On the quantization of continuous non-ultralocal integrable systems

We discuss the quantization of non-ultralocal integrable models directly in the continuous case, using the example of the Alday-Arutyunov-Frolov model. We show that by treating fields as distributions and regularizing the operator product, it is possible to avoid all the singularities, and allow to obtain results consistent with perturbative calculations. We illustrate these results by considering the reduction to the massive free fermion model and extracting the quantum Hamiltonian as well as other conserved charges directly from the regularized trace identities. Moreover, we show that our regularization recovers Maillet's prescription in the classical limit.