36.21Vacuum Polarization

Vacuum polarization is an important effect in effectively reducing the charge on a particle. The
reduction is dependent on distance and hence on the energy scale.

The termVacuum Polarizationis descriptive of the effect. A charged particle will polarize the
vacuum in a way analogous to the way a dielectric is polarized. Avirtual electron positron pair
in the vacuum will be affected by the charge. If the original chargedsource is a nucleus for example,
the virtual electron will be attracted and the virtual positron repelled, causing a net polarization of
the vacuum whichscreens the nuclear charge. At very short distances from the nucleus, the bare
charge is seen, while at long distances the screening is important. This causes the basic couplingα
to vary a bit with distance and therefore with energy. This polarization of the vacuum is similar
to the polarization of a dielectric material. In this case, what is being polarized are the virtual
electrons and positrons in the vacuum. Of course other particles than the electron can be polarized
in the vacuum so theenergy variation of the coupling “constant”is an interesting subject for
research.

The effect of vacuum polarization on Hydrogen would be to lower the energy ofsstates relative
to others since they are close to the nucleus and therefore see anunscreened charge. This effect is
actually rather small even compared to the Lamb shift and of opposite sign. Vacuum Polarization
has larger effects at higher energies at which shorter distances are probed. In fact we can say that the
electromagnetic coupling varies slowly with the energy scale, increasing (logarithmically) at higher
energies. This is referred to as the running of the coupling constant.

We can get some qualitative understanding of the origin ofZitterbewegungfrom the idea of virtual
pair production in the field of the nucleus. The diagram below shows a photon from the Coulomb
field of the nucleus producing an electron positron pair. The originalreal electron from the atom
then anihillates with the positron, coupling to another field photon. The electron from the pair is
left over and becomes the new atomic electron, however, it need not be in the same place as the
original electron.

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