Canonical Nambu mechanics: relevance to string/M-theory and approaches to quantization
Abstract
We review some aspects of Nambu mechanics on the basis of the works previously published separately by the present author. Main focuses are on three themes, its various symmetry structures, their possible relevance to string/M theory, and a Hamilton-Jacobi like reformulation. We try to elucidate the basic ideas, most of which were rooted in more or less the same ground, and to explain motivations behind these works from a unified and vantage viewpoint. Various unsolved questions are mentioned. We also include some historical account on the genesis of the Nambu mechanics, and discuss (in the Appendix) some parallelism of various ideas behind the Nambu's paper with Dirac's old works which are related to the description of vortical flows in terms of gauge potentials.
Cite
@article{arxiv.2103.12918,
title = {Canonical Nambu mechanics: relevance to string/M-theory and approaches to quantization},
author = {Tamiaki Yoneya},
journal= {arXiv preprint arXiv:2103.12918},
year = {2021}
}
Comments
Written version of an invited talk in the workshop "Space-time topology behind formation of micro-macro magneto-vortical structure by Nambu mechanics", Osaka City University, Sept. 28--Oct.1, 2020, corrected typos, added sentences, and added references, version to be published in a special section of the journal PTEP