LXII. On the use of canonical transformations for collision problems

Abstract

Summary A perturbation theory for collisions between free particles is developed by means of a canonical transformation with the following features : 1. (i) The state of a free particle is redefined by inclusion of its virtual quanta.2. (ii) The self-energies of all states are included in the definition of the energies.3. (iii) The amplitude of the collision cross-section is given by an integral equation whose kernel is the transformed Hamiltonian and is given by an expansion in powers of the coupling parameter. A simplified derivation for the higher order corrections to the Compton effect is given and the analogous problem of meson scattering is discussed.