Deformation Quantization of Superintegrable Systems and Nambu Mechanics

Details Deformation Quantization of Superintegrable Systems and Nambu Mechanics Deformation Quantization of Superintegrable Systems and Nambu Mechanics

2002-05-07

arxiv.org/abs/hep-th/0205063v4

New J.Phys.4:83,2002

Physics

High Energy Physics

High Energy Physics - Theory

LateX2e, 18 pages

Scientific paper

10.1088/1367-2630/4/1/383

Phase Space is the framework best suited for quantizing superintegrable systems, naturally preserving the symmetry algebras of the respective hamiltonian invariants. The power and simplicity of the method is fully illustrated through new applications to nonlinear sigma models, specifically for de Sitter N-spheres and Chiral Models, where the symmetric quantum hamiltonians amount to compact and elegant expressions. Additional power and elegance is provided by the use of Nambu Brackets to incorporate the extra invariants of superintegrable models. Some new classical results are given for these brackets, and their quantization is successfully compared to that of Moyal, validating Nambu's original proposal.

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