Quantum inverse scattering method and algebraized matrix Bethe-Ansatz

Within the framework of the quantum inverse scattering method, an algebraic formalism is proposed for finding the eigenvectors and eigenvalues of the trace of the monodromy matrices of systems with internal degrees of freedom, i.e., a matrix Bethe-Ansatz. The results obtained are a generalization of the Gaudin-Yang method for multicomponent systems. The paper gives applications of the formalism developed, in particular, to the theory of exactly solvable models of quantum field theory with asymptotic freedom in two-dimensional space-time.