Differential Geometry and Gauge Fields

The book presents a lucid account of modern differential geometry in a manner that renders the subject accessible to both mathematicians and physicists without sacrificing mathematical rigor. A detailed introduction of the concept of differentiable manifold is followed by an extensive development of exterior algebra and exterior calculus on manifolds. The theory of Lie groups is presented in a somewhat unorthodox manner that is based almost entirely on the properties of the composition functions and their concomitants. This background material forms the basis of an approach to the theory of connections and curvature on principal fibre bundles that is both natural and readily comprehensible. The development of the calculus of variations of multiple integrals within this context provides the foundation of a detailed description of the theory of classical gauge fields.