FeynCalc manual (development version)

TarcerToFC

TarcerToFC[expr, {q1, q2}] translates loop integrals in the TARCER-notation to the FeynCalc notation.

See TFI for details on the convention.

As in the case of ToTFI, the 1πD\frac{1}{\pi^D} and 1πD/2\frac{1}{\pi^{D/2}} prefactors are implicit, i.e. TarcerToFC doesn’t add them.

To recover momenta from scalar products use the option ScalarProduct e.g. as in TarcerToFC[TBI[D, pp^2, {{1, 0}, {1, 0}}], {q1, q2}, ScalarProduct -> {{pp^2, p1}}]

See also

Overview, ToFI.

Examples

Tarcer`TFI[D, Pair[Momentum[p, D], Momentum[p, D]], {0, 0, 3, 2, 0}, 
  {{4, 0}, {2, 0}, {1, 0}, {0, 0}, {1, 0}}]

TarcerˋTFI(D,p2,{0,0,3,2,0},(4020100010))\text{Tarcer$\grave{ }$TFI}\left(D,p^2,\{0,0,3,2,0\},\left( \begin{array}{cc} 4 & 0 \\ 2 & 0 \\ 1 & 0 \\ 0 & 0 \\ 1 & 0 \\ \end{array} \right)\right)

TarcerToFC[%, {q1, q2}]

(p  q1)3(p  q2)2(q12)4.(q22)2.(q1p)2.(q1q2)2\frac{(p\cdot \;\text{q1})^3 (p\cdot \;\text{q2})^2}{\left(\text{q1}^2\right)^4.\left(\text{q2}^2\right)^2.(\text{q1}-p)^2.(\text{q1}-\text{q2})^2}

a1 Tarcer`TBI[D, pp^2, {{1, 0}, {1, 0}}] + b1 Tarcer`TBI[D, mm1, {{1, 0}, {1, 0}}]

a1  TarcerˋTBI(D,pp2,(1010))+b1  TarcerˋTBI(D,mm1,(1010))\text{a1} \;\text{Tarcer$\grave{ }$TBI}\left(D,\text{pp}^2,\left( \begin{array}{cc} 1 & 0 \\ 1 & 0 \\ \end{array} \right)\right)+\text{b1} \;\text{Tarcer$\grave{ }$TBI}\left(D,\text{mm1},\left( \begin{array}{cc} 1 & 0 \\ 1 & 0 \\ \end{array} \right)\right)

TarcerToFC[%, {q1, q2}, ScalarProduct -> {{pp^2, p1}, {mm1, p1}}, FCE -> True]

a1q12.(q1p1)2+b1q12.(q1p1)2\frac{\text{a1}}{\text{q1}^2.(\text{q1}-\text{p1})^2}+\frac{\text{b1}}{\text{q1}^2.(\text{q1}-\text{p1})^2}