Diagonal form factors in Landau-Lifshitz models

Abstract We perturbatively study form factors in the Landau-Lifshitz model and the generalisation originating in the study of the N $$ \mathcal{N} $$ = 4 super-Yang-Mills dilatation generator. In particular we study diagonal form factors which have previously been related to gauge theory structure constants. For the Landau-Lifshitz model, due to the non-relativistic nature of the theory, we are able to compute all orders in perturbation theory and to resum the series to find quantum form factors for low numbers of external particles. We apply our form factors to the study of deformations of the integrable theory by means of form factor perturbation theory. As a check of our method we compute spin-chain S-matrix elements for the Leigh-Strassler family of marginal deformations to leading order in the deformation parameters