Quantum inverse scattering method

Quantum spin chains are examples of one-dimensional quantum integrable models where the algebraic framework responsible for integrability also provides a viable approach for an exact computation of its correlation functions and form factors. Quantum inverse scattering method first introduced by Faddeev, Sklyanin and Taktajan is a prime example of this technique that has led to, at first the determinant representations for correlation functions and form factors of the Heisenberg's isotropic and anisotropic XXZ quantum spin chains, while their asymptotic analysis has further given exact results in thermodynamic limit in more specific cases. In this talk I will introduce the quantum inverse scattering method and discuss some of the results obtained using it. I will also try to present the challenges facing us in extending this approach to compute correlation or form factors in fully anisotropic XYZ quantum spin chain.