Unifying Ancient and Modern Geometries Through Octonions

23rd International Conference on Integrable Systems and Quantum Symmetries

Catto, Sultan^1,2 ; Gürcan, Yasemin^3 ; Khalfan, Amish^4 ; Kurt, Levent^3

Physics Department, Graduate School, City University of New York, New York

NY

10016-4309, United States^1

Theoretical Physics Group, Rockefeller University, 1230 York Avenue, New York

NY

10021-6399, United States^2

Department of Science, Borough of Manhattan CC, City University of NY, New York

NY

10007, United States^3

Physics Department, LaGuardia CC, City University of New York, LIC, NY

11101, United States^4

关键词: Desargues;    Division algebras;    Hadronic physics;    Octonions;    Quark physics;    Unified description;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/670/1/012016/pdf
DOI  :  10.1088/1742-6596/670/1/012016

来源: IOP

【 摘 要 】

We show the first unified description of some of the oldest known geometries such as the Pappus' theorem with more modern ones like Desargues' theorem, Monge's theorem and Ceva's theorem, through octonions, the highest normed division algebra in eight dimensions. We also show important applications in hadronic physics, giving a full description of the algebra of color applicable to quark physics, and comment on further applications.