2006/10/30 by Jay R. Yablon, Yablon, Jay R.
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #hep-ph
paper · pdf · doi:10.48550/arxiv.hep-ph/0610377
29 pages, 3 figures. Version 2 revises section 4 and adds a new figure and four new references to present transverse Ward-Takahasi terms uncovered after posting of version 1
openalex publication_date 2006/10/30 · arxiv created 2006/11/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well-known that following summing Feynman graphs, the fermion-boson coupling vertex is modified according to gammau-->Gammau=gammau+Deltau, with Deltau representing non-divergent perturbative corrections. Here, we calculate the anticommutators specified by Gammauv=.5Gammau,Gammav, and then explore some consequences of employing these as a metric tensor guv=Gammauv(p',q,p) in momentum space. The challenge is that Gammau and Gammauv must them be introduced in place of gammau and nuv throughout the Lagrangian density, denoted L', resulting in what appears, superficially, to be different physics from what is known and observed. However, with a suitable reparameterization of fermion rest masses m', interaction charges e' and momentum vectors pu' into their observed counterparts m, e and pu, it turns out that L' can be made to describe physics identical to that of the customary QED Lagrangian density L at low photon momentum qu-->0, including the observed magnetic anomaly. That is,we prove that one is able to obtain L(m,e,pu)=L'(m',e',pu') for qu-->0. We find through the Ward-Takahashi identity, as summarized in Figure 2, that interaction vertexes are proportional to the difference between the ordinary and covariant momentum-space derivatives of the metric tensor, and thus an indicator of curvature. Finally, we obtain additional non-longitudinal terms in the Ward-Takahashi relation.