Retraction of "On a theory of half-integral spin particles with gauge invariant coupling to the electromagnetic potential: Towards higher spin QED"

TL;DR

This paper retracts a previous claim about a relativistic wave equation representing spin 3/2 particles, clarifying that the underlying algebraic representation is reducible and does not support the original assertion.

Contribution

The authors correct their earlier work by demonstrating the reducibility of the superalgebra representation, invalidating their previous claim of describing spin 3/2 particles.

Findings

The superalgebra so(2,1) representation is fully reducible.

The even part of the algebra is a direct sum of two spin 1/2 representations.

The original claim of a spin 3/2 particle description is invalid.

Abstract

The representation of the superalgebra so(2,1) that resulted in the relativistic wave equation (2.1) and Eq. (2.4) is fully reducible. In fact, its even part that lead to Eq. (3.1) 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.