Integrable Quantum Field Theories

Abstract

Abstract An integrable quantum field theory is characterized by an infinite number of conserved charges. In classical mechanics, the existence of a sufficient number of integrals of motion allows us to pass from the initial coordinates and momenta to the angle-action variables, thus finding the exact solution of the equation of motion by quadrature. Similarly, if in a quantum field theory there are an infinite number of conservation laws, we can derive the exact mass spectrum of its excitations, the S-matrix of the scattering processes, the correlation functions, the thermodynamics, and so on, in short its exact solution. For reasons that will become clearer later, non-trivial integrable quantum field theories can only occur in (1 + 1) dimensions.1 In higher dimensions, in fact, they are either free theories or models with non-local interactions. Hence we focus our attention only on two-dimensional models.