On a microscopic representation of space–time IV
- 作者: Dahm R.1
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隶属关系:
- Beratung für Informationssysteme und Systemintegration
- 期: 卷 80, 编号 3 (2017)
- 页面: 512-519
- 栏目: Elementary Particles and Fields Theory
- URL: https://journal-vniispk.ru/1063-7788/article/view/191901
- DOI: https://doi.org/10.1134/S1063778817030048
- ID: 191901
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详细
We summarize some previous work on SU(4) describing hadron representations and transformations as well as its noncompact “counterpart” SU*(4) being the complex embedding of SL(2,H). So after having related the 16-dim Dirac algebra to SU*(4), on the one hand we have access to real, complex, and quaternionic Lie group chains and their respective algebras, on the other hand it is of course possible to relate physical descriptions to the respective representations. With emphasis on the common maximal compact subgroup USp(4), we are led to projective geometry of the real 3-space and various transfer principles which we use to extend the previous work on the rank 3-algebras above. On real spaces, such considerations are governed by the groups SO(n,m) with n + m = 6. The central thread, however, focuses here on line and Complex geometry which finds its well-known counterparts in descriptions of electromagnetism and special relativity as well as—using transfer principles—in Dirac, gauge, and quantum field theory. We discuss a simple picture where Complexe of second grade play the major and dominant rôle to unify (real) projective geometry, complex representation theory and line/Complex representations in order to proceed to dynamics.
作者简介
Rolf Dahm
Beratung für Informationssysteme und Systemintegration
编辑信件的主要联系方式.
Email: dahm@bf-IS.de
德国, Mainz
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