# Does $2\to 2$ particle scattering occur in a plane?

I am reading a physics textbook which implicitly uses this assumption in dealing with photon electron scattering. In general, I don't see why this is true. I can imagine the first two particle momenta spanning the x-y plane and the second two spanning the x-z plane, for instance, as long as the z-components of the final momenta are equal and opposite.

• They are probably using the center of mass frame, in which the scattering does occur in a plane. – Javier Oct 11 '17 at 20:59
• You can always perform a Lorentz transformation to a frame where the scattering is in a plane. – Prahar Oct 11 '17 at 21:24
• @Prahar I am looking specifically at Schwartz's QFT problem 9.1. where he considers $\gamma \phi \to \gamma \phi$ in scalar QED in the COM frame. Now it is clear to me that there exists some frame where scattering is in a plane. But I don't see why it holds for the COM frame. – Dwagg Oct 12 '17 at 19:50
• @Javier (I tried to tag you as well) – Dwagg Oct 12 '17 at 19:50
• It holds in the COM frame because the initial velocities are parallel and hence don't define a plane, only a line, and the same happens for the final velocities. Therefore, initial+final velocities define a plane. – Javier Oct 12 '17 at 19:52