Classical and Quantum Nambu Mechanics

TL;DR

This paper reviews and develops classical and quantum Nambu mechanics, resolving fundamental issues and demonstrating a consistent non-Abelian quantum approach through examples and standard quantization methods.

Contribution

It provides a comprehensive analysis and resolution of core issues in classical and quantum Nambu mechanics, introducing a consistent non-Abelian quantum framework.

Findings

Quantum Nambu mechanics is consistent with proper interpretation.

Classical Nambu mechanics is developed with varied examples.

Quantization uses standard Hilbert space methods.

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.