Photon self - energy in QED

<< HighEnergyPhysics`fc`

FeynCalc 4.1.1    For help, type ?FeynCalc,  use the built-in help system  or visit www.feyncalc.org

Loading PHI

Loading FeynArts

ME/: MakeBoxes[ME,  fmt_] := InterpretationBox[SubscriptBox[m,  e],  ME]

EL/: MakeBoxes[EL,  fmt_] := InterpretationBox[e,  ME]

t11 = CreateTopologies[1, 1 -> 1, Adjacencies -> {3}];

graf = 
      InsertFields[t11, V[1] -> V[1], 
        Restrictions -> {QEDOnly, NoGeneration2, NoGeneration3}, 
        ExcludeParticles -> {F[3 | 4]}, InsertionLevel -> Classes ];

Paint[graf, PaintLevel -> {Classes}, SheetHeader -> False, 
      Numbering -> False, ColumnsXRows -> {1, 1}];

Now generate the amplitude and divide out the polarization vectors and replace the class mass by the electron mass (use InputForm to help identify exactly what to type to remove them).

\(amp1\  = 
      \(CreateFCAmp[graf, Sum -> False]/
              Pair[LorentzIndex[
                  Momentum[p1, \ 
\ \ \ \ \ \ \ \ SpaceTimeDimensions], \ 
                  SpaceTimeDimensions], \ 
\ \ \ \ \ \ 
                Momentum[
                  Polarization[V[1], \ I, \ 
\ \ \ \ \ \ \ \ 
                    SUNIndex[
                      LorentzIndex[μ1, \ 
\ \ \ \ \ \ \ \ \ \ 
                        SpaceTimeDimensions]]], \ 
\ \ \ \ \ \ \ 
                  SpaceTimeDimensions]]\)/
\ \ \ \ \ 
            Pair[LorentzIndex[
                Momentum[p3, \ 
\ \ \ \ \ \ \ \ SpaceTimeDimensions], \ 
                SpaceTimeDimensions], \ 
\ \ \ \ \ \ 
              Momentum[
                Polarization[V[1], \ I, \ 
\ \ \ \ \ \ \ \ 
                  SUNIndex[
                    LorentzIndex[μ2, \ 
\ \ \ \ \ \ \ \ \ \ 
                      SpaceTimeDimensions]]], \ 
\ \ \ \ \ \ \ 
                SpaceTimeDimensions]] /. \ 
          MLE[Index[Generation, \ 1]] -> ME // Simplify\)

amp2 = 
      amp1 /. (DiracTraceEvaluate -> False) -> 
            (DiracTraceEvaluate -> True) // Simplify

OneLoop[q1, amp2]

test = -I/Pi^2 FAD[{q, m}] // FCI

OneLoop[q, test]