Lamb shift and the QFT vacuum....

In summary, the Lamb shift can be explained entirely in terms of radiative corrections to the electron's interaction with the quantized electromagnetic field, without involving vacuum polarization or related concepts such as vacuum fluctuations. However, a small contribution from vacuum polarization is still present.
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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.)?
 
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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.
 
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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.
 
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Edit (Dale): a large number of thread hijack posts have been removed
 
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FAQ: Lamb shift and the QFT vacuum....

What is the Lamb shift and how does it relate to QFT vacuum?

The Lamb shift is a small but significant difference in the energy levels of an electron in a hydrogen atom, compared to what is predicted by the Schrodinger equation. This shift was first discovered by physicist Willis Lamb in 1947, and it was later explained by quantum electrodynamics (QED), which is a type of quantum field theory (QFT) that describes the interactions between light and matter.

How does QFT explain the Lamb shift?

In QFT, the vacuum is not an empty void, but rather a sea of virtual particles constantly popping in and out of existence. These virtual particles interact with the electron in the hydrogen atom, causing a small change in its energy levels and resulting in the Lamb shift. This phenomenon is known as vacuum polarization, and it is a key concept in understanding the Lamb shift.

Can the Lamb shift be observed experimentally?

Yes, the Lamb shift has been observed in numerous experiments, including precision measurements of the energy levels of hydrogen atoms using spectroscopic techniques. The Lamb shift is an extremely small effect, but modern technology allows us to measure it with great accuracy.

Are there other examples of QFT vacuum effects in particle physics?

Yes, the vacuum polarization effect that causes the Lamb shift is just one example of how the vacuum can influence the behavior of particles. QFT predicts the existence of other vacuum effects, such as the Casimir effect, which is the attractive force between two parallel metal plates in a vacuum.

What are the implications of the Lamb shift and QFT vacuum for our understanding of the universe?

The Lamb shift and other QFT vacuum effects demonstrate the complex and dynamic nature of the vacuum in our universe. They also highlight the importance of quantum field theory in understanding the fundamental interactions between particles and the role of the vacuum in these interactions. These concepts have greatly advanced our understanding of the universe and continue to be a subject of ongoing research in particle physics.

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