A unified approach to spinor duals via Clifford algebras and $G_\Omega$ groups

Abstract

Recent developments in the construction of generalized Dirac duals have revealed, within the structure of the Clifford algebra $\mathbb{C}\otimes\mathcal{C}\ell_{1,3},$ the existence of distinct algebraic formulations of spinors duals with potential applications in quantum field theoretic models. In this work, after reviewing the matrix formulation, we employ the recent covariant formulation of the generalized spinor dual and establish its interplay with the algebra $\mathcal{C}\ell_{1,3}$. We construct dual mappings governed by groups denoted by $G_\Omega$ and introduce the notion of $\Omega$-equivalence classes as a tool to classify dual spinors from a group-theoretic perspective.