Scattering in Quantum Field Theory

We show that the use of the perturbation expansion around the free field Hamiltonian imposes severe constraints for the scattering formalism to be applicable. We present the physical assumptions which are necessary in order to define the asymptotic states and the scattering matrix in quantum field theory. A very important physical requirement is the property of short range for all interactions, which implies the absence of zero mass particles. We derive the reduction formula and obtain the Feynman rules for the scattering amplitude. We give examples of low order computations for the electron Compton scattering, the electron–positron annihilation into a muon pair and the decay of charged pions.