# The Heisenberg spinor field classification and its interplay with the Lounesto's classification

## TL;DR

This paper develops a classification scheme for Heisenberg spinor fields, extending previous work on Dirac spinors, and explores how this classification interacts with Lounesto's established spinor classification system.

## Contribution

It introduces a comprehensive classification for Heisenberg spinor fields encompassing all Lounesto classes, expanding the understanding of spinor field structures.

## Key findings

- Derived a new classification scheme for Heisenberg spinor fields.
- Analyzed the relationship between Heisenberg and Lounesto's classifications.
- Provided insights into the structure of non-linear spinor fields.

## Abstract

Dirac linear spinor fields were obtained from non-linear Heisenberg spinors, in the literature. Here we extend that idea by considering not only Dirac spinor fields but spinor fields in any of the Lounesto's classes. When one starts considering all these classes of fields, the question of providing a classification for the Heisenberg spinor naturally arises. In this work the classification of Heisenberg spinor fields is derived and scrutinized, in its interplay with the Lounesto's spinor field classification.