FeynCalc manual (development version)

LightConePerpendicularComponent

LightConePerpendicularComponent[LorentzIndex[mu],Momentum[n],Momentum[nb]] denotes the perpendicular component of the Lorentz index mu with respect to the lightcone momenta n and nb.

LightConePerpendicularComponent[Momentum[p],Momentum[n],Momentum[nb]] denotes the perpendicular component of the 4-momentum p with respect to the lightcone momenta n and nb.

See also

Overview, LorentzIndex, Momentum.

Examples

4-dimensional Lorentz vector

Pair[LightConePerpendicularComponent[LorentzIndex[\[Mu]], Momentum[n],Momentum[nb]], 
  LightConePerpendicularComponent[Momentum[p], Momentum[n], Momentum[nb]]]

\overline{p}^{\mu }{}_{\perp }

Metric tensor

Pair[LightConePerpendicularComponent[LorentzIndex[\[Mu]], Momentum[n],Momentum[nb]], 
  LightConePerpendicularComponent[LorentzIndex[\[Nu]], Momentum[n], Momentum[nb]]]

\bar{g}^{\mu \nu }{}_{\perp }

Dirac matrix

DiracGamma[LightConePerpendicularComponent[LorentzIndex[\[Mu]], Momentum[n], Momentum[nb]]]

\bar{\gamma }^{\mu }{}_{\perp }

Contractions

DiracGamma[LightConePerpendicularComponent[LorentzIndex[\[Mu]], 
      Momentum[n], Momentum[nb]]] FV[p, \[Mu]] // Contract 
 
% // StandardForm

\bar{\gamma }\cdot \overline{p}_{\perp }

(*DiracGamma[LightConePerpendicularComponent[Momentum[p], Momentum[n], Momentum[nb]]]*)