A note on Harmonic Gauge(s) in Massive Gravity

Understand

We consider the harmonic gauge condition in linearized gravity, seen as a gauge theory for a symmetric tensor field.

• Once the harmonic gauge condition is implemented, as customary, according to the Faddeev-Popov procedure, the gauge fixed action still depends on one gauge parameter.
• Consequently, the harmonic gauge appears to be a class of conditions, rather than a particular one.
• This allows to give a physical motivation for the covariant harmonic gauge(s), which emerges when the gravitational perturbation is given a mass term.