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 1 π D \frac{1}{\pi^D} π D 1 and 1 π D / 2 \frac{1}{\pi^{D/2}} π D /2 1 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 }}]
Tarcer ˋ TFI ( D , p 2 , { 0 , 0 , 3 , 2 , 0 } , ( 4 0 2 0 1 0 0 0 1 0 ) ) \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) Tarcer ˋ TFI D , p 2 , { 0 , 0 , 3 , 2 , 0 } , 4 2 1 0 1 0 0 0 0 0
( p ⋅ q1 ) 3 ( p ⋅ q2 ) 2 ( q1 2 ) 4 . ( q2 2 ) 2 . ( q1 − p ) 2 . ( q1 − q2 ) 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} ( q1 2 ) 4 . ( q2 2 ) 2 . ( q1 − p ) 2 . ( q1 − q2 ) 2 ( p ⋅ q1 ) 3 ( p ⋅ q2 ) 2
a1 Tarcer`TBI[ D , pp^ 2 , {{ 1 , 0 }, { 1 , 0 }}] + b1 Tarcer`TBI[ D , mm1, {{ 1 , 0 }, { 1 , 0 }}]
a1 Tarcer ˋ TBI ( D , pp 2 , ( 1 0 1 0 ) ) + b1 Tarcer ˋ TBI ( D , mm1 , ( 1 0 1 0 ) ) \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) a1 Tarcer ˋ TBI ( D , pp 2 , ( 1 1 0 0 ) ) + b1 Tarcer ˋ TBI ( D , mm1 , ( 1 1 0 0 ) )
TarcerToFC[ % , { q1, q2}, ScalarProduct -> {{ pp^ 2 , p1}, { mm1, p1}}, FCE -> True ]
a1 q1 2 . ( q1 − p1 ) 2 + b1 q1 2 . ( q1 − p1 ) 2 \frac{\text{a1}}{\text{q1}^2.(\text{q1}-\text{p1})^2}+\frac{\text{b1}}{\text{q1}^2.(\text{q1}-\text{p1})^2} q1 2 . ( q1 − p1 ) 2 a1 + q1 2 . ( q1 − p1 ) 2 b1