The Mathematical Foundations of Gauge Theories

Theoretical physicists tend to discuss their theories in the language of mathematics. However, the adequate mathematical formulation may not yet be available when the physical law is first discovered. Mathematical physicists trying to develop the relevant mathematics for these theories, may obtain new insights into old mathematical structures or may even disclose entirely new structures. Gauge Theory is such a gift from physics to mathematics. This volume presents a self-contained development of a differential geometric formulation of gauge theories, in particular, the theory of Yang-Mills fields. The book is aimed at advanced graduate students and research workers in theoretical physics and pure and applied mathematics who are acquainted with the elements of the theory of differential manifolds. It enables the reader to apply this theory to gauge theories and to understand the role of gauge theories in high energy physics, gravitation theory and electromagnetism.