Classical Integrable Systems and Gauge Theory
Mathematical Physics
2019-01-01 v1 High Energy Physics - Theory
math.MP
Exactly Solvable and Integrable Systems
Abstract
This is an introductory survey written in Japanese on classical integrability from the viewpoint of symmetry reduction of 4-dimensional anti-self-dual Yang-Mills equations. Twistor construction methods are discussed in detail in 4-dimension. Exact local solutions are, in this article, presented in terms of quasideterminants in a compact form. Some integrable aspects in lower-dimension are clarified in the context of the reduction. Noncommutative extension and higher-dimensional extension are briefly discussed.
Cite
@article{arxiv.1712.10228,
title = {Classical Integrable Systems and Gauge Theory},
author = {Masashi Hamanaka},
journal= {arXiv preprint arXiv:1712.10228},
year = {2019}
}
Comments
14 pages; Introductory survey in Japanese, published on November 2017 in a Japanese magazine of mathematical science: Suurikagaku Vol.55-11 (No.653), 49-55