The continuous spin limit of higher spin field equations

TL;DR

This paper demonstrates how continuous spin representations emerge as a limit of massive higher-spin equations, providing a gauge-invariant formulation and extending to higher dimensions with arbitrary little group representations.

Contribution

It introduces a novel limiting procedure connecting massive higher-spin equations to continuous spin representations, including a gauge-invariant reformulation and higher-dimensional generalizations.

Findings

Wigner equations derived as a limit of massive higher-spin equations

Gauge-invariant Fronsdal-like form obtained for continuous spin

Extension to higher dimensions with arbitrary little group representations

Abstract

We show that the Wigner equations describing the continuous spin representations can be obtained as a limit of massive higher-spin field equations. The limit involves a suitable scaling of the wave function, the mass going to zero and the spin to infinity with their product being fixed. The result allows to transform the Wigner equations to a gauge invariant Fronsdal-like form. We also give the generalisation of the Wigner equations to higher dimensions with fields belonging to arbitrary representations of the massless little group.