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

TL;DR

This paper develops a method to construct gauge-invariant Lagrangians for arbitrary half-integer spin fields interacting with a constant electromagnetic field, extending to higher spins and arbitrary even dimensions.

Contribution

It introduces an algebraic approach to derive gauge-invariant interactions for half-integer spins in external fields, including explicit forms for spins 3/2 and 5/2.

Findings

Explicit interaction Lagrangians for spins 3/2 and 5/2

Method applicable to arbitrary even-dimensional spacetimes

Framework reduces to algebraic problem of operator search

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.