A New Type of Quaternionic Regularity
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.
Vajiac, A. A New Type of Quaternionic Regularity. Adv. Appl. Clifford Algebras 33, 51 (2023). https://doi.org/10.1007/s00006-023-01292-w