A Square-Integrable Spinor Solution to Non-Interacting Dirac Equations

TL;DR

This paper presents a novel square-integrable spinor solution to the Dirac equation in polar form with a tensorial connection, demonstrating localization and exponential decay without external potentials.

Contribution

It introduces a new class of localized solutions to the Dirac equation incorporating tensorial connections, expanding understanding of spinor behaviors in such contexts.

Findings

Solution is localized around the origin

Exhibits decreasing exponential behavior radially

Applicable without external potential

Abstract

We consider the Dirac equation written in polar form, without any external potential but equipped with a non-zero tensorial connection, and we find a new type of solution that is localized around the origin with a decreasing exponential behaviour in the radial coordinate.