On an integrable reduction of the Dirac equation

TL;DR

This paper demonstrates that a symmetry reduction of the Dirac equation leads to a system of ODEs whose integrability is linked to the stationary mKdV hierarchy, revealing a deep connection between quantum equations and integrable systems.

Contribution

It introduces a novel reduction of the Dirac equation that connects its solutions to the stationary mKdV hierarchy, expanding understanding of integrable structures in quantum equations.

Findings

Reduction yields ODE system linked to mKdV hierarchy

Integrability of the system is established by quadratures

Reveals a new connection between Dirac equation and integrable systems

Abstract

A symmetry reduction of the Dirac equation is shown to yield the system of ordinary differential equations whose integrability by quadratures is closely connected to the stationary mKdV hierarchy.