description = "Ga -> Ga Ga Ga Ga, QED, amplitude, 1-loop";
If[ $FrontEnd === Null,
$FeynCalcStartupMessages = False;
Print[description];
];
If[ $Notebooks === False,
$FeynCalcStartupMessages = False
];
$LoadAddOns = {"FeynArts"};
<< FeynCalc`
$FAVerbose = 0;
FCCheckVersion[9, 3, 1];\text{FeynCalc }\;\text{10.0.0 (dev version, 2023-12-20 22:40:59 +01:00, dff3b835). For help, use the }\underline{\text{online} \;\text{documentation}}\;\text{, check out the }\underline{\text{wiki}}\;\text{ or visit the }\underline{\text{forum}.}
\text{Please check our }\underline{\text{FAQ}}\;\text{ for answers to some common FeynCalc questions and have a look at the supplied }\underline{\text{examples}.}
\text{If you use FeynCalc in your research, please evaluate FeynCalcHowToCite[] to learn how to cite this software.}
\text{Please keep in mind that the proper academic attribution of our work is crucial to ensure the future development of this package!}
\text{FeynArts }\;\text{3.11 (3 Aug 2020) patched for use with FeynCalc, for documentation see the }\underline{\text{manual}}\;\text{ or visit }\underline{\text{www}.\text{feynarts}.\text{de}.}
\text{If you use FeynArts in your research, please cite}
\text{ $\bullet $ T. Hahn, Comput. Phys. Commun., 140, 418-431, 2001, arXiv:hep-ph/0012260}
Nicer typesetting
MakeBoxes[mu, TraditionalForm] := "\[Mu]";
MakeBoxes[nu, TraditionalForm] := "\[Nu]";
MakeBoxes[rho, TraditionalForm] := "\[Rho]";
MakeBoxes[k1, TraditionalForm] := "\!\(\*SubscriptBox[\(k\), \(1\)]\)";
MakeBoxes[k2, TraditionalForm] := "\!\(\*SubscriptBox[\(k\), \(2\)]\)";
MakeBoxes[k3, TraditionalForm] := "\!\(\*SubscriptBox[\(k\), \(3\)]\)";
MakeBoxes[k4, TraditionalForm] := "\!\(\*SubscriptBox[\(k\), \(4\)]\)";
MakeBoxes[k5, TraditionalForm] := "\!\(\*SubscriptBox[\(k\), \(5\)]\)";diags = InsertFields[CreateTopologies[1, 1 -> 4],
{V[1]} -> {V[1], V[1], V[1], V[1]}, InsertionLevel -> {Particles},
ExcludeParticles -> {S[_], V[_], U[_], F[3 | 4], F[2, {2 | 3}]}];
Paint[diags, ColumnsXRows -> {4, 1}, Numbering -> Simple,
SheetHeader -> None, ImageSize -> {512, 256}];
The 1/(2Pi)^D prefactor is implicit.
amp[0] = FCFAConvert[CreateFeynAmp[diags, PreFactor -> 1,
Truncated -> True], IncomingMomenta -> {k1},
OutgoingMomenta -> {k2, k3, k4, k5}, LoopMomenta -> {q},
LorentzIndexNames -> {mu, nu, rho}, UndoChiralSplittings -> True,
ChangeDimension -> D, List -> True, SMP -> True]\left\{-\frac{i \;\text{tr}\left(\left(\gamma \cdot \left(-k_2-k_3-k_4-k_5+q\right)+m_e\right).\left(-i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_4-k_5+q\right)+m_e\right).\left(-i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_4+q\right)+m_e\right).\left(-i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(q-k_2\right)+m_e\right).\left(-i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot q+m_e\right).\left(-i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_2){}^2-m_e^2\right).\left((-k_2-k_4+q){}^2-m_e^2\right).\left((-k_2-k_4-k_5+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(\gamma \cdot \left(-k_2-k_3-k_4-k_5+q\right)+m_e\right).\left(i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_4-k_5+q\right)+m_e\right).\left(i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_4+q\right)+m_e\right).\left(i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(q-k_2\right)+m_e\right).\left(i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot q+m_e\right).\left(i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_2){}^2-m_e^2\right).\left((-k_2-k_4+q){}^2-m_e^2\right).\left((-k_2-k_4-k_5+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(m_e-\gamma \cdot q\right).\left(i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(k_2-q\right)+m_e\right).\left(i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_5-q\right)+m_e\right).\left(i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_4+k_5-q\right)+m_e\right).\left(i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_4+k_5-q\right)+m_e\right).\left(i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_2){}^2-m_e^2\right).\left((-k_2-k_5+q){}^2-m_e^2\right).\left((-k_2-k_4-k_5+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(m_e-\gamma \cdot q\right).\left(-i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(k_2-q\right)+m_e\right).\left(-i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_5-q\right)+m_e\right).\left(-i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_4+k_5-q\right)+m_e\right).\left(-i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_4+k_5-q\right)+m_e\right).\left(-i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_2){}^2-m_e^2\right).\left((-k_2-k_5+q){}^2-m_e^2\right).\left((-k_2-k_4-k_5+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(\gamma \cdot \left(-k_2-k_3-k_4-k_5+q\right)+m_e\right).\left(-i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3-k_5+q\right)+m_e\right).\left(-i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3+q\right)+m_e\right).\left(-i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(q-k_2\right)+m_e\right).\left(-i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot q+m_e\right).\left(-i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_2){}^2-m_e^2\right).\left((-k_2-k_3+q){}^2-m_e^2\right).\left((-k_2-k_3-k_5+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(\gamma \cdot \left(-k_2-k_3-k_4-k_5+q\right)+m_e\right).\left(i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3-k_5+q\right)+m_e\right).\left(i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3+q\right)+m_e\right).