Continuous-spin field propagator and interaction with matter

TL;DR

This paper develops a formalism for continuous-spin fields, deriving their actions from fundamental equations, introduces a matter coupling current, and analyzes the particle's propagator and degrees of freedom in interactions.

Contribution

It provides a method to derive continuous-spin field actions from equations and explores their interaction with matter and propagator properties.

Findings

Derived continuous-spin actions from Fronsdal-like equations.

Introduced a matter coupling current for continuous-spin fields.

Analyzed the propagator and degrees of freedom in interactions.

Abstract

Action principles for the single and double valued continuous-spin representations of the Poincare group have been recently proposed in a Segal-like formulation. We address three related issues: First, we explain how to obtain these actions directly from the Fronsdal-like and Fang-Fronsdal-like equations by solving the traceless constraints in Fourier space. Second, we introduce a current, similar to the one of Berends, Burgers and Van Dam, which is bilinear in a pair of scalar matter fields, to which the bosonic continuous-spin field can couple minimally. Third, we investigate the current exchange mediated by a continuous-spin particle obtained from this action principle and investigate whether it propagates the right degrees of freedom, and whether it reproduces the known result for massless higher-spin fields in the helicity limit.