Remarks on a Gauge Theory for Continuous Spin Particles

Victor O. Rivelles

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

paper

Remarks on a Gauge Theory for Continuous Spin Particles

arXiv:1607.01316 · doi:10.1140/epjc/s10052-017-4927-1

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 $x^{μ}$ and on a covector $η_{μ}$ . We discuss how fields can be expanded in $η_{μ}$ 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 $η$ -hyperboloid $η^{2} + 1 = 0$ and we show how it restricts the dynamics of the gauge field to the $η$ -hyperboloid. 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 make some comments about the coupling to gravity.

21 pages, typos corrected, improved presentation of section VI, final version

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Current Interactions and Holography from the 0-Form Sector of Nonlinear Higher-Spin Equations

Remarks on a Gauge Theory for Continuous Spin Particles

Abstract

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