On a microscopic representation of space–time IV

Journal Article · Mon May 15 04:00:00 EDT 2017 · Physics of Atomic Nuclei

DOI:https://doi.org/10.1134/S1063778817030048· OSTI ID:22759697

Dahm, Rolf ^[1]

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1. Beratung für Informationssysteme und Systemintegration (Germany)

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.

• OSTI ID: 22759697
• Journal Information: Physics of Atomic Nuclei, Journal Name: Physics of Atomic Nuclei Journal Issue: 3 Vol. 80; ISSN 1063-7788; ISSN PANUEO
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
CHAINS
DIRAC EQUATION
ELECTROMAGNETISM
GEOMETRY
HADRONS
QUANTUM FIELD THEORY
RELATIVITY THEORY
SU-4 GROUPS