Quantum electrodynamics calculation of lepton anomalous magnetic moments. Numerical approach to the perturbation theory of QED

In this review, we summarize the results of our numerical work carried out over nearly ten years on the complete determination of the 10th-order contribution to the anomalous magnetic moments of leptons in the perturbation theory of quantum electrodynamics. Our approach is based on a reorganized renormalization method in which no divergent quantities appear explicitly in any part of the calculation, which is crucial for the feasibility of numerical integration. The enormous number of 10th-order diagrams and the complexity of the renormalization procedure are such that we could not have handled this problem without the development of an automated code-generating algorithm. The systematic approach to these problems is described in some detail. (author)