RightNablaD[i]
denotes , acting to the right.
Overview, ExpandPartialD, FCPartialD, LeftNabalD.
[i] RightNablaD
[i] . QuantumField[A, LorentzIndex[\[Mu]]]
RightNablaD
= ExpandPartialD[%] ex
// StandardForm
ex
(*-QuantumField[FCPartialD[CartesianIndex[i]], A, LorentzIndex[\[Mu]]]*)
[i] // StandardForm
RightNablaD
(*RightNablaD[CartesianIndex[i]]*)