Lagrangian of the electron field is the heart of how electrons behave in quantum field theory. There are two layers to this:

• Electron interacting with electromagnetism (real world)
• Electron by itself (free field)

Electrons aren’t isolated — they interact with the electromagnetic field$A_\mu(x)$Aμ​(x).

This term produces Coulomb force, magnetic force, photon emission, photon absorption and All QED Feynman diagrams.