Eur. Phys. J. C (2017) 77: 433
https://doi.org/10.1140/epjc/s10052-017-4927-1

Regular Article - Theoretical Physics

Remarks on a gauge theory for continuous spin particles

Instituto de Física, Universidade de São Paulo, Rua do Matão, 1371, São Paulo, SP, 05508-090, Brazil

^* e-mail: rivelles@fma.if.usp.br

Received: 4 November 2016
Accepted: 17 May 2017
Published online: 29 June 2017

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 and on a covector . We discuss how fields can be expanded in 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 -hyperboloid and we show how it restricts the dynamics of the gauge field to the -hyperboloid and its first neighbourhood. We then show that on-shell the field carries one single irreducible unitary representation of the Poincaré 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 we make some comments about the coupling to gravity.