Hyperspherical approach to quantum electrodynamics: sixth-order magnetic moment

Abstract

We present the details of a powerful new technique used in an exact calculation of the contribution of 6 sixth-order vertex graphs to the anomalous magnetic moment of the electron. By introducing four-dimensional spherical coordinates, the momentum-space integrals can be evaluated directly. The angular integrations are performed using some simple properties of the Gegenbauer polynomials. For these graphs, the remaining convergent radial integrands are simple rational functions which are readily integrated. The divergent integrals are treated separately to extract all terms which do not vanish in the infrared and ultraviolet limits. The actual processing of the many terms involved was done using the algebraic computer program ASHMEDAI. DOI: http://dx.doi.org/10.1103/PhysRevD.9.421 © 1974 The American Physical Society