# Polar solutions with tensorial connection of the spinor equation

## TL;DR

This paper investigates Dirac spinor equations in a background with a specific tensorial connection, finding localized polar solutions that are square-integrable, thus contributing to understanding spinor fields in non-trivial geometries.

## Contribution

It introduces a novel approach to solving Dirac equations with tensorial connections, revealing localized polar solutions without external interactions.

## Key findings

- Localized square-integrable solutions found
- Solutions exhibit polar form with specific tensorial connection
- Advances understanding of spinor fields in complex backgrounds

## Abstract

Dirac field equations are studied for spinor fields without any external interaction and when they are considered on a background having a tensorial connection with a specific non-vanishing structure some solution can be found in polar form displaying a square-integrable localized behaviour.