I Lamb shift and the QFT vacuum....

[asimov42]

I think I already know the answer to this, but I'm looking for a source: Can the Lamb shift be explained entirely in terms of radiative corrections due to the self-interaction of the hydrogen's electron with its own EM field? That is, is it necessary to reference vacuum polarization or related concepts (vacuum fluctuations, etc.)?

 

[A. Neumaier]

The Lamb shift is always calculated from a Dirac equation for a single electron in a Coulomb field, with radiative corrections incorporated into a form factor due to the interaction with the quantized electromagnetic field - the vacuum is not involved at all.

The computation of the form factor at lowest order involves the evaluation of an integral corresponding to a Feynman diagram, and hence has (like any perturbative calculation in quantum field theory) an interpretation in terms of vacuum expectation values of the bare, unphysical, free theory. The latter is responsible for the misleading talks about vacuum fluctuations as if that were something physical.

On the other hand, vacuum polarization is a real physical contribution to the photon self-energy; it has almost nothing to do with the Lamb shift, contributing only a small fraction.

 

[vanhees71]

A minor part of the Lamb shift is also the vacuum polarization of the photon (according to Weinberg, QT of Fields, Vol. 1, its contribution is -37.13 MHz, which is indeed small compared to the total of ~1058 MHz). Of course "vacuum polarization" is just a name for the radiative corrections to the photon propagator and has nothing to do with vacuum fluctuations but with fluctuations of the photon and charged-matter fields in the Standard Model.

 

[DrClaude]

Closed pending moderation.

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