Vertex bootstrap for the fine-structure constant

Abstract

The possibility of converting the Baker-Johnson-Adler eigenvalue equationF(α)=0 for the fine-structure constant into a simpler condition is discussed in the framework of the self-consistent (bootstrap) formulation of massless quantum electrodynamics. It is shown that the imposition of a strong convergence condition on the vertex bootstrap equation in the canonical (generalized Landau) gauge leads to an eigenvalue equation for α,\(\tilde Z_{1c} \left( \alpha \right) = 0\), which is consistent with the gauge covariance of the theory and impliesF(α)=0. The function\(\tilde Z_{1c} \left( \alpha \right)\) may be expanded in a power series in α through Feynman graphs.