Yang-Mills Theory in the Geometric Formalism of Principal Bundles

Abstract

This study seeks to articulate a geometric formulation of the Yang-Mills theory by examining how both the Yang-Mills equations and the associated Lagrangian emerge within the formalism of differential forms and Cartan’s calculus. Particular attention is given to the role of principal bundles, whose geometric and topological structures provide the underlying framework of the theory and illuminate its physical representations. By emphasizing these connections, the analysis reveals the profound interplay between the mathematical architecture of gauge fields and their physical consequences, offering a unified perspective for approaching Yang-Mills theory through geometry.