Sitter algebras.The commutation relations of the algebra contain a parameter λ, which is used for the calculations of perturbative expansions. For such κ-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 λ. We demonstrate that in the commutators of quantum space-time coordinates and momenta of the quantum-deformed Heisenberg algebra the terms generated by κ-deformation are dominating over β-dependent ones for small values of λ.

Item Type:	Article
Uncontrolled Keywords:	kappa-deformed extended Snyder models; de Sitter algebras; Heisenberg double; generalized quantum phase space; dual generalized momenta sector; commutation relations; perturbative expansions; quantum space-time coordinates; quantum-deformed Heisenberg algebra; parameter lambda
Subjects:	NATURAL SCIENCES > Physics NATURAL SCIENCES > Physics > Nuclear Physics NATURAL SCIENCES > Physics > Astronomy and Astrophysics
Divisions:	Theoretical Physics Division
Depositing User:	Kristina Ciglar
Date Deposited:	13 Apr 2026 13:13
URI:	http://fulir.irb.hr/id/eprint/11670
DOI:	10.1016/j.physletb.2023.137709

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