Show that in the nonrelativistic limit, the Gordon decomposition, (6.7), of the electron current, (6.6), separates the electron interaction with an electromagnetic field $A_\mu$ into a part arising from its charge, $-e$, and a part due to its magnetic moment, $-e / 2 m$. Assume that $A_\mu$ is independent of $t$, so that (6.4) becomes
$$
T_{f i}=-i 2 \pi \delta\left(E_f-E_i\right) \int j_\mu^{f i} A^\mu d^3 x
$$
To identify the magnetic moment interaction $(-\mu \cdot \mathbf{B})$, it suffices to show that
$$
\int\left[-\frac{e}{2 m} \bar{\psi}_f i \sigma_{\mu \nu}\left(p_f-p_i\right)^\nu \psi_i\right] A^\mu d^3 x=\int \psi_A^{f \dagger}\left(\frac{e}{2 m} \boldsymbol{\sigma} \cdot \mathbf{B}\right) \psi_A^j d^3 x,
$$
where $\psi_A$ denotes the upper two (or "large") components of $\psi$; compare with eqs. (5.31) and (5.32).