Discrete Classical Electromagnetic Fields

TL;DR

This paper introduces a formalism with discrete, localized electromagnetic fields representing classical photons, eliminating non-physical photon modes and clarifying the origin of divergences in standard quantum electrodynamics.

Contribution

It presents a novel discrete field formalism for classical electromagnetic fields that excludes scalar and longitudinal photons, providing insights into the physical nature of photons and divergences.

Findings

Discrete fields are all transversal photons.

Standard Maxwell fields emerge from averaging these discrete fields.

Scalar and longitudinal photons are artifacts of averaging, not fundamental.

Abstract

The classical electromagnetic field of a spinless point electron is described in a formalism with extended causality by discrete finite transverse point-vector fields with discrete and localized point interactions. These fields are taken as a classical representation of photons, ``classical photons". They are all transversal photons; there are no scalar nor longitudinal photons as these are definitely eliminated by the gauge condition. The angular distribution of emitted photons coincides with the directions of maximum emission in the standard formalism. The Maxwell formalism and its standard field are retrieved by the replacement of these discrete fields by their space-time averages, and in this process scalar and longitudinal photons are necessarily created and added. Divergences and singularities are by-products of this averaging process. This formalism enlighten the meaning and the origin of the non-physical photons, the ones that violate the Lorentz condition in manifestly covariant quantization methods.