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Spinning particles, their partition functions, and picture changing operators

E. Boffo1,*, P. A. Grassi2,3,†, O. Hulik4,‡, and I. Sachs5,§

  • *Contact author: boffo@karlin.mff.cuni.cz
  • †Contact author: pietro.grassi@uniupo.it
  • ‡Contact author: ondra.hulik@gmail.com
  • §Contact author: Ivo.Sachs@physik.uni-muenchen.de
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Phys. Rev. D 112, 106012 – Published 21 November, 2025

DOI: https://doi.org/10.1103/rmr9-t7jy

Abstract

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 two- and 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.

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Phys. Rev. D 112, 106012– Published 21 November, 2025
  • Received 15 June 2025
  • Accepted 21 October 2025
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