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.
Keywords
Cite
@article{arxiv.1612.08509,
title = {Generalized Hamilton-Jacobi theory of Nambu Mechanics},
author = {Tamiaki Yoneya},
journal= {arXiv preprint arXiv:1612.08509},
year = {2019}
}
Comments
43 pages, the version to be published in Progress of Theoretical and Experimental Physics, minor corrections of spellings, wordings and typos