\left(i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(q-k_2\right)+m_e\right).\left(i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot q+m_e\right).\left(i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_2){}^2-m_e^2\right).\left((-k_2-k_3+q){}^2-m_e^2\right).\left((-k_2-k_3-k_5+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(m_e-\gamma \cdot q\right).\left(i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(k_2-q\right)+m_e\right).\left(i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_5-q\right)+m_e\right).\left(i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_5-q\right)+m_e\right).\left(i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_4+k_5-q\right)+m_e\right).\left(i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_2){}^2-m_e^2\right).\left((-k_2-k_5+q){}^2-m_e^2\right).\left((-k_2-k_3-k_5+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(m_e-\gamma \cdot q\right).\left(-i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(k_2-q\right)+m_e\right).\left(-i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_5-q\right)+m_e\right).\left(-i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_5-q\right)+m_e\right).\left(-i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_4+k_5-q\right)+m_e\right).\left(-i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_2){}^2-m_e^2\right).\left((-k_2-k_5+q){}^2-m_e^2\right).\left((-k_2-k_3-k_5+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(\gamma \cdot \left(-k_2-k_3-k_4-k_5+q\right)+m_e\right).\left(-i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3-k_4+q\right)+m_e\right).\left(-i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3+q\right)+m_e\right).\left(-i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(q-k_2\right)+m_e\right).\left(-i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot q+m_e\right).\left(-i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_2){}^2-m_e^2\right).\left((-k_2-k_3+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(\gamma \cdot \left(-k_2-k_3-k_4-k_5+q\right)+m_e\right).\left(i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3-k_4+q\right)+m_e\right).\left(i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3+q\right)+m_e\right).\left(i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(q-k_2\right)+m_e\right).\left(i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot q+m_e\right).\left(i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_2){}^2-m_e^2\right).\left((-k_2-k_3+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(m_e-\gamma \cdot q\right).\left(i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(k_2-q\right)+m_e\right).\left(i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_4-q\right)+m_e\right).\left(i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_4-q\right)+m_e\right).\left(i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_4+k_5-q\right)+m_e\right).\left(i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_2){}^2-m_e^2\right).\left((-k_2-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(m_e-\gamma \cdot q\right).\left(-i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(k_2-q\right)+m_e\right).\left(-i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_4-q\right)+m_e\right).\left(-i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_4-q\right)+m_e\right).\left(-i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_4+k_5-q\right)+m_e\right).\left(-i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_2){}^2-m_e^2\right).\left((-k_2-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(\gamma \cdot \left(-k_2-k_3-k_4-k_5+q\right)+m_e\right).\left(-i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3-k_5+q\right)+m_e\right).\left(-i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3+q\right)+m_e\right).\left(-i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(q-k_3\right)+m_e\right).\left(-i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot q+m_e\right).\left(-i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_3){}^2-m_e^2\right).\left((-k_2-k_3+q){}^2-m_e^2\right).\left((-k_2-k_3-k_5+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(\gamma \cdot \left(-k_2-k_3-k_4-k_5+q\right)+m_e\right).\left(i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3-k_5+q\right)+m_e\right).\left(i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3+q\right)+m_e\right).\left(i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(q-k_3\right)+m_e\right).\left(i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot q+m_e\right).\left(i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_3){}^2-m_e^2\right).\left((-k_2-k_3+q){}^2-m_e^2\right).\left((-k_2-k_3-k_5+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(m_e-\gamma \cdot q\right).\left(i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(k_3-q\right)+m_e\right).\left(i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(k_3+k_5-q\right)+m_e\right).\left(i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_5-q\right)+m_e\right).\left(i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_4+k_5-q\right)+m_e\right).\left(i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_3){}^2-m_e^2\right).\left((-k_3-k_5+q){}^2-m_e^2\right).\left((-k_2-k_3-k_5+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(m_e-\gamma \cdot q\right).\left(-i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(k_3-q\right)+m_e\right).\left(-i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(k_3+k_5-q\right)+m_e\right).