Supersymmetric actions for spinning particles

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Abstract
We review and investigate a number of supersymmetric actions describing a "classical particle of spin 1/2." The supersymmetry is introduced by extending the one-dimensional parameter space used to describe a conventional point particle to a two-dimensional superspace. The structure of this superspace is studied and a tensor calculus is developed. Different ways to modify the action of a conventional point particle to a superspace action are then considered. The superspace actions are simplified by a gauge choice and by elimination of some superfluous variables. Finally, the anticommuting parameter is eliminated, and the models are shown to be identical to models which have been studied earlier and shown to describe a "classical spin-1/2 particle". We take care to prove that the variable eliminations and gauge choices do not change the content of the models and to exhibit clearly the symmetries at each stage.