Classical and quantum Nambu mechanics

2003/10/06 by Thomas Curtright, Cosmas Zachos · 1 voice · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Noncommutative and Quantum Gravity Theories

paper · doi:10.1103/physrevd.68.085001

openalex publication_date 2003/10/06 · 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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• Generalized Virasoro algebra: left-symmetry and related algebraic and\n hydrodynamic properties

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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