A Hydrodynamics Formulation for a Nonlinear Dirac Equation

TL;DR

This paper develops a hydrodynamics framework for a nonlinear Dirac equation with a nonlinear mass term, utilizing Clifford algebra, and proves global existence for a regularized version.

Contribution

It introduces a novel hydrodynamics formulation for a nonlinear Dirac equation that preserves homogeneity and employs Clifford algebra tools.

Findings

Hydrodynamics formulation derived for the nonlinear Dirac equation.

Global existence proved for a regularized version.

Symmetric split into left and right-handed spinor components achieved.

Abstract

We derive a hydrodynamics formulation for a modified Dirac equation with a nonlinear mass term that preserves the homogeneity of the original Dirac equation. The nonlinear Dirac equation admits a symmetric split into the left and right-handed spinor components. It is formulated using Clifford algebra tools. We prove global existence for a regularized equation.