nLab quantum inverse scattering method

Idea

The quantum inverse scattering method (QISM) is a method for solving quantum integrable systems?, inspired by the classical inverse scattering method and Bethe Ansatz. It springs from the quantum inverse scattering problem: find the quantum potential from given scattering data.

Quantum groups were discovered within development of QISM, where they play a prominent role.

References

• Wikipedia: Quantum inverse scattering method

A readable monograph is

• Vladimir E. Korepin, N. M. Bogoliubov, A. G. Izergin: Quantum inverse scattering method and correlation functions, Cambridge Monographs on Mathematical Physics, Cambridge University Press (1993) [doi:10.1017/CBO9780511628832, arXiv:cond-mat/9301031]

A monograph emphasising (bi)hamiltonian methods is

• Ludwig D. Faddeev, Leon A. Takhtajan, Hamiltonian methods in the theory of solitons, Springer (2007) [doi:10.1007/978-3-540-69969-9]

The reflection equation is introduced in the case with boundary conditions in:

• I. V. Cherednik: Factorizing particles on a half-line and root systems, Theoretical and Mathematical Physics 61 (1984) 977-983 [doi:10.1007/BF01038545, doi:10.1007/BF01038545]

category: physics