Reducible Quantum Electrodynamics. III. The emergence of the Coulomb forces

TL;DR

This paper proposes a simplified quantum electrodynamics model using only transverse photons, demonstrating how Coulomb forces emerge and showing potential bound states between electron and photon fields, with implications for understanding electromagnetic interactions.

Contribution

It introduces a mathematical transformation that captures Coulomb forces with only transverse photons, offering a new perspective on QED interactions and bound state formation.

Findings

Coulomb forces emerge from the transformed transverse photon fields.

Bound states between electron and photon fields are possible, especially at long wavelengths.

The model provides insights analogous to the polaron problem in condensed matter physics.

Abstract

The assumption is made that only transversely polarized photons are needed for a correct description of Quantum Electrodynamics. A simple mathematical transformation is used to introduce new field operators which satisfy the full Maxwell equations. In particular, they reproduce Coulomb forces between different regions of the charge field. The analogy with the polaron problem can give some insight in the physics underlying the transformation. In this context it is shown that the interaction of the electron field with a transversely polarized photon field can form bound states. The binding energy peaks for long wavelength photons.