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arXiv · 2304.12945

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

R. J. Bueno Rogerio·R. T. Cavalcanti·J. M. Hoff da Silva·C. H. Coronado Villalobos
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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 $\mathcal{C}, \mathcal{P}, \mathcal{T}$. 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.

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R. J. Bueno Rogerio, R. T. Cavalcanti, J. M. Hoff da Silva, C. H. Coronado Villalobos. 2023-04-24. Revisiting Takahashi's inversion theorem in discrete symmetry-based dual frameworks. https://doi.org/10.1016/j.physleta.2023.129028

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