Bundles and Gauges, a Math-Physics Duality - the case of Gravity

Abstract: A modern and straight forward summary of the necessary tools andconcepts needed to understand and work with gauge theory in a fibre bundle formalism. Due to the aim of being a quick but thorough introductionfull derivations are rarely included, but references to such are given wherethey have been omitted. General Relativity, although being a geometrical theory, in the sense that the gravitational force is described by the curvature of space-time, may not be derived from geometry like the other fundamental forces as in Yang-Mills theory. Thus, a possibility of unification lies in a geometrical derivation of gravity from gauge principles. By applying the presented formalism to the case of Gravity such a derivationis pursued along the lines of nonlinear realizations of the gauge group.