In field theory: [H,P]=0 So shouldn't that mean there can be no scattering? If you have momentum state |p1p2> then it is an eigenvalue of P with eigenvalue p1+p2. But it should be a simultaneous eigenstate of H too, so e^(-iHt)|p1p2>= |p1p2> up to a phase factor. But in general, |p1p2> can go into |p3p4> so long as p1+p2=p3+p4. However, the above argument seems to say that |p1p2> must stay at |p1p2>.