FeynCalc manual (development version)

LeftRightPartialD2

LeftRightPartialD2[mu] denotes \overleftrightarrow{\partial }_{\mu }, acting to the left and right.

ExplicitPartialD[LeftRightPartialD2[mu]] gives (RightPartialD[mu] + LeftPartialD[mu]).

See also

Overview, ExplicitPartialD, ExpandPartialD, FCPartialD, LeftPartialD, RightPartialD.

Examples

LeftRightPartialD2[\[Mu]] 
 
ExplicitPartialD[%]

\overleftrightarrow{\partial }_{\mu }

\overleftarrow{\partial }_{\mu }+\vec{\partial }_{\mu }

LeftRightPartialD2[\[Mu]] . QuantumField[A, LorentzIndex[\[Nu]]] 
 
ExpandPartialD[%]

\overleftrightarrow{\partial }_{\mu }.A_{\nu }

\left.(\partial _{\mu }A_{\nu }\right)+\overleftarrow{\partial }_{\mu }.A_{\nu }

QuantumField[A, LorentzIndex[\[Mu]]] . LeftRightPartialD2[\[Nu]] . QuantumField[A, LorentzIndex[\[Rho]]] 
 
ExpandPartialD[%]

A_{\mu }.\overleftrightarrow{\partial }_{\nu }.A_{\rho }

A_{\mu }.\left(\left.(\partial _{\nu }A_{\rho }\right)\right)+\left(\left.(\partial _{\nu }A_{\mu }\right)\right).A_{\rho }