Model link and knot mapping in quantum electrodynamics

Abstract

A heuristic mapping onto links and knots of Feynman diagrams in quantum electrodynamics at infinitesimal distances is investigated. This model map is formulated by treating the asymptotic photon propagator as composite electron and positron propagators, and exploiting Feynman's picture of positrons as electrons moving backward in time. The mapping is applied to the calculation in Feynman gauge of the divergent part of the inverse charge renormalization constant to sixth order in the bare charge of the electron as an illustration of Kreimer's classification of the divergent part of Feynman diagrams in terms of transcendental numbers and knots. In particular, I elucidate the mapping of a vacuum polarization graph with two crossed photo propagators onto the trefoil knot.