Singular spinors as expansion coefficients of local spin-half fermionic and bosonic fields: On the two-fold Wigner degeneracy

TL;DR

This paper explores the role of singular spinors in constructing local fermionic and bosonic fields, emphasizing Lorentz covariance, Wigner degeneracy, and the classification of spinors to ensure symmetry and physical consistency.

Contribution

It provides a detailed analysis of singular spinors as expansion coefficients for local fields, clarifies the adjoint structure, and incorporates Wigner degeneracy to preserve rotational symmetry.

Findings

Singular spinors can serve as expansion coefficients for local fields.

Proper adjoint definitions map singular spinors into class-2.

Wigner degeneracy preserves rotational symmetry in the formalism.

Abstract

By scrutinizing the singular sector of the Lounesto spinor classification, we investigate the correct definition of the expansion coefficient functions of local fermionic fields within a fully Lorentz covariant theory. As we can observe, a careful definition of the adjoint structure, directed towards local fields, maps singular spinors into class-2 according to a general spinor classification. Furthermore, we investigate all the necessary mathematical tools for constructing local fermionic and bosonic fields and provide insights into the physical implications for the other singular classes. Besides, we also show that incorporating \emph{Wigner degeneracy} maintains the rotational symmetry formalism working in general.