FeynCalc manual (development version)

GenPaVe

GenPaVe[i, j, ..., {{0, m0}, {Momentum[p1], m1}, {Momentum[p2], m2}, ...] denotes the invariant (and scalar) Passarino-Veltman integrals, i.e. the coefficient functions of the tensor integral decomposition. In contrast to PaVe which uses the LoopTools convention, masses and external momenta in GenPaVe are written in the same order as they appear in the original tensor integral, i.e. FAD[{q,m0},{q-p1,m1},{q-p2,m2},...].

See also

Overview, PaVe.

Examples

FVD[q, \[Mu]] FVD[q, \[Nu]] FAD[{q, m0}, {q + p1, m1}, {q + p2, m2}]/(I*Pi^2) 
 
TID[%, q, UsePaVeBasis -> True] 
 
TID[%%, q, UsePaVeBasis -> True, GenPaVe -> True]

iqμqνπ2(q2m02).((p1+q)2m12).((p2+q)2m22)-\frac{i q^{\mu } q^{\nu }}{\pi ^2 \left(q^2-\text{m0}^2\right).\left((\text{p1}+q)^2-\text{m1}^2\right).\left((\text{p2}+q)^2-\text{m2}^2\right)}

gμν  C00(p12,p22,2(p1  p2)+p12+p22,m12,m02,m22)+p1μ  p1ν  C11(p12,2(p1  p2)+p12+p22,p22,m02,m12,m22)+p2μ  p2ν  C11(p22,2(p1  p2)+p12+p22,p12,m02,m22,m12)+(p1ν  p2μ+p1μ  p2ν)  C12(p12,2(p1  p2)+p12+p22,p22,m02,m12,m22)g^{\mu \nu } \;\text{C}_{00}\left(\text{p1}^2,\text{p2}^2,-2 (\text{p1}\cdot \;\text{p2})+\text{p1}^2+\text{p2}^2,\text{m1}^2,\text{m0}^2,\text{m2}^2\right)+\text{p1}^{\mu } \;\text{p1}^{\nu } \;\text{C}_{11}\left(\text{p1}^2,-2 (\text{p1}\cdot \;\text{p2})+\text{p1}^2+\text{p2}^2,\text{p2}^2,\text{m0}^2,\text{m1}^2,\text{m2}^2\right)+\text{p2}^{\mu } \;\text{p2}^{\nu } \;\text{C}_{11}\left(\text{p2}^2,-2 (\text{p1}\cdot \;\text{p2})+\text{p1}^2+\text{p2}^2,\text{p1}^2,\text{m0}^2,\text{m2}^2,\text{m1}^2\right)+\left(\text{p1}^{\nu } \;\text{p2}^{\mu }+\text{p1}^{\mu } \;\text{p2}^{\nu }\right) \;\text{C}_{12}\left(\text{p1}^2,-2 (\text{p1}\cdot \;\text{p2})+\text{p1}^2+\text{p2}^2,\text{p2}^2,\text{m0}^2,\text{m1}^2,\text{m2}^2\right)

gμν  GenPaVe({0,0},(0  m0  p1  m1  p2  m2))+p1μ  p1ν  GenPaVe({1,1},(0  m0  p1  m1  p2  m2))+p2μ  p2ν  GenPaVe({2,2},(0  m0  p1  m1  p2  m2))+(p1ν  p2μ+p1μ  p2ν)  GenPaVe({1,2},(0  m0  p1  m1  p2  m2))g^{\mu \nu } \;\text{GenPaVe}\left(\{0,0\},\left( \begin{array}{cc} 0 & \;\text{m0} \\ \;\text{p1} & \;\text{m1} \\ \;\text{p2} & \;\text{m2} \\ \end{array} \right)\right)+\text{p1}^{\mu } \;\text{p1}^{\nu } \;\text{GenPaVe}\left(\{1,1\},\left( \begin{array}{cc} 0 & \;\text{m0} \\ \;\text{p1} & \;\text{m1} \\ \;\text{p2} & \;\text{m2} \\ \end{array} \right)\right)+\text{p2}^{\mu } \;\text{p2}^{\nu } \;\text{GenPaVe}\left(\{2,2\},\left( \begin{array}{cc} 0 & \;\text{m0} \\ \;\text{p1} & \;\text{m1} \\ \;\text{p2} & \;\text{m2} \\ \end{array} \right)\right)+\left(\text{p1}^{\nu } \;\text{p2}^{\mu }+\text{p1}^{\mu } \;\text{p2}^{\nu }\right) \;\text{GenPaVe}\left(\{1,2\},\left( \begin{array}{cc} 0 & \;\text{m0} \\ \;\text{p1} & \;\text{m1} \\ \;\text{p2} & \;\text{m2} \\ \end{array} \right)\right)