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Quantum Twist-Deformed D=4 Phase Spaces with Spin Sector and Hopf Algebroid Structures

Lukierski, Jerzy; Meljanac, Stjepan; Woronowicz, Mariusz (2019) Quantum Twist-Deformed D=4 Phase Spaces with Spin Sector and Hopf Algebroid Structures. Physics Letters B, 789 . pp. 82-87. ISSN 0370-2693

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Abstract

We consider the generalized (10+10) -dimensional D=4 quantum phase spaces containing translational and Lorentz spin sectors associated with the dual pair of twist-quantized Poincare Hopf algebra H and quantum Poincare Hopf group Gˆ . Two Hopf algebroid structures of generalized phase spaces with spin sector will be investigated: first one H(10, 10) describing dynamics on quantum group algebra Gˆ provides by the Heisenberg double algebra HD=H⋊Gˆ , and second, denoted by H˜(10, 10) , describing twisted Hopf algebroid with base space containing twisted noncommutative Minkowski space xˆμ . We obtain the first explicit example of Hopf algebroid structure of relativistic quantum phase space which contains quantum-deformed Lorentz spin sector.

Item Type: Article
Uncontrolled Keywords: Noncommutative geometry ; phase space ; deformation: twist ; Hopf algebroid
Subjects: NATURAL SCIENCES > Physics
Divisions: Theoretical Physics Division
Depositing User: Stjepan Meljanac
Date Deposited: 10 Sep 2019 15:46
Last Modified: 10 Sep 2019 15:47
URI: http://fulir.irb.hr/id/eprint/5002
DOI: 10.1016/j.physletb.2018.11.055

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