Attempts at a Determination of the Fine-Structure Constant from First Principles: A Brief Historical Overview

It has been a notably elusive task to find a remotely sensical ansatz for a calculation of Sommerfeld\u27s electrodynamic fine-structure constant αQED ≈ 1 /137.036 based on first principles. However, this has not prevented anumber of researchers to invest considerable effort into the problem, despite theformidable challenges, and a number of attempts have been recorded in the literature.Here, we review a possible approach based on the quantum electrodynamic (QED)β function,and on algebraic identities relating αQED to invariant properties of\u27internal\u27 symmetry groups, as well as attempts to relate the strength of theelectromagnetic interaction to the natural cutoff scale for other gauge theories.Conjectures based on both classical as well as quantum-field theoretical considerationsare discussed. We point out apparent strengths and weaknesses of the most prominentattempts that were recorded in the literature. This includes possible connections toscaling properties of the Einstein-Maxwell Lagrangian which describes gravitational andelectromagnetic interactions on curved space-times. Alternative approaches inspired bystring theory are also discussed. A conceivable variation of the fine-structure constantwith time would suggest a connection of αQED to global structures of theUniverse, which in turn are largely determined by gravitational interactions