1997/07/22 by A. Bashir, Adnan Bashir, A. Kizilersu +2 · 5 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Fermion #Graph #Logarithm #Massless particle #Mathematical analysis #Mathematical physics #Mathematics #Multiplicative function #Particle physics theoretical and experimental studies #Perturbation theory (quantum mechanics) #Physics #Propagator #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Quantum mechanics #Vertex (graph theory) #Vertex function #hep-ph
paper · pdf · doi:10.1103/physrevd.57.1242
published as Phys.Rev. D57 (1998) 1242-1249 · 18 pages, Latex, 2 figures
arxiv created 1997/07/22 · openalex publication_date 1998/01/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Dong, Munczek, and Roberts have shown how the full 3-point vertex that appears in the Schwinger-Dyson equation for the fermion propagator can be expressed in terms of a constrained function W1 in massless quenched QED. However, this analysis involved two key assumptions: that the fermion anomalous dimension vanishes in the Landau gauge and that the transverse vertex has a simplified dependence on momenta. Here we remove these assumptions and find the general form for a new constrained function U1 that ensures the multiplicative renormalizability of the fermion propagator nonperturbatively. We then study the restriction imposed on U1 by recent perturbative calculations of the vertex and compute its leading logarithmic expansion. Since U1 should reduce to this expansion in the weak coupling regime, this should serve as a guide to its nonperturbative construction. We comment on the perturbative realization of the constraints on U1.