Address:
School of Mathematics & Physics, Anhui Jianzhu University, Hefei, P.R. China
Center for Pure Mathematics, School of Mathematical Sciences, Anhui University, Hefei, P.R. China
E-mail:
cwq@ahjzu.edu.cn
cding@ahu.edu.cn
Abstract: Rarita-Schwinger fields are solutions to the relativistic field equation of spin-$3/2$ fermions in four dimensional flat spacetime, which are important in supergravity and superstring theories. Bureš et al. generalized it to arbitrary spin $k/2$ in 2002 in the context of Clifford algebras. In this article, we introduce a higher spin $\Pi $-operator related to the Rarita-Schwinger operator. Further, we investigate norm estimates, mapping properties and the adjoint operator of the higher spin $\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 $\Pi $-operator.
AMSclassification: primary 30G35; secondary 30G20, 35A22.
Keywords: Rarita-Schwinger operator, integral transform, higher spin \Pi -operator, higher spin Beltrami equation.
DOI: 10.5817/AM2026-3-89