Thomas L Curtright and Cosmas K Zachos 2002 New J. Phys. 4 83 doi:10.1088/1367-2630/4/1/383
Deformation quantization of superintegrable systems and Nambu mechanics
Thomas L Curtright1 and Cosmas K Zachos2
Show affiliationsPhase 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 σ-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.
- PACS
- MSC
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58D19 Group actions and symmetry properties
53D55 Deformation quantization, star products
81S10 Geometry and quantization, symplectic methods (See also 53D50)
- Subjects
- Dates
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Issue 1 (October 2002)
Received 23 August 2002
Published 29 October 2002
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Deformation quantization of superintegrable systems and Nambu mechanics
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