- #1
center o bass
- 545
- 2
For a phi-four theory the LSZ reduction formula, as stated in peskin and schroeder essentially boils down to
$$\langle \vec{p'_1},\vec{p'_2}, \ldots ,\vec{p'_m}| S| \vec{p_1}, \vec{p_2}, \ldots, \vec{p_n}\rangle = Z^{(n+m)/2} \mathcal{M}_{\text{on shell}}$$
where we have n incoming and m outgoing particles and ##\mathcal M## is the amputated amplitude for the physical process. I know LSZ-reduction also exist for photons and electrons, and that there it is related to the field strength renormalization factors ##Z_2## and ##Z_3##. I know that Srednicki writes about this, but he uses quite another approach than peskin and schroeder. So what is the corresponding formula for a QED process? For two would it for example be correct to write
$$\langle \vec{k_1}, \vec{k_2}|S |\vec{p_1}, \vec{p_1}\rangle = Z_2 Z_3 \mathcal{M}_{\text{on shell}}$$
for a process involving two outgoing photons with k-momenta and two incoming electrons with p-momenta?
$$\langle \vec{p'_1},\vec{p'_2}, \ldots ,\vec{p'_m}| S| \vec{p_1}, \vec{p_2}, \ldots, \vec{p_n}\rangle = Z^{(n+m)/2} \mathcal{M}_{\text{on shell}}$$
where we have n incoming and m outgoing particles and ##\mathcal M## is the amputated amplitude for the physical process. I know LSZ-reduction also exist for photons and electrons, and that there it is related to the field strength renormalization factors ##Z_2## and ##Z_3##. I know that Srednicki writes about this, but he uses quite another approach than peskin and schroeder. So what is the corresponding formula for a QED process? For two would it for example be correct to write
$$\langle \vec{k_1}, \vec{k_2}|S |\vec{p_1}, \vec{p_1}\rangle = Z_2 Z_3 \mathcal{M}_{\text{on shell}}$$
for a process involving two outgoing photons with k-momenta and two incoming electrons with p-momenta?