FeynCalc manual (development version)

ExplicitPartialD

ExplicitPartialD[exp] inserts the definitions for LeftRightPartialD, LeftRightPartialD2, LeftRightNablaD, LeftRightNablaD2, LeftNablaD and RightNablaD

See also

Overview, ExpandPartialD, LeftRightPartialD, LeftRightPartialD2, LeftRightNablaD, LeftRightNablaD2, LeftNablaD, RightNablaD.

Examples

LeftRightPartialD[\[Mu]] 
 
ExplicitPartialD[%]

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

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

LeftRightPartialD2[\[Mu]] 
 
ExplicitPartialD[%]

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

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

LeftRightPartialD[OPEDelta] 
 
ExplicitPartialD[%]

Δ\overleftrightarrow{\partial }_{\Delta }

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

16 LeftRightPartialD[OPEDelta]^4 
 
ExplicitPartialD[%]

16Δ416 \overleftrightarrow{\partial }_{\Delta }^4

(ΔΔ)4\left(\vec{\partial }_{\Delta }-\overleftarrow{\partial }_{\Delta }\right){}^4

Notice that by definition i=i=i\nabla^i = \partial_i = - \partial^i, where the last equality depends on the metric signature.

LeftNablaD[i] 
 
ExplicitPartialD[%]

i\overleftarrow{\nabla }^i

i-\overleftarrow{\partial }_i

RightNablaD[i] 
 
ExplicitPartialD[%]

i\vec{\nabla }^i

i-\vec{\partial }_i

LeftRightNablaD[i] 
 
ExplicitPartialD[%]

i\overleftrightarrow{\nabla }_i

12ii\frac{1}{2} \overleftarrow{\partial }_i-\vec{\partial }_i

LeftRightNablaD2[\[Mu]] 
 
ExplicitPartialD[%] 
  
 

μ\overleftrightarrow{\nabla }_{\mu }

μμ-\overleftarrow{\partial }_{\mu }-\vec{\partial }_{\mu }