QED is the field theory that describes the interaction between the photon and the charged fermions. In the Lorentz gauge [see Equations (4.21) and (4.22)], the Lagrangian is given by
L = − 14 Fµν(x)F µν(x) − 12 α ( ∂µ Aµ(x)
)2 + ∑ f
f (x)(iγ µ Dµ − m f ) f (x).