A note on hidden classes in spinor classification

Abstract

The Lounesto classification is a well-established scheme for categorizing spinors based on their physical content, 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 classes. These developments indicate the potential for extending the standard Lounesto classification. This paper explores all possible subclasses that could extend the Lounesto scheme. We highlight the most relevant subclasses by imposing constraints on their corresponding dual structures, thus broadening our understanding of spinors and their applications in theoretical physics.