Dirac Fields in Hydrodynamic Form and their Thermodynamic Formulation

TL;DR

This paper reformulates Dirac spinor fields using a covariant splitting approach, decomposing their dynamical equations and applying the framework to analyze the hydrogen atom.

Contribution

It introduces a novel 1+1+2 covariant splitting method for Dirac fields, providing new insights into their hydrodynamic and thermodynamic formulations.

Findings

Decomposition of Dirac equations in covariant form

Application to hydrogen atom analysis

Enhanced understanding of spinor field dynamics

Abstract

We consider the theory of spinor fields written in polar form and we re-express it in terms of the so-called 1+1+2 covariant splitting: after this is done for the basic kinematic variables, we proceed to decompose the dynamical equations, both for the case of the Dirac differential field equations and for the case of the energy density tensor. As an explicit example of a real physical application we deal with the hydrogen atom. Comments are addressed in the end.