Retraction of "Half-integer spin representations of the graded extension of so(2,1) Lie algebra: Spin 3/2 particle in the Dirac-Oscillator potential"

TL;DR

This paper retracts a previous claim that a certain superalgebra representation described a spin 3/2 particle in the Dirac-Oscillator potential, clarifying that the representation is fully reducible and does not correspond to such a particle.

Contribution

The authors clarify that the previously claimed representation does not describe a spin 3/2 particle, correcting the earlier misconception about the superalgebra's physical interpretation.

Findings

The superalgebra representation is fully reducible.

It is composed of two spin 1/2 representations.

It does not represent a spin 3/2 particle.

Abstract

The representation of the superalgebra SO(2,1) which is given by Eq. (3.1) and which resulted in the relativistic wave equation (4.1) is fully reducible. In fact, its even part is the direct sum of two spin 1/2 representations of the Lorentz group and does not represent spin 3/2 particle as we claimed. Consequently, we retract our claim and withdraw the manuscript.