FeynCalc manual (development version)

LeftRightPartialD

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

ExplicitPartialD[LeftRightPartialD[mu]] gives 1/2 (RightPartialD[mu] - LeftPartialD[mu]).

See also

Overview, ExplicitPartialD, ExpandPartialD, FCPartialD, LeftPartialD, LeftRightPartialD2, RightPartialD.

Examples

LeftRightPartialD[\[Mu]] 
 
ExplicitPartialD[%]

μ\overleftrightarrow{\partial }_{\mu }

12(μμ)\frac{1}{2} \left(\vec{\partial }_{\mu }-\overleftarrow{\partial }_{\mu }\right)

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

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

12((μAν)μ.Aν)\frac{1}{2} \left(\left.(\partial _{\mu }A_{\nu }\right)-\overleftarrow{\partial }_{\mu }.A_{\nu }\right)

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

Aμ.ν.AρA_{\mu }.\overleftrightarrow{\partial }_{\nu }.A_{\rho }

12(Aμ.((νAρ))((νAμ)).Aρ)\frac{1}{2} \left(A_{\mu }.\left(\left.(\partial _{\nu }A_{\rho }\right)\right)-\left(\left.(\partial _{\nu }A_{\mu }\right)\right).A_{\rho }\right)