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2023, no. 3-4


Trell E.

In previous PIRT conferences I have reported on a differential geometry structural make-up of the standard model of the elementary particles and the periodic system of the atoms following Marius Sophus Lie's Ph.D. dissertation Over en Classe Geometriske Transformationer at Christiana (now Oslo) University in 1871. This thesis essentially describes Nature at the infinitesimal level it appears as by "a transition from a point to a straight line as element" both mathematically and materially of a coherent differential constitution. Under nucleosynthetic conditions its partial derivative square wave steps "of length equal to zero" goes into a spacefilling modular "urve-net" formation. In the first generation, from the 10?15 meter size of the Nucleon radius, this is a bi-layer wave-packet accumulation of palindromic Bohr Aufbau configuration, whose repeated application like in an oriental tiling or carpet first outlines its pattern in the periodic table over the more than 10,000 times larger extension of the atom cross-section area. When an integral surface layer is covered by a full excursion of the knot returning to the origin, the train continues by moving upward the Nucleon shaft to a new facet of the crystal which retains the shape of its infinitesimal module and so can self-assemble into a polymeric nanostructure cluster of itself or molecular combinations with other atoms exactly and extensively as specified in established chemical formulas. This is here exemplified by some basic and more advanced organic compounds including the proteinogenic amino acids and DNA.

Keywords: Atoms, Aufbau, Differential Geometry, Lie algebra, Molecules, Periodic System.

UDC: 514

PACS: 02.40.-k

DOI: 10.17238/issn2226-8812.2023.3-4.299-313

Please cite this article in English as:
Trell E. Lie differential geometry aufbau of the atoms and molecules. Space, Time and Fundamental Interactions, 2023, no. 3-4, pp. 299-313.