Construction and exact solution of a nonlinear quantum field model in quasi-higher dimension

TL;DR

This paper introduces a novel quantum nonlinear Schrödinger model in quasi-two dimensions, utilizing an innovative Lax matrix approach and revealing exact solutions and rich scattering properties, expanding the scope of integrable quantum field theories.

Contribution

It develops a new Lax matrix method for quasi-higher-dimensional quantum integrable models, providing exact solutions and demonstrating the model's integrability and complex scattering behavior.

Findings

Exact Bethe ansatz solution obtained

Discovery of a unique field commutator confirming integrability

Rich scattering and bound-state properties revealed

Abstract

Nonperturbative exact solutions are allowed for quantum integrable models in one space-dimension. Going beyond this class we propose an alternative Lax matrix approach, exploiting the hidden multi-time concept in integrable systems and construct a novel quantum nonlinear Schroedinger model in quasi-two dimensions. An intriguing field commutator is discovered, confirming the integrability of the model and yielding its exact Bethe ansatz solution with rich scattering and bound-state properties. The universality of the scheme is expected to cover diverse models, opening up a new direction in the field.