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Classical and Quantum Nambu Mechanics
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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.
Forward citations
Cited by 3 Pith papers
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Towards Quantizing Null p-branes: Light-Cone Gauge Analysis and Physical Hilbert Space
Quantized null p-branes in light-cone gauge have physical Hilbert spaces split into p+1 classes of standing-wave states.
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Dynamics of the Density Cube
Derives an equation of motion for the density cube from ternary Nambu quantization, yielding oscillation between pairs of triple-path interferences.
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Nambu variant of Local Resolution of Problem of Time and Background Independence
The paper extends a local resolution of the Problem of Time to Nambu n-ary bracket formalism, introducing Nambu-Dirac and Nambu algorithms and a claimed uniqueness theorem for Nambu observables.
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