2022/03/14 by John Mashford, Mashford, John
Materials Science · Mathematics · Physics and Astronomy · #Anomalous magnetic dipole moment #Atomic and Molecular Physics #Combinatorics #Covariant transformation #Electron #Electron and X-Ray Spectroscopy Techniques #Lorentz transformation #Mathematical analysis #Mathematical physics #Mathematics #Minkowski space #Physics #Quantum and Classical Electrodynamics #Quantum mechanics #Regularization (linguistics) #Renormalization #Vertex (graph theory) #Vertex function #Vertex model #hep-ph #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.2203.07903
published in arXiv (Cornell University) (Cornell University) · 36 pages, 5 figures
openalex publication_date 2022/03/14 · arxiv created 2022/07/11 · arxiv updated 2022/07/12 · openalex created_date 2022/07/13 · openalex updated_date 2026/08/06
The vertex function is analyzed using covariant spectral regularization without encountering any divergence, either UV or IR. The mathematics of covariant spectral regularization for covariant matrix valued measures with one Lorentz index on open subsets of Minkowski space is described. This is then applied to the case of the vertex function and expressions for the densities associated with the vertex function in the t channel and the s channel with respect to Lebesgue measure on Minkowski space are obtained. These densities are well defined, non-divergent and analytic over their domains of definition and are obtained without using renormalization or needing to consider final state radiation. The limit of the expression for the vertex function in the t channel at low energy and low momenta is computed resulting in the classical result for the leading order (LO) contribution to the anomalous magnetic moment of the electron. Also the density for the vertex function in the s channel is used to compute the LO vertex correction contribution to the high energy limit of the cross section for the process e+e-→μ+μ-.