Spinning particles and higher spin field equations

TL;DR

This paper reviews worldline actions for relativistic particles with higher spins, showing how they lead to higher spin field equations and discussing extensions to reducible representations, massive particles, and (A)dS spaces.

Contribution

It introduces a unified worldline framework for describing higher spin fields, including reducible representations and connections to Vasiliev's theory.

Findings

Derivation of higher spin field equations from worldline actions.

Extension to reducible representations carrying multiple spins.

Discussion of massive particles and (A)dS space propagation.

Abstract

Relativistic particles with higher spin can be described in first quantization using actions with local supersymmetry on the worldline. First, we present a brief review of these actions and their use in first quantization. In a Dirac quantization scheme the field equations emerge as Dirac constraints on the Hilbert space, and we outline how they lead to the description of higher spin fields in terms of the more standard Fronsdal-Labastida equations. Then, we describe how these actions can be extended so that the propagating particle is allowed to take different values of the spin, i.e. carry a reducible representation of the Poincar\'e group. This way one may identify a four dimensional model that carries the same degrees of freedom of the minimal Vasiliev's interacting higher spin field theory. Extensions to massive particles and to propagation on (A)dS spaces are also briefly commented upon.