On Fractional Supersymmetric Quantum Mechanics: The Fractional Supersymmetric Oscillator

TL;DR

This paper explores fractional supersymmetric quantum mechanics by deriving the Hamiltonian of a fractional supersymmetric oscillator through three different approaches, including decomposition, algebraic generalization, and quantum algebra methods.

Contribution

It introduces a comprehensive derivation of the fractional supersymmetric oscillator Hamiltonian using decomposition, generalized algebra, and quantum algebra techniques.

Findings

Derived Hamiltonian from three different approaches

Connected fractional supersymmetry with generalized Weyl-Heisenberg algebra

Linked the oscillator to quantum algebra Uq(sl(2)) at roots of unity

Abstract

The Hamiltonian for a fractional supersymmetric oscillator is derived from three approaches. The first one is based on a decomposition in which a Q-uon gives rise to an ordinary boson and a k-fermion (a k-fermion being an object interpolating between boson and fermion). The second one starts from a generalized Weyl-Heisenberg algebra. Finally, the third one relies on the quantum algebra Uq(sl(2)) where q is a root of unity.