Correlation functions and the space of local operators in off-critical models and conformal quantum field theories

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Our project has two complementary main objectives, which, at first sight, might look rather unrelated. On the one hand we wish to gain a deeper understanding of the dynamical correlation functions of the XXZ quantum spin chain. For this model we would like to understand the general structure of the dynamical two-point functions of arbitrary local operators which we would like to study by means of efficient and explicit form factor series representations. The latter will allow us to evaluate the correlation functions that are relevant in applications numerically as well as asymptotically. On the other hand, we aim at getting a better understanding of the space of local operators in quantum field theories that can be interpreted as scaling limits of the XXZ model, or rather of the underlying six-vertex model. Technically, our two seemingly different goals are connected by means of the Fermionic basis approach that has been behind much of the progress in the understanding of the correlation functions of integrable lattice models and quantum field theories in the recent past.