FeynCalc manual (development version)

LeftRightNablaD2

LeftRightNablaD2[mu] denotes i\overleftrightarrow{\nabla }_{i}, acting to the left and right.

ExplicitPartialD[LeftRightNablaD2[mu]] gives (RightNablaD[i] + LeftNablaD[i]).

See also

Overview, ExplicitPartialD, ExpandPartialD, FCPartialD, LeftNablaD, RightNablaD.

Examples

LeftRightNablaD2[i] 
 
ExplicitPartialD[%]

i\overleftrightarrow{\nabla }_i

ii-\overleftarrow{\partial }_i-\vec{\partial }_i

LeftRightNablaD2[i] . QuantumField[A, LorentzIndex[\[Nu]]] 
 
ExpandPartialD[%]

i.Aν\overleftrightarrow{\nabla }_i.A_{\nu }

(iAν)i.Aν-\left(\partial _iA_{\nu }\right)-\overleftarrow{\partial }_i.A_{\nu }

QuantumField[A, LorentzIndex[\[Mu]]] . LeftRightNablaD2[i] . QuantumField[A, LorentzIndex[\[Rho]]] 
 
ExpandPartialD[%] 
  
 

Aμ.i.AρA_{\mu }.\overleftrightarrow{\nabla }_i.A_{\rho }

Aμ.(iAρ)(iAμ).Aρ-A_{\mu }.\left(\partial _iA_{\rho }\right)-\left(\partial _iA_{\mu }\right).A_{\rho }