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