Revisiting Takahashi's inversion theorem in discrete symmetry-based dual frameworks

Abstract

The so-called Takahashi's \emph{Inversion Theorem}, the reconstruction of a given spinor based on its bilinear covariants, are re-examined, considering alternative dual structures. In contrast to the classical results, where the Dirac dual structure plays the central role, new duals are built using the discrete symmetries $\mathcal{C},\mathcal{P},\mathcal{T}$. Their combinations are also taken into account. Furthermore, the imposition of a new adjoint structure led us also to re-examine the representation of the Clifford algebra basis elements, uncovering new bilinear structures and a new Fierz aggregate. Those results might help construct theories for new beyond standard model fields.

7 pages

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Cited by in corpus (5)

• Singular spinors as expansion coefficients of local spin-half fermionic and bosonic fields: On the two-fold Wigner degeneracy
• A note on hidden classes in spinor classification
• Hermitian formulation for mass dimension one fermions: Flat and curved space-times
• A Covariant Framework for Generalized Spinor Dual Structures
• Unraveling the Physical Meaning Behind Elko's Dual structure