English

The higher spin $\Pi$-operator in Clifford analysis

Complex Variables 2026-03-10 v2

Abstract

Rarita-Schwinger fields are solutions to the relativistic field equation of spin-3/23/2 fermions in four dimensional flat spacetime, which are important in supergravity and superstring theories. Bure\v s et al. generalized it to arbitrary spin k/2k/2 in 2002 in the context of Clifford algebras. In this article, we introduce the higher spin Π\Pi-operator related to the Rarita-Schwinger operator. Further, we investigate norm estimates, mapping properties and the adjoint operator of the higher spin Π\Pi-operator. As an application, a higher spin Beltrami equation is introduced, and existence and uniqueness of solutions to this higher spin Beltrami equation is established by the norm estimate of the higher spin Π\Pi-operator.

Cite

@article{arxiv.2508.11271,
  title  = {The higher spin $\Pi$-operator in Clifford analysis},
  author = {Wanqing Cheng and Chao Ding},
  journal= {arXiv preprint arXiv:2508.11271},
  year   = {2026}
}
R2 v1 2026-07-01T04:51:13.483Z