On the supersymmetry of the Klein-Gordon oscillator

TL;DR

This paper demonstrates that the three-dimensional Klein-Gordon oscillator possesses an unbroken supersymmetric algebraic structure, which helps derive its spectral properties and Green's function, linking it to the non-relativistic harmonic oscillator.

Contribution

It reveals the supersymmetric structure of the Klein-Gordon oscillator and uses it to analytically determine its spectral properties and Green's function.

Findings

Supersymmetry is unbroken with a vanishing Witten index.

Spectral properties are derived analytically.

Green's function has a closed-form expression.

Abstract

The three-dimensional Klein-Gordon oscillator is shown to exhibit an algebraic structure known from supersymmetric quantum mechanics. The supersymmetry is found to be unbroken with a vanishing Witten index, and it is utilized to derive the spectral properties of the Klein-Gordon oscillator, which is closely related to that of the non-relativistic harmonic oscillator in three dimensions. Supersymmetry also enables us to derive a closed-form expression for the energy-dependent Green's function.