Integral Formulas for Higher Order Conformally Invariant Fermionic Operators

TL;DR

This paper develops higher order integral formulas for conformally invariant fermionic operators in higher spin theory, extending fundamental integral formulas to more complex operators in this mathematical framework.

Contribution

It introduces higher order Borel-Pompeiu and Cauchy's integral formulas for fermionic operators in higher spin theory, advancing the mathematical understanding of conformally invariant differential operators.

Findings

Established higher order Borel-Pompeiu formulas for fermionic operators

Derived higher order Cauchy's integral formulas for these operators

Extended integral formulas in higher spin conformal geometry

Abstract

In this paper, we establish higher order Borel-Pompeiu formulas for conformally invariant fermionic operators in higher spin theory, which is the theory of functions on m-dimensional Euclidean space taking values in arbitrary irreducible representations of the Spin group. As applications, we provide higher order Cauchy's integral formulas for those fermionic operators. This paper continues the work of building up basic integral formulas for conformally invariant differential operators in higher spin theory.