Compton Scattering Using Mandel-Stam Variables

[americanforest]

Homework Statement

Not homework, just for fun. I want to derive Compton Scattering equations using Mandel-Stam variables as opposed to the way that I have done it in class using the usual energy and momentum conservation

Homework Equations

$$(p_\mu+p_{ei}_\mu)^2=(p'_\mu+p_e_\mu)^{2}=s$$
p is the momentum of incoming photon and pei is of initially stationary electron. p' is final photon and p_e_\mu is final electron.

The Attempt at a Solution

I'm going to try to do the right side in the CMS frame and the left side in the lab frame for convencience.

$$Em_e=2EE_e_$$
...skip a few easy steps using
$$E=\sqrt{p^{2}+m^{2}}$$
$$E^{2}-E'^{2}=\frac{p_e_^2}{me^{2}}$$

Which isn't right. What's wrong here?

 

[pam]

You have to do both in the lab system because you need the photon energies in the lab system. Your first equation can't be right. You can't use the same E in each system.
Stanley's name is Mandelstam. He is only one person.