Group Structure Of Gauge Theories

Description:
This monograph provides an account of the structure of gauge theories from a group theoretical point of view. The first part of the text is devoted to a review of those aspects of compact Lie groups (the Lie algebras, the representation theory, and the global structure) which are necessary for the application of group theory to the physics of particles and fields. The second part describes the way in which compact Lie groups are used to construct gauge theories. Models that describe the known fundamental interactions and the proposed unification of these interactions (grand unified theories) are considered in some detail. The book concludes with an up to date description of the group structure of spontaneous symmetry breakdown, which plays a vital role in these interactions. This book will be of interest to graduate students and to researchers in theoretical physics and applied mathematics, especially those interested in the applications of differential geometry and group theory in physics.

Table of Contents:
Preface; Part I. Group Structure: 1. Global properties of groups and Lie groups; 2. Local properties of Lie groups; 3. Lie algebras; 4. Hermitian irreducible representations of compact simple Lie algebras; 5. Continuous unitary irreducible representations (CUIRs) of compact Lie groups; 6. Rigid internal groups; Part II. Gauge Theory: 7. The gauge principle; 8. Spontaneous symmetry breaking; 9. Gauge theory of the non-gravitational interactions; 10. Grand unification; 11. Orbit structure; 12. The scalar potential; References; Glossary; Index.