Transverse Symmetry and Spin-3/2 Fields

TL;DR

This paper explores covariant Lagrangians for spin-3/2 particles, revealing an alternative to the Rarita-Schwinger formulation and analyzing supersymmetry constraints in related fields.

Contribution

It introduces a gamma-traceless Lagrangian for spin-3/2 particles and investigates supersymmetry conditions involving traceless spin-2 fields.

Findings

Both Lagrangians produce identical physical predictions.

No supersymmetric spin-3/2 action exists with traceless spin-2 fields.

Interaction between spin-3/2 and traceless spin-2 fields is possible.

Abstract

We study the possible covariant Lagrangians that describe the propagation of pure spin-3/2 particles. We show that, apart from the well-known Rarita-Schwinger Lagrangian, there is another possibility where the field is described by a gamma-traceless combination and that both Lagrangians yield the same physical predictions for the interaction of conserved sources. We also prove that for the case when the spin-2 field is described by a traceless field, there is no possible spin-3/2 action that makes the system supersymmetric. Nevertheless, the interaction between this field andthe spin-3/2 field may be possible.