Quantum Inverse Scattering Method and scalar products of Bethe vectors

I will talk about a new method for calculating scalar products in the framework of the quantum method of the inverse problem. We consider scalar products in which one of the vectors is an eigenvector of the transfer matrix (on-shell vector of Bethe). Such scalar products play a key role in the calculation of correlation functions. The new method is based on the formula of the transfer matrix action on Bethe vectors. This formula allows us to obtain a system of linear equations, the solutions of which are the scalar products mentioned above.