Spinning particles, their partition functions, and picture changing operators

We compute the partition function for the N = 1 spinning particle, including pictures and the large Hilbert space, and show that it counts the dimension of the Becchi-Rouet-Stora-Tyutin cohomology in twoand four-dimensional target space.We also construct a quadratic action in the target space. Furthermore, we find a consistent interaction as a derived bracket based on the associative product of worldline fields, leading to an interacting theory of multiforms in space-time. Finally, we comment on the equivalence of the multiform theory with a Dirac fermion. We also identify the chiral anomaly of the latter with a Hodge anomaly for the multiform theory, which manifests itself as a deformation of the gauge fixing.