2002/05/31 by Thomas Curtright, Thomas L Curtright, Cosmas Zachos +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1367-2630/4/1/383
published as New J.Phys.4:83,2002 · LateX2e, 18 pages
arxiv created 2002/10/09 · openalex publication_date 2002/10/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.