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This is a Quantitative Study study.

September 23, 2025Open Access

Towards a derivation of Classical ElectroDynamics of charges and fields from QED

Key Points

Deriving the Newton-Maxwell equation enhances the understanding of electrodynamics, linking quantum mechanics and classical principles.
The study confirms global well-posedness of the Newton-Maxwell system on energy-spaces, addressing critical assumptions.
Incorporation of semiclassical techniques represents a novel approach within the analysis of the Newton-Maxwell equation.
Global solutions are constructed using quantum propagation properties, suggesting significant advancements in theoretical physics.

Abstract

The purpose of this article is twofold: (1) On one hand, we rigorously derive the Newton–Maxwell equation in the Coulomb gauge from first principles of quantum electrodynamics in agreement with the formal Bohr correspondence principle of quantum mechanics. (2) On the other hand, we establish the global well-posedness of the Newton–Maxwell system on energy-spaces under weak assumptions on the charge distribution. Both results improve the state of the art, and are obtained by incorporating semiclassical and measure theoretical techniques. One of the novelties is the use of quantum propagation properties in order to build global solutions of the Newton–Maxwell equation.

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