LATTICE APPROACH TO INTEGRABLE QUANTUM FIELD THEORIES AND APPLICATIONS

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We consider conformal quantum field theories and integrable massive quantum field theories starting from their lattice regularizations provided by the six-vertex model. In previous work we have completely clarified the structure of the correlation functions of this model. We could explain their factorization that was observed before, by means of a hidden Fermionic structure on the space of (quasi-) local operators. In this project we will study different scaling limits of the Fermionic structure. For conformal field theories we want to show that the scaling limit of this structure induces a basis on the Verma moduls. We plan to study the operator product expansion in this new basis. We expect that the recursion relation for the conformal blocks will simplify in this basis. To achieve our goal we will have to generalize the factorization theorem for the six-vertex-model of Jimbo, Miwa and Smirnov from correlation functions to form factors. If this is successful we will have a new and direct access to the correlation functions of the Sine-Gordon model.