Fuzzy sphere and hyperbolic space from deformation quantization | Zendy

Isao Kishimoto | Zendy

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Fuzzy sphere and hyperbolic space from deformation quantization

Author(s) -

Isao Kishimoto

Publication year - 2001

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2001/03/025

Subject(s) - noncommutative geometry , constant curvature , mathematics , quantization (signal processing) , noncommutative algebraic geometry , noncommutative quantum field theory , symplectic geometry , pure mathematics , fuzzy sphere , curvature , gauge theory , algebra over a field , mathematical physics , mathematical analysis , geometry , algorithm

We explicitly construct noncommutative * products on circularly symmetric twodimensional space by using the technique of Fedosov's deformation quantization.Especially, on constant curvature spaces i.e., S^2 and H^2, we get su(2) andsu(1,1) algebra respectively. These are candidates of * products applicable tononcommutative field theories or noncommutative gauge theories on spaces withnontrivial symplectic structure.Comment: 10pages, references added, typos correcte

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