Here, we present the calculations of the self-energy of photon and
electron. First the renormalization scheme of photon is discussed in connection with
the triangle diagrams which have no divergence at all, and therefore the self-energy
of photon is not related to any physical observables. Then, we discuss the renormalization
scheme of fermion self-energy term which is still connected with the vertex
correction in QED. Also, we discuss briefly the physics of Lamb shifts which should
be treated in detail in chapter 7. Then, we present the calculation of the photonphoton
scattering cross section and some possible experiments on the photon-photon
cross section. Finally, the problem of the chiral anomaly equation is discussed, and
we see that there are neither anomaly equation nor the violation of the axial current
conservation in physical world.
Keywords: renormalization scheme, self-energy of photon and fermion, local gauge
invariance, Lamb shifts, photon-photon scattering, chiral anomaly equation.
