The Hydrodynamic Representation of the Quantum Relativistic Dynamics of the Electron

TL;DR

This paper derives the relativistic electron's action from a hydrodynamic perspective of the Dirac equation, linking spin interactions with vorticity and deriving the second order Dirac equation via Fisher Information minimization.

Contribution

It introduces a hydrodynamic formulation of the Dirac equation and connects quantum dynamics with information theory principles.

Findings

Electron's four-velocity modeled as an Eulerian field

Spin interacts with vorticity in the hydrodynamic framework

Second order Dirac equation derived from Fisher Information minimization

Abstract

In this work, the action of the relativistic electron is derived from the hydrodynamic formulation of the Dirac equation. In particular, in the hydrodynamic scenario, the four-velocity of the electron is regarded as an Eulerian field and the electron spin interacts with the corresponding vorticity field. In the second part of the work, it is shown how the second order Dirac equation can be derived from a principle of Minimum Fisher Information.