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 Poincaré 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.
Highlights
Relativistic particles with higher spin can be described in first quantization using actions with local supersymmetry on the worldline
Spinning particle actions based on local supersymmetry on the worldline [1, 2] identify amusing systems that exemplify several theoretical constructions and form an arena where to test various methods and ideas
The H, Q, Qconstraints guarantee unitarity, as they can be used to eliminate the negative norm states generated by the variables x0, ψ0, ψ0, while the J constraint guarantees irreducibility of the model, i.e. it describes a particle that carries an irreducible representation of the Poincare group of target space
Summary
Spinning particle actions based on local supersymmetry on the worldline [1, 2] identify amusing systems that exemplify several theoretical constructions and form an arena where to test various methods and ideas. Relativistic particles with higher spin can be described in first quantization using actions with local supersymmetry on the worldline. 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 Poincare group.
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