I am currently struggling with the formula for an exact current in QFT, a fermion with an upcoming momentum $p$ and an outgoing momentum $p'$. My problem is to show whether or not a term of the form $\bar{u}(p')F(q^2)i\sigma^{\mu\nu}(p+p')^{\nu}$ where $\sigma^{\mu\nu}=\frac{i}{2}[\gamma^{\mu},\gamma^{\nu}]$. I would like it to be forbidden by current conservation but I can't prove it, is my intuition wrong?
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Your term is allowed, and in fact present in QED. It gives the anomalous magnetic form factor contribution to the current. In QED, The number $2F(0)$ is the anomalous magnetic moment of the electron. See Peskin/Schroeder p.186-188.
answered Mar 14, 2012 at 14:07
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$\begingroup$ Thanks, managed to show that this term is proportional to $\bar{u}(p')\gamma^{\mu}u(p)$ by using the Dirac equation. $\endgroup$– tootCommented Mar 15, 2012 at 17:56