We approach the study of non-integrable models of two-dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact S-matrix and Form Factors of the integrable field theories we obtain the first order corrections to the mass ratios, the vacuum energy density and the S-matrix of the non-integrable theories. As interesting applications of the formalism, we study the scaling region of the Ising model in an external magnetic field at T ∼ T c and the scaling region around the minimal model M 2,7 . For these models, a remarkable agreement is observed between the theoretical predictions and the data extracted by a numerical diagonalization of their Hamiltonian.

Using Watson's and the recursive equations satisfied by matrix elements of local operators in two-dimensional integrable models, we compute the form factors of the elementary field φ(x) and the stress-energy tensor T µν (x) of Sinh-Gordon theory. Form factors of operators with higher spin or with different asymptotic behaviour can easily be deduced from them. The value of the correlation functions are saturated by the form factors with lowest number of particle terms. This is illustrated by an application of the form factors of the trace of T µν (x) to the sum rule of the c-theorem.