Massive Spin 3/2 Electrodynamics
S. Deser, V. Pascalutsa, A. Waldron
TL;DR
This work constructs a general non-minimally coupled charged massive spin-3/2 model in flat space as an effective theory, enforcing correct degrees of freedom to reduce the naive five-parameter non-minimal sector to a two-parameter family. Using low-energy theorems, the authors connect these parameters to the gyromagnetic ratio $g$ via the relation to the magnetic moment, and they verify the LET structure through soft-photon and Compton amplitudes. They analyze unitarity and causality, showing that while $g=2$ is required by low-energy unitarity for purely electromagnetic processes, tree-level unitarity can fail at high energy for generic $g$, and, crucially, acausal propagation persists for all DOF-consistent non-minimal models in flat space. The paper also discusses higher-spin generalisations and notes that dynamical gravity might cure causality issues in curved space, highlighting the limited but useful role of these models as EFTs for higher-spin interactions and low-energy phenomenology.
Abstract
We study the general non-minimally coupled charged massive spin 3/2 model both for its low energy phenomenological properties and for its unitarity, causality and degrees of freedom behaviour. When the model is viewed as an effective theory, its parameters (after ensuring the correct excitation count) are related to physical characteristics, such as the magnetic moment g factor, by means of low energy theorems. We also provide the corresponding higher spin generalisation. Separately, we consider both low and high energy unitarity, as well as the causality aspects of our models. None (including truncated N=2 supergravity) is free of the minimal model's acausality.