SquareAmplitude[m1, m2] multiplies the amplitudes from
the list m1 with their complex conjugate from the list
m2 to obtain the list of products m1_i m2_j. This function can be useful when
exporting amplitudes obtained with FeynCalc to FORM.
Clear[a1, a2, a3, b1, b2, b3]SquareAmplitude[{a1, a2, a3}, {b1, b2, b3}]\{\text{a1} \;\text{b1},\text{a1} \;\text{b2},\text{a1} \;\text{b3},\text{a2} \;\text{b1},\text{a2} \;\text{b2},\text{a2} \;\text{b3},\text{a3} \;\text{b1},\text{a3} \;\text{b2},\text{a3} \;\text{b3}\}
SquareAmplitude[{a1, a2, a3}, {b1, b2, b3}, List -> False]\text{a1} \;\text{b1}+\text{a1} \;\text{b2}+\text{a1} \;\text{b3}+\text{a2} \;\text{b1}+\text{a2} \;\text{b2}+\text{a2} \;\text{b3}+\text{a3} \;\text{b1}+\text{a3} \;\text{b2}+\text{a3} \;\text{b3}
When the option Real is set to True, the
amplitudes are assumed to have no imaginary part
SquareAmplitude[{a1, a2, a3}, {b1, b2, b3}, Real -> True, List -> False]\text{a1} \;\text{b1}+2 \;\text{a2} \;\text{b1}+\text{a2} \;\text{b2}+2 \;\text{a3} \;\text{b1}+2 \;\text{a3} \;\text{b2}+\text{a3} \;\text{b3}
The option Indexed allows us to attach a marker to each
contribution
SquareAmplitude[{a1, a2, a3}, {b1, b2, b3}, Real -> True, List -> False, Indexed -> mark]\text{a1} \;\text{b1} \;\text{mark}(1,1)+2 \;\text{a2} \;\text{b1} \;\text{mark}(2,1)+\text{a2} \;\text{b2} \;\text{mark}(2,2)+2 \;\text{a3} \;\text{b1} \;\text{mark}(3,1)+2 \;\text{a3} \;\text{b2} \;\text{mark}(3,2)+\text{a3} \;\text{b3} \;\text{mark}(3,3)