RightPartialD[mu]
denotes , acting to the right.
Overview, ExpandPartialD, FCPartialD, LeftPartialD.
[\[Mu]] RightPartialD
[\[Mu]] . QuantumField[A, LorentzIndex[\[Mu]]]
RightPartialD
= ExpandPartialD[%] ex
// StandardForm
ex
(*QuantumField[FCPartialD[LorentzIndex[\[Mu]]], A, LorentzIndex[\[Mu]]]*)
[\[Mu]] // StandardForm
RightPartialD
(*RightPartialD[LorentzIndex[\[Mu]]]*)