Abstract
I introduce a notion of quaternionic regularity using techniques based on hypertwined analysis, a refined version of general hypercomplex theory. In the quaternionic and biquaternionic cases, I show that hypertwined holomorphic (regular) functions admit a decomposition in a hypertwined sum of regular functions in certain subalgebras. The hypertwined quaternionic regularity lies in between slice regularity and the modified Cauchy–Fueter theories, and proves to have a direct impact on reformulations of quaternionic and spacetime algebra quantum theories.
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Data sharing not applicable to this article as no datasets were generated or analysed during the current study. I have no relevant financial or non-financial interests to disclose. I have no competing interests to declare that are relevant to the content of this article. I certify that I have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.
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Communicated by Paula Cerejeiras.
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Vajiac, A. A New Type of Quaternionic Regularity. Adv. Appl. Clifford Algebras 33, 51 (2023). https://doi.org/10.1007/s00006-023-01292-w
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DOI: https://doi.org/10.1007/s00006-023-01292-w