Physical Origin of the Lamb Shift

According to QED an electron continuously emits and absorbs virtual photons (see the leading order diagram in Fig. 2.1) and as a result its electric charge is spread over a finite volume instead of being pointlike  

In order to obtain this estimate of the electron radius we have taken into account that the electron is slightly off mass shell in the bound state. Hence, the would be infrared divergence in the electron charge radius is cut off by its virtuality p = m which is of order of the nonrelativistic binding 

The finite radius of the electron generates a correction to the Coulomb potential (see, e.g., [2]) 

It is very easy to estimate this splitting (shift of the S level energy) 

Another obvious contribution to the Lamb shift of the same leading order is connected with the polarization insertion in the photon propagator (see Fig. 2.2). This correction also induces a correction to the Coulomb potential 

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