On First Order Symmetry Operators for the Field Equations of Differential Forms

TL;DR

This paper investigates first order symmetry operators for differential p-form field equations in arbitrary dimensions, providing explicit forms for p=1,2, and proposing a general class for all p and D.

Contribution

It offers explicit symmetry operators for p=1,2 and introduces a general class of symmetry operators for any p and D, extending previous specific cases.

Findings

Explicit symmetry operators for p=1 and p=2 cases.

A proposed general class of symmetry operators for arbitrary p and D.

Framework applicable to both massless and massive p-form fields.

Abstract

We consider first order symmetry operators for the equations of motion of differential $p$-form fields in general $D$-dimensional background geometry of any signature for both massless and massive cases. For $p=1$ and $p=2$ we give the general forms of the symmetry operators. Then we find a class of symmetry operators for arbitrary $p$ and $D$, which is naturally suggested by the lower $p$ results.