A non-symmetric Yang-Baxter algebra for the quantum nonlinear Schr\"odinger model (PhD Thesis)

TL;DR

This thesis develops a non-symmetric Yang-Baxter algebra framework for the quantum nonlinear Schrödinger model, extending the algebraic structures and wavefunction representations beyond symmetric cases.

Contribution

It introduces a non-symmetric wavefunction construction and generalizes Yang-Baxter relations within the quantum nonlinear Schrödinger model context.

Findings

Non-symmetric wavefunctions linked to the QNLS model are constructed.

Generalized Yang-Baxter commutation relations for non-symmetric cases.

Vertex operator formalism is adapted for non-symmetric wavefunction generation.

Abstract

We study certain non-symmetric wavefunctions associated to the quantum nonlinear Schr\"odinger (QNLS) model, introduced by Komori and Hikami using representations of the degenerate affine Hecke algebra. In particular, they can be generated using a vertex operator formalism analogous to the recursion that defines the symmetric QNLS wavefunction in the quantum inverse scattering method. Furthermore, some of the commutation relations encoded in the Yang-Baxter equation are generalized to the non-symmetric case.