ABSTRACT
We begin our study of electromagnetic interactions by considering the simplest case, that of the scattering of a (hypothetical) positively charged spin-0 particle ‘s+’ by a fixed Coulomb potential, treated as a classical field. This will lead us to the relativistic generalization of the Rutherford formula for the cross section. We shall use this example as an exercise to gain familiarity with the quantum field-theoretic approach of chapter 6, since it can also be done straightforwardly using the ‘wavefunction’ approach familiar from nonrelativistic quantum mechanics, when supplemented by the work of chapter 3. We shall also look at ‘s−’ Coulomb scattering, to test the antiparticle prescriptions of chapter 3. Incidentally, we call these scalar particles s± to emphasize that they are not to be identified with, for instance, the physical pions π ±, since the latter are composite https://www.w3.org/1998/Math/MathML"> ( q q ¯ ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429185380/ff4bb25b-a24f-4cfc-aaf9-29987e8a57ff/content/ieq0842.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> systems, and hence their interactions are more complicated than those of our hypothetical ‘point-like’ s± (as we shall see in section 8.4). No point-like charged scalar particles have been discovered, as yet.
