{"title":"A New Type of Quaternionic Regularity","authors":"A. Vajiac","doi":"10.1007/s00006-023-01292-w","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 5","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-023-01292-w.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Clifford Algebras","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00006-023-01292-w","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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.
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