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- fermions in four dimensional flat spacetime, which are important in supergravity and superstring theories. Bure\v s et al. generalized it to arbitrary spin in 2002 in the context of Clifford algebras. In this article, we introduce the higher spin -operator related to the Rarita-Schwinger operator. Further, we investigate norm estimates, mapping properties and the adjoint operator of the higher spin -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 -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}
}