On the quantization of continuous non-ultralocal integrable systems

TL;DR

This paper presents a method for quantizing continuous non-ultralocal integrable systems, exemplified by the Alday-Arutyunov-Frolov model, using distributional fields and regularization to handle singularities.

Contribution

It introduces a regularization approach that avoids singularities in the quantization of non-ultralocal models and recovers classical Maillet's prescription in the classical limit.

Findings

Regularization allows consistent quantization of non-ultralocal models.

Quantum Hamiltonian and conserved charges derived from regularized trace identities.

Method aligns with perturbative calculations and classical prescriptions.

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.