Srednicki — Quantum Field Theory · Problem 81.6

Canonical Quantization of Scalar Fields — Mark Srednicki

Physics — QFT · scattering-qcd

Problem

Consider the partial amplitude

A(1^-_{\bar{q}}, 2^+_q, 3^-, 4^+, 5^+)

. Show that, with the choice

q_3 = k_2

and

q_4 = q_5 = k_1

, there are just two contributing diagrams. Evaluate them. After some manipulations, you should be able to put your result in the form

A(1^-_{\bar{q}}, 2^+_q, 3^-, 4^+, 5^+) = \frac{\langle 1\,3\rangle^3 \langle 2\,3\rangle}{\langle 1\,2\rangle\langle 2\,3\rangle\langle 3\,4\rangle\langle 4\,5\rangle\langle 5\,1\rangle} . \tag{81.60}