Sixth order studies of quantum electrodynamics

Details are presented of a new technique used in the calculation of the contributions of five sixth-order vertex graphs to the anomalous magnetic moment of the electron. By itroducing dispersion relations and four-dimensional spherical coordinates, the angular integrations are performed by use of some simple properties of the Gegenbauer polynomials. The remaining integrations over three variables are done numerically, after the appropriate renormalizations. The results are compared to previous evaluations. Some properties of massless quantum electrodynamics are discussed in the coordinatespace formalism. The fourth-order vacuum polarization tensor is calculated directly from Feynman rules and compared with that of momentum space. They are not in agreement. The sixth-order vacuum polarization tensor is also calculated to show the dependence of the results on the order of integrations. These two calculational ambiguities may be attributable to hidden delta-functions in the second-order vertex correction