Towards new relativistic doubly κ-deformed D=4 quantum phase spaces

Lukierski, J.; Meljanac, Stjepan; Mignemi, S.; Pachoł, A.; Woronowicz, M. (2025) Towards new relativistic doubly κ-deformed D=4 quantum phase spaces. The European Physical Journal Plus, 140 (5). ISSN 2190-5444

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Abstract

We propose new noncommutative models of quantum phase spaces, containing a pair of kappa-deformed Poincare algebras, with two independent double (kappa, (kappa) over tilde)-deformations in space-time and four-momenta sectors. The first such quantum phase space can be obtained by contractions M, R -> infinity of recently introduced doubly kappa-deformed (kappa, (kappa) over tilde)-Yang models, with the parameters M, R describing inverse space-time and four-momenta curvatures and constant four-vectors a(mu), b(mu) determining nine types of (kappa, (kappa) over tilde)-deformations. The second considered model is provided by the nonlinear doubly kappa-deformed TSR algebra spanned by 14 coset (o) over cap (1, 5)/(o) over cap (2) generators. The basic algebraic difference between the two models is the following: the first one, described by (o) over cap (1, 5) Lie algebra can be supplemented by the Hopf algebra structure, while the second model contains the quantum phase space commutators [(x) over cap (mu), (q) over cap (nu)], with the standard numerical i (h) over bar eta(mu nu) term; therefore, it describes the quantum-deformed Heisenberg algebra relations which cannot be equipped with the Hopf algebra.

Item Type:	Article
Uncontrolled Keywords:	classical and quantum gravity, commutative rings and algebras; K-theory; quantum optics; topological groups and lie groups
Subjects:	NATURAL SCIENCES > Physics
Divisions:	Theoretical Physics Division
Depositing User:	Sofija Konjević
Date Deposited:	30 Dec 2025 08:24
URI:	http://fulir.irb.hr/id/eprint/10689
DOI:	10.1140/epjp/s13360-025-06312-1

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