Classical and Quantum Nambu Mechanics

2002/12/31 by Thomas Curtright, Cosmas Zachos · 1 voice · 17 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Noncommutative and Quantum Gravity Theories #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1103/physrevd.68.085001

published as Phys.Rev.D68:085001,2003 · 44 pages, 1 figure, 1 table Minor changes to conform to journal version

arxiv created 2003/05/22 · openalex publication_date 2003/10/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The classical and quantum features of Nambu mechanics are analyzed and fundamental issues are resolved. The classical theory is reviewed and developed utilizing varied examples. The quantum theory is discussed in a parallel presentation, and illustrated with detailed specific cases. Quantization is carried out with standard Hilbert space methods. With the proper physical interpretation, obtained by allowing for different time scales on different invariant sectors of a theory, the resulting non-Abelian approach to quantum Nambu mechanics is shown to be fully consistent.

Citations

• M-theory and Deformation Quantization

Cited by

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• 𝒩 = 8 superconformal Chern-Simons theories
• A new approach to deformation equations of noncommutative KP hierarchies
• w∞3-algebra
• Necessary conditions for ternary algebras
• Topics on n-ary algebras
• Unexpected features of supersymmetry with central charges
• A N = 8 action for multiple M2-branes with an arbitrary number of colors
• Hidden quartic symmetry inN= 2 supersymmetry
• Quantized Nambu–Poisson manifolds and n-Lie algebras
• The partially alternating ternary sum in an associative dialgebra
• Remarks on the formulation of quantum mechanics on noncommutative phase spaces
• Laplace–Runge–Lenz vector [wikipedia]
• Nambu mechanics [wikipedia]

Discussions

• Landau & Lifdhitz Mechanics should have standard answers to all your (essentials standard) questions. It's the big picture of mechanics as motions (trajectories) in phase space. If you know mechanics, [stackexchange, 1 points]

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