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Modèle de jauge de Yang-Mills par les transformations locale et globale associées à l'algèbre de Weil

Modèle de jauge de Yang-Mills par les transformations locale et globale associées à l'algèbre de Weil

          
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About the Book

Thèse de Bachelor de l'année 2014 dans le domaine Physique - Autres, note: 76,0, cours: Théorie de Yang-Mills - Physique Théorique, langue: Français, résumé Ce travail est consacré à l'étude des transformations locale et globale de Jauge du modèle de Yang-Mills. Nous avons montré qu'à partir de la géométrie non commutative munies des algèbres d'endomorphismes, que les notions de connexions et courbures pouvaient bien substituer les formulations fibrées pour des raisons purement physiques: la description directe des champs de Jauge. Mais, cependant, cette approche souffrait de l'incapacité à fournir une expression globale (symétrie globale) combinée à une expression locale (symétrie locale) des transformations de Jauge, ce qui est nécessaire pour la généralisation des transformations de Jauge. Ainsi, il a été proposé dans ce travail une approche en topologie algébrique obtenue à partir de fibrés vectoriels en algèbres de Weil dans un espace topologique, qui construit également de manière naturelle les courbures et les connexions. De telles sortes que, les connexions sont considérées comme des invariants cohomologiques des fibrés vectoriels, et toutes transformations de Jauge devient une application continue entre plusieurs topologies. Enfin, chaque courbure est exprimée au moyen d'un polynôme invariant développé à un degré de liberté propre à la courbure. Grâce à cette nouvelle structure topologique, certains objets deviennent plus facilement manipulables et/ou caractérisés de manière plus directe. Enfin notons que le fait d'avoir une présentation algébrique des théories de jauge permet de se rapprocher des techniques utilisées en théorie quantique des champs. Ce modèle peut aussi être considérer comme une généralisation du théorème de Gauss-Bonnet, qui établit un lien remarquable entre une courbure locale et un invariant topologique global. Les apports de cette approche sont: o La transformation générale de jauge tenant compte de la courbure locale (symétri


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Product Details
  • ISBN-13: 9783656735755
  • Publisher: Grin Publishing
  • Binding: Paperback
  • Language: French
  • Returnable: N
  • Weight: 163 gr
  • ISBN-10: 3656735751
  • Publisher Date: 18 Sep 2014
  • Height: 210 mm
  • No of Pages: 116
  • Spine Width: 7 mm
  • Width: 148 mm


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