<<HighEnergyPhysics`FeynCalc`

Loading FeynCalc from C:\Archivos de programa\Wolfram Research\Mathematica\8.0\AddOns\Applications\HighEnergyPhysics

FeynCalc 8.1.0 For help, type ?FeynCalc, open FeynCalcRef8.nb or visit www.feyncalc.org

Loading FeynArts, see www.feynarts.de for documentation

FeynArts 3.4 patched for use with FeynCalc

ScalarProduct[p1,p1]=ScalarProduct[p2,p2]=(m^2);
ScalarProduct[k1,k1]=ScalarProduct[k2,k2]=0;
ScalarProduct[k1,k2]=ScalarProduct[p1,p2]-(m^2);
ScalarProduct[k1,p2]=ScalarProduct[k2,p1];
ScalarProduct[k2,p2]=ScalarProduct[k1,p1];
ScalarProduct[p1,p2]=(m^2)+ScalarProduct[k1,p1]-ScalarProduct[k2,p1];

M1=e^2*Spinor[p2,m].(GA[ν].(GS[p1+k1]+m).GA[μ]/(SP[p1+k1,p1+k1]-m^2)+GA[μ].(GS[p1-k2]+m).GA[ν]/(SP[p1-k2,p1-k2]-m^2)).Spinor[p1,m]*PolarizationVector[k1,μ]*Conjugate[PolarizationVector[k2,ν]];
M1A=ComplexConjugate[M1] /. μ-> μ2 /.  ν-> ν2;
A=(M1A  M1/4 // DoPolarizationSums // Contract // FermionSpinSum) /. DiracTrace->TR
Collect[A,m]

ClearScalarProducts;
Clear[p1,p2,k1,k2];
SetMandelstam[s,t,u,p1,k1,-p2,-k2,m,0,m,0];
TrickMandelstam[A,{s,t,u,2m^2}]

(*Otras comprobaciones intermedias*)
t1=4*Tr[(GS[p2]+m).GS[p1].(GS[p1]+m).GS[p1]](*t1*)
%-16m^2*SP[p1,p2]-16m^4 // Simplify

t2=-2*Tr[(GS[p2]+m).GA[ν].(GS[p1]+m).GA[ν].GS[k2].GS[p1]](*t2*)
%-(32*SP[p1,p2]*SP[p1,k2]-16m^2*SP[p2,k2]-32m^2*SP[k2,p1]) // Expand // Simplify

t3=2*Tr[(GS[p2]+m).GS[p1].GS[k1].GA[μ].(GS[p1]+m).GA[μ]](*t3*)
%-(-32*SP[k1,p1]*SP[p1,p2]+16m^2*SP[p2,k1]+32m^2*SP[k1,p1]) //Simplify

t4=-Tr[(GS[p2]+m).GA[ν].GS[k1].GA[μ].(GS[p1]+m).GA[ν].GS[k2].GA[μ]](*t4*)
%-(32*SP[p2,p1]*SP[k1,k2]-16m^2SP[k1,k2])// Simplify

Tr[GS[p2].GA[ν].GS[k1].GA[μ].GS[p1].GA[ν].GS[k2].GA[μ]](*t4a)
% -(-32SP[p1,p2]SP[k1,k2])

Tr[GA[ν].GS[k1].GA[μ].GA[ν].GS[k2].GA[μ]] (*t4b*)
% -(16SP[k1,k2])

T2=-Tr[(GS[p2]+m).GA[ν].(2 FV[p1,μ]+GS[k1].GA[μ]).(GS[p1]+m).(2FV[p1,ν]-GA[ν].GS[k2]).GA[μ]](*T2*)
%-(-32m^4-16m^2*(ScalarProduct[k1,p1]-ScalarProduct[k1,p2]))//Simplify