Generalized Hamilton-Jacobi theory of Nambu Mechanics

Abstract

We develop a Hamilton-Jacobi-like formulation of Nambu mechanics. The Nambu mechanics, originally proposed by Nambu more than four decades ago, provides a remarkable extension of the standard Hamilton equations of motion in even dimensional phase space with a single Hamiltonian to a phase space of three (and more generally, arbitrary) dimensions with two Hamiltonians (n Hamiltonians in the case of (n+1)-dimensional phase space) from the viewpoint of the Liouville theorem. However, it has not been formulated seriously in the spirit of Hamilton-Jacobi theory. The present study is motivated to suggest a possible direction towards quantization from a new perspective.

43 pages, the version to be published in Progress of Theoretical and Experimental Physics, minor corrections of spellings, wordings and typos

References in corpus (2)

• Nambu bracket and M-theory
• Nambu Quantum Mechanics on Discrete 3-Tori

Cited by in corpus (4)

• Generalization of Hamiltonian Mechanics to a Three Dimensional Phase Space
• Hidden Nambu mechanics II: Quantum/semiclassical dynamics
• Generalizing Hamiltonian Mechanics with Closed Differential Forms
• A Lorentz Covariant Matrix Model for Bosonic M2-Branes: Nambu Brackets and Restricted Volume-Preserving Deformations