Finite temperature correlation functions in integrable models: derivation of the semiclassical limit from the formfactor expansion

We propose an approach to the problem of finite temperature dynamical correlation functions in integrable one-dimensional models with a spectral gap. The approach is based on the analysis of the singularities of the operator matrix elements and is not model specific. For the long time, large distance asymptotics of the correlation functions we obtain a formula which, as a particular case, contains the expression for the dynamical susceptibility of Quantum Ising model suggested by Sachdev and Young, Phys. Rev. Lett. {\bf 78}, 2220 (1997).