A note on hidden classes in spinor classification

TL;DR

This paper explores potential extensions to the Lounesto classification of spinors, considering new subclasses arising from theories beyond the standard model, and highlights relevant subclasses through imposed constraints.

Contribution

It systematically investigates possible extensions to the established spinor classification, broadening the theoretical framework for spinor analysis in physics.

Findings

Identification of potential new subclasses of spinors.

Constraints that highlight relevant extended classes.

Broadened understanding of spinor structures in advanced theories.

Abstract

The Lounesto classification is a well-established scheme for categorizing spinors based on their physical content, which are determined by their associated bilinear forms. It consists of six disjoint classes encompassing the known spinors within the context of the standard model of high-energy physics. However, advancements in theories beyond the standard model have opened the door to potential new spinorial adjoint structures, leading to new unforeseen classess. These developments indicate the potential for extending the standard Lounesto classification. In this paper, we explore all possible subclasses that could extend the Lounesto scheme. We highlight the most relevant subclasses by imposing constraints to their corresponding dual structures, thus broadening our understanding of spinor and its applications in theoretical physics.