Quantum inverse scattering method

Summary

The quantum inverse scattering method is an algebraic framework for quantum integrable models in one space dimension. The Leningrad school of Faddeev developed it in the late 1970s. It builds a family of commuting operators, the transfer matrices, from a solution of the Yang–Baxter equation. The Hamiltonian is one member of this family. The eigenvectors are created by matrix entries of the monodromy matrix; this is the algebraic form of the Bethe ansatz. It is the quantum version of the classical inverse scattering transform and led to the theory of quantum groups.