Connections in classical and quantum field theory

Geometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models in field theory and mechanics. This book is an encyclopaedia of modern geometric methods in theoretical physics. It collects together the basic mathematical facts about various types of connections, and provides a detailed exposition of relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental fields. The authors have tried to give all the necessary mathematical background, thus making the book self-contained. This book should be useful to graduate students, physicists and mathematicians who are interested in the issue of deep interrelations between theoretical physics and geometry.

This book collects together the basic mathematical facts about various types of connections, and provides a detailed description of the relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental interactions. The volume presents several levels of complexity, from the elementary to the advanced, and provides a considerable number of exercises. The authors have tried to give all the necessary mathematical background, thus making the book self-contained.