Why Does Term Not Appear in Classical Lagrangian for Spin 1/2 Electrodynamics?

[dextercioby]

There's been quite a while since reading some serious physics, so i forgot some key points. The question I'm about to ask may seem trivial for a knowledgeable person, but I can't find the answer and I thought it is easier to get a right answer here, than wondering through a dozen of QFT books.

So here goes:

Why does the term

$$\frac{e}{2} \bar{\Psi} (x) \Sigma^{\mu\nu} F_{\mu\nu}(x) \Psi (x)$$

NOT appear in the classical lagrangian for the spin 1/2 parity invariant electrodynamics ?

p.s. I hope the notation is obvous, Sigma is the spin matrix = <i/2> times the commutator of the gamma matrices, the F is the e-m field tensor and the big Psi-s are the Dirac spinors.

 

[Bob_for_short]

There is a couple of reasons; one of them - the theory is non-renormalizable with this term.

If you consider a usual, non secondary quantized Dirac equation, this term is allowed in dynamics of charged hadrons (protons) with an anomalous magnetic moment.

 

[dextercioby]

I don't know why they got you banned, but can you sustain your <non-renormalizability> reasoning with some article published in a peer-reviewed journal or a book on QFT/QED ?

Thank you.

P.S. This question is, of course, again open to other people as well, since this is (up to moderation) a free forum.

LATE EDIT: Okay, I've seen the argumentation in the first volume of Weinberg's book on QFT. It's due to <power counting> and the nonrenormalizability is induced by the presence of the derivative in the e-m tensor.