Quasi-exactly solvable models as constrained systems

TL;DR

This paper presents a universal algebraic framework for quasi-exactly solvable models, interpreting them as constrained Hamiltonian systems with finite physical states, exemplified by a Lie algebra su(3) system.

Contribution

It introduces a novel algebraic approach to quasi-exactly solvable models, connecting them to constrained Hamiltonian systems and reproducing known Lie algebraic examples.

Findings

Unified algebraic framework for QES models

Interpretation of QES models as constrained systems

Reproduction of su(3) Lie algebraic QES system

Abstract

We discuss a universal algebraic approach to quasi-exactly solvable models which allows us to interpret them as constrained Hamiltonian systems with a finite number of physical states. Using this approach we reproduce well-known two-dimensional Lie-algebraic quasi-exactly solvable system based on Lie algebra su(3).