Remarks on a Gauge Theory for Continuous Spin Particles

TL;DR

This paper systematically analyzes a gauge theory for continuous spin particles, clarifying its formulation, constraints, and representation properties, and discusses the challenges of coupling to background fields.

Contribution

It provides a detailed formulation of the gauge theory on a cotangent bundle, explores field expansions, and clarifies the representation and coupling issues for continuous spin particles.

Findings

Field equations restrict dynamics to the η-hyperboloid

On-shell fields carry a single irreducible Poincaré representation

Minimal coupling to background gauge fields is not possible

Abstract

We discuss in a systematic way the gauge theory for a continuous spin particle proposed by Schuster and Toro. We show that it is naturally formulated in a cotangent bundle over Minkowski spacetime where the gauge field depends on the spacetime coordinate ${x^\mu}$ and on a covector $\eta_\mu$. We discuss how fields can be expanded in $\eta_\mu$ in different ways and how these expansions are related to each other. The field equation has a derivative of a Dirac delta function with support on the $\eta$-hyperboloid $\eta^2+1=0$ and we show how it restricts the dynamics of the gauge field to the $\eta$-hyperboloid. We then show that on-shell the field carries one single irreducible unitary representation of the Poincar\'e group for a continuous spin particle. We also show how the field can be used to build a set of covariant equations found by Wigner describing the wave function of one-particle states for a continuous spin particle. Finally we show that it is not possible to couple minimally a continuous spin particle to a background abelian gauge field, and make some comments about the coupling to gravity.