Notes on scaling limits in SOS models, local operators and form factors

Scaling limits of the SOS and RSOS models in the regime~III are considered. These scaling limits are believed to be described by the sine-Gordon model and the restricted sine-Gordon models (or perturbed minimal conformal models) respectively. We study two different scaling limits and establish the correspondence of the scaling local height operators to exponential or primary fields in quantum field theory. An integral representation for form factors is obtained in this way. In the case of the sine-Gordon model this reproduces Lukyanov's well known representation. The relation between vacuum expectation values of local operators in the sine-Gordon model and perturbed minimal models is also discussed.