Supersymmetry in the Half-Oscillator - Revisited

TL;DR

This paper re-examines the supersymmetry properties of the half-oscillator, concluding that supersymmetry is broken due to the absence of a zero-energy ground state when restricted to the positive domain.

Contribution

It provides a detailed analysis challenging previous claims, showing that the spectrum does not support unbroken supersymmetry in the half-oscillator case.

Findings

No zero-energy ground state in the spectrum.

Supersymmetry is broken in the half-oscillator.

Contradicts previous studies claiming unbroken supersymmetry.

Abstract

Following a recent study by Das and Pernice [Nucl. Phys. B561, (1999) 357], we have carefully analyzed the half-harmonic oscillator. In contrast to their observations, our analysis reveals that the spectrum does not allow for a zero energy ground state and hence the supersymmetry is broken when the domain is restricted to the positive half of the real axis.