Abstract
Using the Dirac (Clifford) algebra \(\gamma ^{\mu }\) as initial stage of our discussion, we summarize previous work with respect to the isomorphic 15 dimensional Lie algebra su*(4) as complex embedding of sl(2,\(\mathbb {H}\)), the relation to the compact group SU(4) as well as subgroups and group chains. The main subject, however, is to relate these technical procedures to the geometrical (and physical) background which we see in projective and especially in line geometry of \(\mathbb {R}^{3}\). This line geometrical description, however, leads to applications and identifications of line Complexe and the discussion of technicalities versus identifications of classical line geometrical concepts, Dirac’s ‘square root of \(p^{2}\)’, the discussion of dynamics and the association of physical concepts like electromagnetism and relativity. We outline a generalizable framework and concept, and we close with a short summary and outlook.
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This article is part of the Topical Collection on Homage to Prof. W.A. Rodrigues Jr. edited by Jayme Vaz Jr..
We thank J. G. Vargas for several interesting discussions during the ICCA-10 conference and especially for pointing out various aspects of Kähler’s work as well as Kähler’s achievements in differential calculus.
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Dahm, R. On a Microscopic Representation of Space-Time III. Adv. Appl. Clifford Algebras 29, 20 (2019). https://doi.org/10.1007/s00006-018-0936-x
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DOI: https://doi.org/10.1007/s00006-018-0936-x