O'Raifeartaigh L. Group Structure of Gauge Theories

Cambridge University Press, 1986 — 184 pp. — (Cambridge Monographs on Mathematical Physics). — ISBN: 0521252938.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.Group Structure:
Global properties of groups and Lie groups
Local properties of Lie groups
Lie algebras
Hermitian irreducible representations of compact simple Lie algebras
Continuous unitary irreducible representations (CUIRs) of compact Lie groups
Rigid internal groups
Gauge Theory:
The gauge principle
Spontaneous symmetry breaking
Gauge theory of the non-gravitational interactions
Grand unification
Orbit structure
The scalar potential