A Non-Renormalized Field Theoretic Treatment of Photon Scattering

In this paper we have presented a generalized treatment of a photon scattering by a harmonic oscillator initially at ground state. We have predicted the scattering cross-section of the oscillator and showed how the treatment invariably requires the formalisms of renormalization. As a special case of our treatment, we discussed about Rayleigh and Thomson Scattering and computed the total cross-section in order to be consistent with experimental results. Two approximations are adopted in order to simplify the problem but without any digression from our goal. A second order perturbation theory is employed where the first excited state of the harmonic oscillator is considered to be the only intermediate state and A dipole approximation is utilized. Throughout this paper we have used Gaussian units.