Remarks on a gauge theory for continuous spin particles

Abstract

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 $${x^\mu }$$ x μ and on a covector $$\eta _\mu $$ η μ . We discuss how fields can be expanded in $$\eta _\mu $$ η μ 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 $$\eta $$ η -hyperboloid $$\eta ^2+1=0$$ η 2 + 1 = 0 and we show how it restricts the dynamics of the gauge field to the $$\eta $$ η -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.