Gordon decomposition of Dirac current: a new interpretation

TL;DR

This paper reinterprets the Gordon decomposition of the Dirac current, linking it to classical charge currents, spin magnetization, and optical vortices, proposing a unified view of electron structure and electromagnetic fields.

Contribution

It introduces a new interpretation of the Gordon current as the classical charge current and relates spin and orbital angular momentum to optical vortices and vortex models of the electron.

Findings

Classical charge current corresponds to Gordon current.

Antisymmetric spin tensor is hidden within the Maxwell tensor.

Optical vortex concepts relate to quantized angular momentum and electron structure.

Abstract

Historically Gordon decomposition of Dirac current played an important role in the interpretation of Dirac equation. We revisit it to understand the correspondence between Maxwell-Dirac and Maxwell-Lorentz theories. Arguments are presented to show that classical charge current corresponds to Gordon current. Consistency with Maxwell-Dirac theory leads to a new result: antisymmetric spin tensor in spin magnetization current of Dirac electron must be hidden as internal part of classical Maxwell tensor. It becomes natural to extend our previous interpretation in which electromagnetic field tensor represents angular momentum of photon or spacetime fluid (aether!) in the presence of sources such that the duality between field and source disappears. Both Gordon current and spin current are proposed to have 'spinning origin'. Formal expression of Gordon current makes it possible to apply the idea of optical vortex in this case, and quantized vortex and quantized orbital angular momentum could be related with the conjecture of mechanical interpretation of electric charge. Separate mass and charge centers for spinning point charge are well known in the literature; we discuss them in the context of two-vortex model of electron and Gordon decomposition.