Why do we never use the SM equations of motions? We know the Lagrangian and therefore could write down the equations of motions for all fields. In principle we could solve the equations numerically. Why do we never do that?
Would a leading order calculation for example for electron positron scattering be equivalent to solving the equations of motions when considering initial conditions where an electron and positron move towards each other?
I guess also a reason why we do not solve the equations of motions is, that quantum effects are not included, right?
