# Identity of Term in Lagrangian

The following term appeared in a Lagrangian I found

$$\bar{\psi}\sigma^{\mu \nu}\psi F_{\mu \nu}.$$

I have never seen this term before, or even the $\bar{\psi}\sigma^{\mu \nu}\psi$ tensor. I was wondering what the physical interpretation of these terms are. It appears to be a coupling between the fields and the particles but it is different from previous Lagrangians terms of this form that I have seen previously.

• Although I could guess it, it's always good to define your notation - what is $\sigma^{\mu\nu}$? – ACuriousMind Nov 16 '16 at 16:10
• It's the commutator of the gamma matrices $[\gamma^{\mu}\gamma^{\nu}]$ – T-Ray Nov 16 '16 at 19:33