Correlation functions of integrable lattice models and quantum field theories

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The main objective of this project is the advancement of methods for the exact and efficient calculation of correlation functions of integrable lattice models and quantum field theories . In previous work we have shown that the correlation functions of the spin-1/2 Heisenberg chain and of related integrable models are characterized by a specific structure which we have called factorization: longer-range correlation functions are polynomials in one-point functions and neighbour-correlators, whose coefficients are determined by the underlying infinite-dimensional symmetry algebra. Here we want to show that the correlation functions of other integrable models factorize as well, and we want to extend the notion of factorization to the matrix elements occuring in the spectral representations of correlation functions. For the Heisenberg chain the factorization relied on the existence of a special 'Fermionic' basis of the space of local operators acting on the space of states of the spin chain. In the scaling limit it turns into a basis of the corresponding quantum field theory. Another goal of this project is to study the relation of the Fermionic basis of the field theory with the Verma module basis of the conformal field theory that determines its ultraviolet behaviour.