The higher spin Dirac operators

TL;DR

This paper explores a family of conformally invariant elliptic operators on Riemannian spin manifolds, focusing on their properties and index calculations, with particular attention to the Rarita-Schwinger operator.

Contribution

It provides a general definition of these operators, analyzes their properties, and computes their indices, highlighting the Rarita-Schwinger operator's role.

Findings

Defined a family of conformally invariant operators including Dirac and Rarita-Schwinger.

Analyzed basic properties of these operators.

Computed indices of the operators.

Abstract

There is a certain family of conformally invariant first order elliptic operators on Riemannian spin manifold which include Dirac operator as its first and simplest member. Their general definition is given and their basic properties are described. A special attention is paid to the Rarita-Schwinger operator the second simplest operator in the row. Its basic properties are described in more details. In the last part indices of discussed operators are computed.