Massive Fields of Arbitrary Half-Integer Spin in Constant Electromagnetic Field

TL;DR

The paper develops an algebraic, pseudo-Hilbert framework to construct gauge-invariant interactions of massive half-integer higher-spin fields with a constant electromagnetic field, valid to linear order in the field. By deforming a closed operator algebra within an auxiliary Fock space, the authors restore gauge invariance and obtain explicit Lagrangians and gauge transformations for arbitrary half-integer spins, with detailed results worked out for spins $3/2$ and $5/2$ in even dimensions. The approach yields a two-parameter family of linear-order interactions, reproducing a gauge-invariant description whose $3/2$ case is largely gauge-redundant while the $5/2$ case remains nontrivial, and it provides a path toward extensions to non-Abelian backgrounds and curved spacetimes. Open questions include higher-order corrections and causality analyses, but the framework offers a systematic route to consistent electromagnetic couplings of massive higher-spin fields and potential applications to propagation in Riemann spaces.

Abstract

We study the interaction of gauge fields of arbitrary half-integer spins with the homogeneous electromagnetic field. We reduce the problem of obtaining the gauge-invariant Lagrangian and transformations of the half-integer spin fields in the external field to an algebraic problem of search for a set of operators with certain algebraical features using the representation of the higher-spin fields as vectors in a pseudo-Hilbert space. We consider such construction at linear order in the external electromagnetic field and also present an explicit form of interaction Lagrangians and gauge transformations for the massive particles of spins 3/2 and 5/2 in terms of symmetric spin-tensor fields. The obtained result is valid for space-time of arbitrary even dimension.