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

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.