First Quantized Electrodynamics

TL;DR

This paper introduces a parametrized Dirac wave equation framework that offers an elementary, operator-based approach to QED phenomena, reproducing key effects like the Lamb shift and anomalous magnetic moment without relying on field quantization.

Contribution

It presents a novel parametrized formalism for QED that directly derives bound state equations and quantum corrections, differing from traditional field-theoretic methods.

Findings

Derives Bethe-Salpeter equation for bound states

Calculates Uehling shift and Lamb shift

Explains electron anomalous magnetic moment

Abstract

The parametrized Dirac wave equation represents position and time as operators, and can be formulated for many particles. It thus provides, unlike field-theoretic Quantum Electrodynamics (QED), an elementary and unrestricted representation of electrons entangled in space or time. The parametrized formalism leads directly and without further conjecture to the Bethe-Salpeter equation for bound states. The formalism also yields the Uehling shift of the hydrogenic spectrum, the anomalous magnetic moment of the electron to leading order in the fine structure constant, the Lamb shift and the axial anomaly of QED.