Compton Scattering
A full lecture reconstruction showing why naive low-order perturbative QED corrections to particle energies are problematic, why Compton scattering is the first clean finite order-α process, and how Lorentz-invariant scattering amplitudes emerge only after coherent addition of all electron and positron intermediate-state processes.
Introduction
This lecture marks a real turning point in the course.
Up to now, perturbative QED has been introduced in a very structural way: - the full Coulomb-gauge QED Hamiltonian was written down, - the fine-structure constant \(\alpha\) was identified as the small expansion parameter, - and time-independent perturbation theory was used to study the vacuum and one-electron states.
That already revealed something important and uncomfortable: the apparently simplest perturbative questions are not actually the easiest ones.
A full lecture reconstruction introducing perturbative quantum electrodynamics from the Coulomb-gauge Hamiltonian, identifying the fine-structure constant as the small expansion parameter, and using time-independent perturbation theory to analyze the QED vacuum and one-electron states.
A full lecture reconstruction introducing path integrals as a Lagrangian reformulation of quantum mechanics, starting from the Feynman–Hibbs phase-space path integral, then developing coherent-state path integrals for bosons and Grassmann coherent-state path integrals for fermions as preparation for Lagrangian perturbation theory in QFT.