# Is it reasonable to interpret the Lamb shift as vacuum induced Stark shifts?

This is a pretty hand-wavy question about interpretation of the Lamb shift. I understand that one can calculate the Lamb shift diagrammatically to get an accurate result, but there exist "interpretations": For example, one can say something like "the fluctuating vacuum E-field causes the electron to wiggle in it's potential, hence see an averaging of the 1/r potential which manifests as a $\sim \delta(r)$ perturbation." (This is from Atom Photon Interactions).

Is the following interpretation reasonable? "The vacuum E-field fluctuation induces a Stark shifts. We know for a ground state the Start shift is negative for red detuning ($\omega-\omega_0<0$, where $\omega_0$ is the resonance frequency between a ground and excited state), and the shift is positive for blue detuning ($\omega-\omega_0>0$). Since $\omega \in [0,\infty)$, there are more blue shifts than red shifts, hence the ground state gets shifted upwards (which is consistent which the effect of the Lamb shift)."

My only concern with this interpretation is that it implies that an excited state (typically a P-state in Hydrogen, for example), should also get a negative shift, but we know that up to 2nd order diagram calculations that it does not (of course, it may in higher order?).

Any discussion would be helpful. Thanks.

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An interesting interpretation! Do you know how to convert it to a calculation, at least an approximate one? –  Luboš Motl Apr 18 '13 at 4:38