Remarks on a gauge theory for continuous spin particles

Victor O. Rivelles

doi:10.1140/epjc/s10052-017-4927-1

EPJ

a
b
c
d
e
ap
st
h
plus
ds
pv
ti
qt
am
n

2023 Impact factor 4.2

Particles and Fields

Open Access

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

Victor O. Rivelles^*

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 ${x^\mu }$ 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 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.