On the quantization of continuous non-ultralocal integrable systems

Abstract

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.

33 pages, extended version of arXiv:1505.01516

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• The Lax pair for the fermionic Bazhanov-Stroganov $R$-operator
• Exceptional solutions to the eight-vertex model and integrability of anisotropic extensions of massive fermionic models
• The tetrahedral Zamolodchikov algebra for the fermionic Bazhanov-Stroganov R-operator
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