SOLVED March 1, 2021! The calculation of the anomalous magnetic moment is done in the magnetic part of the Gordon decomposition. The Feynman diagram and the calculation rules in this case concern interaction with a magnetic field only. In our blog, Feynman diagrams have always been about the Coulomb interaction between charges. That caused the confusion.
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If the electron were a point charge which moves along a circular path with the angular momentum equal to the spin of the real-world electron, then its magnetic moment would be exactly 1/2 of the value predicted by the Dirac equation.
The charge in the electron seems to rotate at 2X the radius of the mass of the electron.
Julian Schwinger in 1948 calculated the QED correction to the gyromagnetic ratio
g_e = 2 + α / π + ...,
where α is the fine structure constant ~ 1/137.
The modern calculation is based on the vertex function of QED. The integral has to be regularized to remove both an infrared divergence and an ultraviolet divergence. QED predicts the measured g_e - 2 with an impressive 10 significant figures.
virtual photon q
~~~~~
\
\
e- --------------------------------
\ /
~~~~~~
virtual photon p
If the vertex function concerns all absorptions of virtual photons by electrons, then it should affect the response of the electron in the Millikan-Fletcher experiment. The measured charge of the electron would appear larger than the "bare" charge. Let the coefficient be, for example, 1.001.
If the Dirac equation is about the bare charge of the electron, then if we use the measured charge in calculations, we already exaggerate the magnetic moment by the factor 1.001. The bare charge, which is assumed to be spinning, is a little smaller than the measured charge.
Why would we need to include the factor 1.001 the second time when we measure the electron magnetic moment in a Penning trap?
Let us check the literature. Has anyone thought about this and come up with an explanation?
How can QED predict the electron anomalous magnetic moment so precisely? Why regularization works?
There is also another mystery in the electron anomalous magnetic moment: how can the Feynman diagram approximation be so precise? The reason might be that the phenomenon is so weak that the perturbative approximation yields good results. The first term, α / π, already calculates the experimental value with a precision of 2 / 1,000. The QED prediction is obtained from the sum of third order diagrams. With good luck, the current precision of 1 / 10^9 is possible.
The prediction of QED depends on regularization, that is, an ad hoc removal of the ultraviolet and infrared divergences in the integrals. Since the prediction is correct, regularization has to be the "right" way to remove the infinities. Why?
A hypothesis is that regularization is the right way to treat an "effective field theory", where infinities arise from extrapolating the known physics to the Planck scale and beyond.
However, it is not clear to us why removing infrared divergences would be associated with the Planck scale.
Our hypothesis in this blog has been that the infinities are removed by analyzing the path integral in position space, not in the conventional momentum space.
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