A New Type of Quaternionic Regularity

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2023-08-29 DOI:10.1007/s00006-023-01292-w

A. Vajiac

引用次数: 0

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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一类新的四元数正则性

我引入了四元数正则性的概念，使用了基于超复杂分析的技术，这是一般超复杂理论的改进版本。在四元数和双四元数的情况下，我证明了超凸全纯（正则）函数允许在某些子代数中的正则函数的超凸和中进行分解。超纠缠四元数正则性介于片正则性和修正的Cauchy–Fueter理论之间，并被证明对四元数和时空代数量子理论的重新表述有直接影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.