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.

中文翻译：

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一种新型的四元正则性

我使用基于超缠绕分析的技术引入了四元正则性的概念，超缠绕分析是一般超复杂理论的精炼版本。在四元数和双四元数的情况下，我证明了超缠绕全纯（正则）函数允许在某些子代数中的正则函数的超缠绕和中进行分解。超缠绕四元数正则性介于切片正则性和修正的柯西-富特理论之间，并被证明对四元数和时空代数量子理论的重构有直接影响。