Ultraviolet divergencies regularization and renormalization

The radiative corrections depicted in Fig.l describe the interaction of the electron with the virtual photons (SE) and with vacuum electric current (VP). This interaction results in the shift of the atomic energy levels (Lamb Shift). It appears that not only the energy of the vacuum but also the energy of the interaction between atomic electron and the vacuum is infinite. Unlike the infinite vacuum energy the infinite interaction energy cannot be simply subtracted and a sophisticated procedure of renormalization is required to 

It can be shown that aJl the possible divergences in QED can be reduced to the combinations of these three bsisic ones. 

Now we can introduce the exact propagators for the electrons (p) and photons G k) in the momentum space. The propagator arises after 

Compact a) and noncompact b) second-order photon self-energy graphs. 

There is no general relation between the vertex r (piP2fe) and the propagators QpJ k). Still such a relation exists in an important particular case, when Pi = P2- This relation is called the Ward identity . It is convenient to introduce the short vertex  

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