  We consider a gauge theory action for continuous spin particles formulated in
a spacetime enlarged by an extra coordinate recently proposed by Schuster and
Toro. It requires one scalar gauge field and has two local symmetries. We show
that the local symmetries are reducible in the sense that the parameters also
have a local symmetry. Using reducibility we get an action which has two scalar
gauge fields and a reducible but simpler local symmetry. We then show how this
action and equations of motion are related to previously proposed formulations
for continuous spin particles and higher spin theories. We also discuss the
physical contents of each formulation to reveal the physical degrees of
freedom.
