English

Noncommutative Solitons and Integrable Systems

High Energy Physics - Theory 2007-05-23 v3 Mathematical Physics math.MP Exactly Solvable and Integrable Systems

Abstract

We review recent developments of soliton theories and integrable systems on noncommutative spaces. The former part is a brief review of noncommutative gauge theories focusing on ADHM construction of noncommutative instantons. The latter part is a report on recent results of existence of infinite conserved quantities and exact multi-soliton solutions for noncommutative Gelfand-Dickey hierarchies. Some examples of noncommutative Ward's conjecture are also presented. Finally, we discuss future directions on noncommutative Sato's theories, twistor theories and so on.

Keywords

Cite

@article{arxiv.hep-th/0504001,
  title  = {Noncommutative Solitons and Integrable Systems},
  author = {Masashi Hamanaka},
  journal= {arXiv preprint arXiv:hep-th/0504001},
  year   = {2007}
}

Comments

27 pages, LaTeX, 3 figures, v3: references added, to appear in proceedings of the COE workshop on Noncommutative Geometry and Physics, Keio, February 26 - March 3, 2004