Propagator Methods

Our aim is calculate transition rates and cross-sections. We begin with a general discussion of the scattering process. The scattering process will be defined in terms of integral equations with boundary conditions incorporating the Stückelberg-Feynman physical interpretation of the positron as a negative-energy electron moving backwards in time.

There are two approaches we could take: 1) a systematic approach of quantizing the field, or 2) the propagator formalism which is more intuitive and leads to being able to perform calculations quickly. The propagator method describes scattering by means of integral equations. Start with scattering processes in the framwork of Dirac's theory (relativistic from beginning), the calculations are exact in principle but practically they will be carried out using perturbation theory (i.e. an expansion in terms of small interaction parameters). Although Stückelberg started the relativistic propogator idea, Feynman exploited it in calculations. J. Schwiger and S. Tomonaga gave alternative formalism and all three were awarded the Nobel Prize in 1965 for the development of quantum electrodynamics.

Quantum electrodynamics (QED) is one of the most successful and most accurate theories known in physics. QED is the archetype for all modern field theories, and important in its own right since it provides the theoretical foundation for atomic physics. The theory also applies to heavy leptons ($\mu$ and $\tau$), and in general can be used to describe the EM interaction of other charged elementary particles.