Calculating Traces with FeynCalc II

In the previous section we did the spin spums by hand in order to transform them in traces and than used FeynCalc to do the traces. But this can handled in a different way which much simpler. specially for many diagrams. We use the example above of Bhabha Scattering ( $e^- e^+ \rightarrow e^- e^+$) in QED

The relevant matrix element can be written as

$M= M_1 + M_2$

where

$$M_1=\frac{e^2}{t} \overline{u}(p_3) \gamma^{\mu} u(p_1) \overline... ...s} \overline{v}(p_2) \gamma^{\mu} u(p_1) \overline{u}(p_3) \gamma_{\mu} v(p_4)$$

with

$s=(p_1+p_2)^2, \qquad t=(p_1-p_3)^2$.

Now we can use FeynCalc to perform the fermion spin sums for you. You have to use the FeynCalc function FermionSpinSum. The mathematica program that evaluates the spin sums using this technique is Bhabha-SpinSums.nb.