Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-03-31
Physics
High Energy Physics
High Energy Physics - Theory
117 pages, 22 figures, LaTeX; This is based on my Ph.D thesis
Scientific paper
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.
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