Higher charges and regularized quantum trace identities in su(1,1) Landau-Lifshitz model

TL;DR

This paper develops a method to solve the operator ordering problem in the quantum su(1,1) Landau-Lifshitz model, enabling the derivation of quantum trace identities and spectra of higher-order charges without discretization.

Contribution

It introduces an operator regularization and renormalization approach that preserves quantum integrability and constructs self-adjoint extensions, offering an alternative to discretization methods.

Findings

Successfully solves the operator ordering problem.

Provides a prescription for quantum trace identities.

Derives spectra for higher-order local charges.

Abstract

We solve the operator ordering problem for the quantum continuous integrable su(1,1) Landau-Lifshitz model, and give a prescription to obtain the quantum trace identities, and the spectrum for the higher-order local charges. We also show that this method, based on operator regularization and renormalization, which guarantees quantum integrability, as well as the construction of self-adjoint extensions, can be used as an alternative to the discretization procedure, and unlike the latter, is based only on integrable representations.