FeynCalc manual (development version)

SquareAmplitude

SquareAmplitude[m1, m2] multiplies the amplitudes from the list m1 with their complex conjugate from the list m2 to obtain the list of products m1im2jm1_i m2_j. This function can be useful when exporting amplitudes obtained with FeynCalc to FORM.

See also

Overview

Examples

Clear[a1, a2, a3, b1, b2, b3]
SquareAmplitude[{a1, a2, a3}, {b1, b2, b3}]

{a1  b1,a1  b2,a1  b3,a2  b1,a2  b2,a2  b3,a3  b1,a3  b2,a3  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]

a1  b1+a1  b2+a1  b3+a2  b1+a2  b2+a2  b3+a3  b1+a3  b2+a3  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}

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]

a1  b1+2  a2  b1+a2  b2+2  a3  b1+2  a3  b2+a3  b3\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]

a1  b1  mark(1,1)+2  a2  b1  mark(2,1)+a2  b2  mark(2,2)+2  a3  b1  mark(3,1)+2  a3  b2  mark(3,2)+a3  b3  mark(3,3)\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)