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Evolution du plan complexe vers le système de coordonnées du Quaternion jusqu'à la géométrie trispatiale

Author:

Michaud, André

Category:

Research Papers

Sub-Category:

Mathematical Physics

Language:

French

Date Published:

June 24, 2024

File:

/Research Papers-Mathematical Physics/Download/9845

Downloads:

Keywords:

Le plan complexe; la Théorie quantique; Les quaternions; la géométrie trispatiale; la mécanique électromagnétique

Abstract:

L'objet de cet article est une analyse comparative des caractéristiques géométriques de l'ensemble des vecteurs unitaires 2D du plan complexe tels qu'ils sont utilisés en Mécanique Quantique et dans le traitement des circuits électriques LC, de l'ensemble 3D des vecteurs unitaires de l'hypersphère de Hamilton tels qu'ils sont utilisés en théorie quantique et enfin de l'ensemble des vecteurs unitaires 3x3D de la géométrie trispatiale tels qu'ils sont utilisés en mécanique électromagnétique. Analyse des implications de l'extension de l'utilisation du système de coordonnées de l'hypersphère au traitement des circuits LC et au système de coordonnées cartésiennes 3D traditionnel, et des conséquences de l'utilisation d'une propriété unique du produit vectoriel croisé des vecteurs unitaires complexes du quaternion d'inverser la direction d'application du vecteur unitaire réel résultant, dans le développement de la mécanique électromagnétique au moyen de la géométrie trispatiale.