Gauge invariant calculation of vacuum polarization phenomena in quantum electrodynamics

Thesis (Ph.D.)--Boston UniversityPLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.A technique capable of describing in detail the various phenomena arising in the limit of low energy photons because of the polarization of the vacuum is obtained by quantizing the gauge invariant effective interaction Lagrangian. This approach then permits the use of the standard covariant calculational tools of Quantum Electro-dynamics. We first apply this technique to the computation of the differential cross section for low energy photon-photon scattering. The well known Euler cross section is thereby derived in a direct manner. As a second example, the probability of the triple breakup of a free photon because of vacuum polarization is explicitly shown to vanish. This, however, is primarily due to the kinematics of the photon breakup. For a third application we calculate the differential cross section for the scattering of a low energy photon from the Coulomb field of a nucleus, that is, Delbruck scattering. Here the exact low energy differential cross section is obtained. However, though the present technique determines completely the angular dependence, it is necessary to introduce a momentum cutoff in the Coulomb field in order to obtain a finite value for the coefficient in front of the angular dependence. A comparison of the resulting expression for the cross section with that for forward scattering given by Rohrlich and Gluckstern (1952) gives the numerical value of this coefficient. A brief comparison between the angular distribution for Delbruck scattering and that for a combination of an electric and magnetic dipole radiator is presented.2031-01-0