2024/10/03 by J. Lukierski, Lukierski, Jerzy, Stjepan Meljanac +5 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2410.02339
openalex publication_date 2024/10/03 · openalex created_date 2024/11/08 · openalex updated_date 2026/07/28
We propose new noncommutative models of quantum phase spaces, containing a pair of κ-deformed Poincaré algebras, with two independent double (κ,κ)-deformations in space-time and four-momenta sectors. The first such quantum phase space can be obtained by contractions M,R→ ∞ of recently introduced doubly κ-deformed (κ,κ)-Yang models, with the parameters M,R describing inverse space-time and four-momenta curvatures and constant four-vectors aμ, bμ determining nine types of (κ,κ)-deformations. The second considered model is provided by the nonlinear doubly κ-deformed TSR algebra spanned by 14 coset o(1,5)/ o(2) generators. The basic algebraic difference between the two models is the following: the first one, described by o(1,5) Lie algebra can be supplemented by the Hopf algebra structure, while the second model contains the quantum phase space commutators [xμ,qν], with the standard numerical iℏημν term; therefore it describes the quantum-deformed Heisenberg algebra relations which cannot be equipped with the Hopf algebra.