$L_{QED}=ψˉ (iℏcD/−mc_{2})ψ−4μ_{0}1 F_{μν}F_{μν}$

- $F$ is the electromagnetic tensor

Note that this is the sum of the:Note that the relationship between $ψ$ and $F$ is not explicit. However, if we knew what type of particle we were talking about, e.g. electron, then the knowledge of psi would also give the charge distribution and therefore $F$

- Dirac Lagrangian, which only describes the "inertia of bodies" part of the equation
- the electromagnetic interaction term $4μ_{0}1 F_{μν}F_{μν}$, which describes term describes forces

As mentioned at the beginning of Quantum Field Theory lecture notes by David Tong (2007):

- by "Lagrangian" we mean Lagrangian density
- the generalized coordinates of the Lagrangian are fields

Like the rest of the Standard Model Lagrangian, this can be split into two parts:

- spacetime symmetry: reaches the derivation of the Dirac equation, but has no interactions
- add the $U(1)$ internal symmetry to add interactions, which reaches the full equation