= Schwinger correction to the electron magnetic moment
{c}
{title2=$a_e=\alpha/(2\pi)+O(\alpha^2)$}
The first <QED> <radiative correction> predicts a positive <anomalous magnetic moment>. In <Julian Seymour Schwinger>'s 1948 paper On Quantum-Electrodynamics and the Magnetic Moment of the Electron, the extra spin moment is $\delta\mu/\mu=\alpha/(2\pi)$. His $e^2/(\hbar c)$ uses the unrationalized charge convention; in rationalized <natural units> the same <fine-structure constant> is $\alpha=e^2/(4\pi)$. He explicitly connected the result to <mass> and <charge renormalization>.https://physics.umd.edu/grt/taj/624c/Schwinger_AnomalousMoment.pdf[p. 416: free-electron mass and experimental charge; additional spin magnetic moment]{ref}
In the <electron spin g-factor> convention used here,
$$
a_e^{(1)}=\frac{\alpha}{2\pi},\qquad
g_s=2\left(1+\frac{\alpha}{2\pi}+O(\alpha^2)\right).
$$
For the deliberately rounded teaching input $\alpha=1/137$, $a_e^{(1)}\simeq0.0011617149$ and $g_s^{(1)}\simeq2.0023234298$. The correction is about $0.116\%$ of the <Dirac equation> spin moment. These digits describe the stipulated calculation, not the precision of a measured <fine-structure constant> or a current experimental comparison.
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