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

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.

33 pages

References in corpus (6)

• Maxwell's Equations in the Myers-Perry Geometry
• Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets
• Symmetry operators and decoupled equations for linear fields on black hole spacetimes
• On symmetry operators for the Maxwell equation on the Kerr-NUT-(A)dS spacetime
• Hidden symmetry and the separability of the Maxwell equation on the Wahlquist spacetime
• First Order Symmetry Operators for the Linearized Field Equation of Metric Perturbations