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

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.

Noncommutative geometry ; phase space ; deformation: twist ; Hopf algebroid

PolishNationalScienceCenter, project2017/27/B