The QED Lagrangian is given by [tex]\mathcal{L}_{\hbox{QED}} = \bar{\psi}(i\partial - m)\psi(adsbygoogle = window.adsbygoogle || []).push({});

- \frac{1}{4}(F_{\mu\nu})^2 - e\bar{\psi}\gamma^\mu\psi A_\mu[/tex]

What is the purpose of the middle term. I know that it represents the energy of the E and B fields. However is that due to the external potential A? I am used to thinking about Lagrangians in terms as equal to the kinetic term minus the potential, T-V. This term doesn't seem to be either and nor does the final interaction term. I didn't put the slash in the partial derivative because I didn't know how to. I understand that it is really a sum of three seperate Lagrangians, that is, [tex]\mathcal{L}_{\hbox{QED}} = \mathcal{L}_{\hbox{Dirac}} + \mathcal{L}_{\hbox{Maxwell}} + \mathcal{L}_{\hbox{int}}.[/tex] What does the middle term represent or what does it do for us?

Thanks a Million.

-EVAC

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Why is the Electromagnetic Field Tensor in the QED Lagrangian?

**Physics Forums | Science Articles, Homework Help, Discussion**