First quantized electrodynamics

• First-quantized electrodynamics of the parametrized Dirac equation is developed.
• Unrestricted entanglement in time is made explicit.
• Bethe and Salpeter’s equation for relativistic bound states is derived without further conjecture.
• One-loop scattering corrections and the axial anomaly are derived using a partial summation.
• Wide utility of semi-classical Quantum Electrodynamics is argued.

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.