Noncommutative CPN and CHN and their physics

6th International Workshop DICE2012 Spacetime – Matter – Quantum Mechanics: From the Planck Scale to Emergent Phenomena

物理学;力学

Sako, Akifumi^1 ; Suzuki, Toshiya^1 ; Umetsu, Hiroshi^1

Kushiro National College of Technology, Otanoshike-Nishi 2-32-1, Kushiro 084-0916, Japan^1

关键词: Fock representation;    Gamma function;    Non-commutative;    Separation of variables;    Star products;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/442/1/012052/pdf
DOI  :  10.1088/1742-6596/442/1/012052

学科分类：力学，机械学

来源: IOP

【 摘 要 】

We study noncommutative deformation of manifolds by constructing star products. We start from a noncommutativedand discuss more genaral noncommutative manifolds. In general, star products can not be described in concrete expressions without some exceptions. In this article we introduce new examples of noncommutative manifolds with explicit star products. Karabegov's deformation quantization of PNand HNwith separation of variables gives explicit calulable star products represented by gamma functions. Using the results of star products between inhomogeneous coordinates, we find creation and anihilation operators and obtain the Fock representation of the noncommutative PNand HN.