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

DOI10.1016/J.PHYSLETA.2023.129028zbMATH Open1530.81098arXiv2304.12945OpenAlexW4384565002WikidataQ122686404 ScholiaQ122686404MaRDI QIDQ6166617

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Publication date: 3 August 2023

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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 $mathcalC,mathcalP,mathcalT$. 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.

Full work available at URL: https://arxiv.org/abs/2304.12945

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