In classical electrodynamics (CED), the most important quantities are the electric and magnetic fields, which directly determine the forces. In quantum electrodynamics (QED), the potentials are the most important quantities; they determine the energy and momentum exchange between the EM field and matter. Gauge invariance, which in CED is just a mathematical curiosity, becomes fundamental in QED, ruling the gauge symmetry that determines the interaction itself.

The Lamb experiment that opened the way is discussed in detail.

Feynman diagrams are graphic representations of mathematical expressions of scattering or decay amplitudes. Without going into the mathematics, we use them to visually suggest the underlying physics. We show how the propagator describes virtual particles, and how uncertainty and relativity principles, joined, imply the existence of antimatter.

The fine-structure constant, which is the dimensionless expression of the electromagnetic charge, depends on the momentum transfer between the probe and the target charge in the scattering experiment we are performing. The ‘running’ of the coupling constants is a property of all the interactions.

The highest precision measurements and theoretical predictions of the magnetic moments of the electron and of the muon. The precision frontier to search for new physics.

Chapter 5 described quantum mechanics in the context of particles moving in a potential. This application of quantum mechanics led to great advances in the 1920s and 1930s in our understanding of atoms, molecules, and much else. But, starting around 1930 and increasingly since then, theoretical physicists have become aware of a deeper description of matter, in terms of fields. Just as Einstein and others had much earlier recognized that the energy and momentum of the electromagnetic field is packaged in bundles, the particles later called photons, so also there is an electron field whose energy and momentum is packaged in particles, observed as electrons, and likewise for every other sort of elementary particle. Indeed, in practice this is what we now mean by an elementary particle: it is the quantum of some field that appears as an ingredient in whatever seem to be the fundamental equations of physics at any stage in our progress.