= QED Lagrangian
{synonym}
{title2}

$$
\mathcal{L}_{\mathrm{QED}} = \bar \psi (i\hbar c {D}\!\!\!\!/\ - mc^2) \psi - {1 \over 4\mu_0} F_{\mu \nu} F^{\mu \nu}
$$
where:
* $F$ is the <electromagnetic tensor>

Note that this is the sum of the:
* <Dirac Lagrangian>, which  only describes the "inertia of bodies" part of the equation
* the <electromagnetic> interaction term ${1 \over 4\mu_0} F_{\mu \nu} F^{\mu \nu}$, which describes term describes forces
Note that the relationship between $\psi$ 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 $F$

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

\Video[https://www.youtube.com/watch?v=I4CjewbJgRQ]
{title=Particle Physics is Founded on This Principle! by Physics with Elliot (2022)}


Quantum electrodynamics Lagrangian