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

• Published in: Progress of theoretical and experimental physics Vol. 2012; no. 1
• Main Authors: Aoyama, Tatsumi, Hayakawa, Masashi, Kinoshita, Toichiro, Nio, Makiko
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.01.2012
• ISSN: 2050-3911; 2050-3911
• DOI: 10.1093/ptep/pts030

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.