Quantum Field Theory and the Standard Model by Schwartz M.D. z-lib.org · Problem 4.1

Old-fashioned perturbation theory — Schwartz M.D. z-lib.org

Physics — QFT · old-fashioned-perturbation-theory-transition-matrix

Problem

Calculate the transition matrix element

T_{ij}

for the process

e^+e^- \to \gamma \to \mu^+\mu^-

. ((a)) Write down the

\frac{1}{E_i - E_0}

terms for the two possible intermediate states, from the two possible time slicings. ((b)) Show that they add up to

\frac{2E_\gamma}{k^2}

, where

k_\mu

is now the 4-momentum of the virtual off-shell photon.