Inconsistency of the interactions between pseudoscalar, spinor and Rarita-Schwinger fields

TL;DR

This paper investigates the inconsistencies in the Dirac quantization of Rarita-Schwinger fields interacting with spinors and pseudoscalar fields, revealing persistent issues even in gauge-invariant interactions, impacting particle phenomenology.

Contribution

It provides a detailed analysis showing that both conventional and gauge-invariant interactions of Rarita-Schwinger fields exhibit inconsistencies under Dirac quantization.

Findings

Conventional pseudoscalar-spinor-Rarita-Schwinger interactions are inconsistent.

Gauge-invariant interactions also lead to inconsistencies.

Results have implications for interpreting experimental data involving Delta(1232) resonances.

Abstract

We perform the Dirac quantization of RS fields interacting with a spinor and the first derivative of a pseudoscalar field. We achieve the calculations for two forms of this interaction: first we review the conventional coupling of lowest derivative order, reproducing the well known inconsistencies in its anticommutator algebra. Then, we perform the analysis on the next order term popularly known as spin 3/2 gauge invariant interaction, which is claimed to be free of these inconsistencies. Nevertheless we find that the direct application of the Dirac formalism leads to inconsistencies in complete analogy to the previous case. This is of high relevance in the particle phenomenology field, where these interactions are used to interpret experimental data involving Delta(1232) resonances.