2003/03/31 by Hamanaka, Masashi
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.hep-th/0303256
This thesis is designed for a comprehensive review of noncommutative (BPS) solitons with applications to D-brane dynamics including our works. We focus on noncommutative instantons and monopoles and study various aspects of the exact solutions by using Atiyah-Drinfeld-Hitchin-Manin (ADHM) and Nahm constructions. Finally we propose noncommutative extensions of integrable systems and soliton theories in lower dimensions in collaboration with Kouichi Toda, which would pioneer a new study area of integrable systems. Appendix is devoted to a brief and systematic review of formal aspects of ADHM/Nahm construction and Nahm transformation on commutative spaces. This article is also a step to a comprehensive review of ADHM/Nahm construction on both commutative and noncommutative spaces. Comments are welcome.