The Dirac equation with anomalous magnetic moment term

[mtak0114]

Hi could someone please explain the story (if there is one) about the Dirac equation with an anomalous magnetic moment term, I have seen this in several old papers but it never seems to be mentioned in textbooks. Was this an old confusion in formulating QFT. In this context I believe the Dirac equaiton with pauli term takes on the following form:

$-i\gamma^\mu(\partial_\mu-ieA_\mu)\psi + m\psi - (\frac 12 g-1)\frac{i e}{2m}F_{\mu\nu} S^{\mu\nu}\psi = 0$

where $S^{\mu\nu}$ are the generators of SL(2,C) and $F_{\mu\nu}$ is the electromagnetic tensor. I've never seen this extra term could you please tell me what it represents and if it is needed why

thanks in advanced

 

[Bill_K]

mak, You're quite right, this expression was used in the early days but no more. In the first place, for the electron the "anomalous" σ^μν term is absent. Well then, the original idea was to use this more general form to describe protons and neutrons, which do have an anomalous magnetic moment. However for any situation where the Dirac equation is needed, this form is not general enough. The interaction needs to be expressed in terms of Form Factors F₁ and F₂ which are functions of momentum.

In momentum space, the electromagnetic interaction for these particles can be written as F₁(q²) γ^μ + F₂(q²) σ^μνq_ν.