Polynomial Algebras and their Applications

TL;DR

This paper introduces a classification method for three-dimensional polynomially deformed algebras, presents their irreducible representations, and discusses applications in quantum mechanics, including supersymmetric systems.

Contribution

It provides a systematic construction and classification of quadratic and cubic polynomial algebras and explores their applications in quantum mechanics.

Findings

Four quadratic algebra classes identified

Twelve cubic algebra classes constructed

Applications to supersymmetric quantum mechanics discussed

Abstract

A way to construct and classify the three dimensional polynomially deformed algebras is given and the irreducible representations is presented. for the quadratic algebras 4 different algebras are obtained and for cubic algebras 12 different classes are constructed. Applications to quantum mechanical systems including supersymmetric quantum mechanics are discussed