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Entwicklung von der komplexen Ebene zum QuaternionKoordinatensystems zur dreiräumlichen Geometrie


Michaud, André


Research Papers


Mathematical Physics



Date Published:

March 23, 2024




Die komplexe Ebene; die Quantentheorie; die Quaternionen; die DreiräumeGeometrie; die elektromagnetische Mechanik.


Gegenstand dieses Artikels ist eine vergleichende Analyse der geometrischen Eigenschaften der 2D-Einheitsvektorenmenge der komplexen Ebene, wie sie in der Quantenmechanik und bei der Verarbeitung von elektrischen LC-Schaltungen verwendet werden, der 3D-Einheitsvektorenmenge der Hamilton-Hypersphäre, wie sie in der Quantentheorie verwendet werden, und schließlich der 3x3DEinheitsvektorenmenge der Dreiräumegeometrie, wie sie in der elektromagnetischen Mechanik verwendet werden. Analyse der Auswirkungen der Ausweitung der Verwendung des HypersphärenKoordinatensystems auf die Behandlung von LC-Schaltungen und auf das traditionelle kartesische 3DKoordinatensystem sowie der Folgen der Verwendung einer einzigartigen Eigenschaft des vektoriellen Kreuzprodukts der komplexen Quaternionen-Einheitsvektoren, nämlich der Umkehrung der Anwendungsrichtung des resultierenden reellen Vektors bei der Entwicklung der elektromagnetischen Mechanik mit Hilfe der dreiräumlichen Geometrie.


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