Dirac hydrodynamics in 19 forms

TL;DR

This paper reformulates the Dirac spinor field theory into a fluid dynamics framework, revealing 19 distinct minimal hydrodynamic systems that are equivalent to the original Dirac equations.

Contribution

It introduces a novel approach to represent Dirac fields as spin fluids with 19 different equivalent hydrodynamic formulations.

Findings

Identifies 19 minimal hydrodynamic systems equivalent to Dirac equations.

Demonstrates the non-uniqueness of the fluid interpretation of spinor fields.

Provides explicit formulations for each of the 19 hydrodynamic systems.

Abstract

We consider the relativistic spinor field theory re-formulated in polar variables so to allow for the interpretation given in terms of fluid variables. After that the dynamics of spinor fields is converted as dynamics of a special type of spin fluid, we demonstrate that such conversion into dynamical spin fluid is not unique but it can be obtained through $19$ different rearrangements, by explicitly showing the $19$ minimal systems of hydrodynamic equations that are equivalent to the Dirac equations.