Motion between events

Last lesson ended on a cliffhanger. The interaction term gave us a vertex — an event at a single point of spacetime, where two electron lines and a photon line meet. But an event at a point is not yet a process. A real calculation connects events: a photon emitted here is absorbed there; an electron created at one vertex travels to another before it interacts again.

Something has to carry the disturbance across the gap. That something is the propagator — the factor a Feynman diagram attaches to every internal line, the lines that begin and end on vertices rather than running off to a detector.

It is the second of three ingredients in the Feynman rulebook: the vertex (done), the propagator (this lesson), and the external-leg factors for the particles that actually come in and go out (next lesson).

This lesson derives QED's two propagators — one for the photon, one for the electron — straight from the free Lagrangian. There is one beautiful subtlety waiting in the photon case. Let's first say precisely what a propagator is.