Deformation quantization of superintegrable systems and Nambu mechanics

Thomas L. Curtright, Cosmas K. Zachos

Research output: Contribution to journalArticle

25 Scopus citations

Abstract

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 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.

Original languageEnglish (US)
Pages (from-to)83.1-83.16
JournalNew Journal of Physics
Volume4
DOIs
StatePublished - Oct 29 2002

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

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