A Gauge Field Theory of Continuous-Spin Particles

TL;DR

This paper introduces the first local, covariant gauge-field action for continuous-spin particles, unifying helicity and continuous-spin degrees of freedom in a consistent quantum framework across dimensions.

Contribution

It presents the first field-theory action for continuous spin particles, extending to any number of dimensions and providing a new local description of particles with arbitrary spin.

Findings

First consistent quantum field theory for continuous spin particles.

Unifies helicity and continuous-spin descriptions in a covariant gauge framework.

Enables gauge-invariant interactions with background currents.

Abstract

We propose and quantize a local, covariant gauge-field action that unifies the description of all free helicity and continuous-spin degrees of freedom in a simple manner. This is the first field-theory action of any kind for continuous spin particles; it is consistent as a quantum theory and generalizes to any number of dimensions. The fields live on the null cone of an internal four-vector "spin-space"; in D dimensions a linearized gauge invariance reduces their physical content to a single function on a Euclidean (D-2)-plane, on which the little group E(D-2) acts naturally. A projective version of the action further reduces the physical content to S^{D-3}, enabling a new local description of particles with any spin structure, and in particular a tower of all integer-helicity particles for D=4. Gauge-invariant interactions with a background current are added in a straightforward manner.