Conformally Covariant Differential Operators: Symmetric Tensor Fields

TL;DR

This paper develops second order conformally covariant differential operators for symmetric traceless tensor fields, explicitly constructs their Green functions in flat space, and verifies their conformal invariance.

Contribution

It extends conformally covariant differential operators to symmetric traceless tensor fields and provides explicit Green functions consistent with conformal invariance.

Findings

Explicit construction of Green functions for these operators

Verification of conformal invariance in flat space

Extension of previous work to tensor fields

Abstract

We extend previous work on conformally covariant differential operators to consider the case of second order operators acting on symmetric traceless tensor fields. The corresponding flat space Green function is explicitly constructed and shown to be in accord with the requirements of conformal invariance.