On the fundamental solution for higher spin Dirac operators

Abstract

In this paper, we will determine the fundamental solution for the higher spin Dirac operator Qλ, which is a generalisation of the classical Rarita–Schwinger operator to more complicated irreducible (half-integer) representations for the spin group in m dimensions. This will allow us to generalise the Stokes theorem, the Cauchy–Pompeiu theorem and the Cauchy integral formula, which lie at the very heart of the function theory behind arbitrary elliptic higher spin operators.