Infinite-dimensional algebras, multibody systems and gauge theories. (English) Zbl 1056.37510
Morozov, A. Yu. (ed.) et al., Moscow Seminar in mathematical physics. Providence, RI: American Mathematical Society (ISBN 0-8218-1388-9/hbk). Transl., Ser. 2, Am. Math. Soc. 191(43), 263-299 (1999).
Summary: In this survey, we present several constructions of Hamiltonian reductions, leading to integrable multibody systems. The original phase spaces are naturally constructed with the help of infinite-dimensional current algebras. Along these lines, we construct integrable systems of Calogero type, and their relativistic and spin generalizations. The degenerations of Hitchin systems are particular cases of these systems. We discuss various dualities relating integrable systems and show that these dualities are easily obtained in the framework of Hamiltonian reductions. We also discuss the applications to solutions of gauge theories in various dimensions.
For the entire collection see [Zbl 0914.00023].
For the entire collection see [Zbl 0914.00023].
MSC:
| 37K30 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures |
| 17B80 | Applications of Lie algebras and superalgebras to integrable systems |
| 37K05 | Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010) |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81V70 | Many-body theory; quantum Hall effect |
