Geometry, Gauge, Gravity

Abstract

General Relativity and Yang-Mills theories are the two pillars of our understanding of the physical world. The fact that the former is a classical field theory whereas the latter are usually presented as quantum field theories, tends to obscure the similarities between them and is often given as a motivation to develop a quantum theory of gravity. In this book we instead treat both as classical theories, putting them on a more even basis. Insisting that the dynamical variables must have a global geometrical meaning exposes their deep common foundations and allows to give precise answers to otherwise vague questions such as whether gravity is a gauge theory. The book contains standard presentations of Yang-Mills theories and General Relativity but covers also several topics that are not very well known, such as the geometry of the Higgs phenomenon, the transformation of spinors under diffeomorphisms, the derivation of General Relativity from the principles of special relativistic field theory.