\left(-i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_5-q\right)+m_e\right).\left(-i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_4+k_5-q\right)+m_e\right).\left(-i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_3){}^2-m_e^2\right).\left((-k_3-k_5+q){}^2-m_e^2\right).\left((-k_2-k_3-k_5+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(\gamma \cdot \left(-k_2-k_3-k_4-k_5+q\right)+m_e\right).\left(-i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3-k_4+q\right)+m_e\right).\left(-i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3+q\right)+m_e\right).\left(-i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(q-k_3\right)+m_e\right).\left(-i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot q+m_e\right).\left(-i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_3){}^2-m_e^2\right).\left((-k_2-k_3+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(\gamma \cdot \left(-k_2-k_3-k_4-k_5+q\right)+m_e\right).\left(i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3-k_4+q\right)+m_e\right).\left(i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3+q\right)+m_e\right).\left(i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(q-k_3\right)+m_e\right).\left(i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot q+m_e\right).\left(i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_3){}^2-m_e^2\right).\left((-k_2-k_3+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(m_e-\gamma \cdot q\right).\left(i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(k_3-q\right)+m_e\right).\left(i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(k_3+k_4-q\right)+m_e\right).\left(i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_4-q\right)+m_e\right).\left(i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_4+k_5-q\right)+m_e\right).\left(i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_3){}^2-m_e^2\right).\left((-k_3-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(m_e-\gamma \cdot q\right).\left(-i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(k_3-q\right)+m_e\right).\left(-i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot \left(k_3+k_4-q\right)+m_e\right).\left(-i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_4-q\right)+m_e\right).\left(-i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(k_2+k_3+k_4+k_5-q\right)+m_e\right).\left(-i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_3){}^2-m_e^2\right).\left((-k_3-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(\gamma \cdot \left(-k_2-k_3-k_4-k_5+q\right)+m_e\right).\left(-i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3-k_4+q\right)+m_e\right).\left(-i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_4+q\right)+m_e\right).\left(-i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(q-k_4\right)+m_e\right).\left(-i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot q+m_e\right).\left(-i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_4){}^2-m_e^2\right).\left((-k_2-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(\gamma \cdot \left(-k_2-k_3-k_4-k_5+q\right)+m_e\right).\left(i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3-k_4+q\right)+m_e\right).\left(i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_4+q\right)+m_e\right).\left(i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(q-k_4\right)+m_e\right).\left(i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot q+m_e\right).\left(i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_4){}^2-m_e^2\right).\left((-k_2-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(\gamma \cdot \left(-k_2-k_3-k_4-k_5+q\right)+m_e\right).\left(-i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3-k_4+q\right)+m_e\right).\left(-i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(-k_3-k_4+q\right)+m_e\right).\left(-i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(q-k_4\right)+m_e\right).\left(-i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot q+m_e\right).\left(-i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_4){}^2-m_e^2\right).\left((-k_3-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)},-\frac{i \;\text{tr}\left(\left(\gamma \cdot \left(-k_2-k_3-k_4-k_5+q\right)+m_e\right).\left(i \gamma ^{\text{Lor5}} \;\text{e}\right).\left(\gamma \cdot \left(-k_2-k_3-k_4+q\right)+m_e\right).\left(i \gamma ^{\nu } \;\text{e}\right).\left(\gamma \cdot \left(-k_3-k_4+q\right)+m_e\right).\left(i \gamma ^{\rho } \;\text{e}\right).\left(\gamma \cdot \left(q-k_4\right)+m_e\right).\left(i \gamma ^{\text{Lor4}} \;\text{e}\right).\left(\gamma \cdot q+m_e\right).\left(i \gamma ^{\mu } \;\text{e}\right)\right)}{\left(q^2-m_e^2\right).\left((q-k_4){}^2-m_e^2\right).\left((-k_3-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4+q){}^2-m_e^2\right).\left((-k_2-k_3-k_4-k_5+q){}^2-m_e^2\right)}\right\}
We obtain 24 diagrams. The sum vanishes because the contribution of each odd diagram is exactly cancelled by the contribution of the next even diagram, i.e. A1+A2=0, A3+A4=0 and so on
amp[1] = amp[0] // FCTraceFactor;amp[2] = Total /@ Partition[amp[1], 2, 2, 1, {}]\{0,0,0,0,0,0,0,0,0,0,0,0\}
amp[3] = Total[amp[2]]0
FCCompareResults[amp[3], 0,
Text -> {"\tVerify Furry's theorem for 5-photons at 1-loop:",
"CORRECT.", "WRONG!"}, Interrupt -> {Hold[Quit[1]], Automatic}];
Print["\tCPU Time used: ", Round[N[TimeUsed[], 4], 0.001], " s."];\text{$\backslash $tVerify Furry's theorem for 5-photons at 1-loop:} \;\text{CORRECT.}
\text{$\backslash $tCPU Time used: }26.748\text{ s.}