Groupes et algèbres de Lie pour la physique

Abstract

Lie groups play a crucial role in understanding the fundamental principles of physics, they are fundamental to ourunderstanding of naturallaws, revealing regularities and constants that shape physical systems. The theory of groups enables the classification and description of these groups, using Lie algebra to formulate the equations that characterize them ; it provides a precise framework for representing and studying thesecomplex structures. The use of this theory has enhanced our understanding of the foundations of natural laws and establishe ddeep connections across different branches of physics . In our work we will concisely explore the essential foundations of Lie groups, investigating the fundamental concepts and principles that define them, we will conduct in-depth studies on Lie groups and there applications in physics, discussing fundamental concepts and properties of groups and Lie algebras. As well some advances in this field, we will employ concrete applications and diagrams to illustrate the fundamental concepts of Lie groups, highlighting similarities and differences among different groups