Group Theory in Physics

This book presents the study of symmetry groups in Physics from a practical perspective, i.e. emphasising the explicit methods and algorithms useful for the practitioner and profusely illustrating by examples.

The first half reviews the algebraic, geometrical and topological notions underlying the theory of Lie groups, with a review of the representation theory of finite groups. The topic of Lie algebras is revisited from the perspective of realizations, useful for explicit computations within these groups. The second half is devoted to applications in physics, divided into three main parts — the first deals with space-time symmetries, the Wigner method for representations and applications to relativistic wave equations. The study of kinematical algebras and groups illustrates the properties and capabilities of the notions of contractions, central extensions and projective representations. Gauge symmetries and symmetries in Particle Physics are studied in the context of the Standard Model, finishing with a discussion on Grand-Unified Theories.

Contents:Outline of the BookGeneralitiesFinite Groups: Basic Structure TheoryFinite Groups: Linear RepresentationsThree-Dimensional Lie GroupsThe Lie Group SU(3)Simple Lie AlgebrasRepresentations of Simple Lie AlgebrasClassical Lie AlgebrasTensor Products and Reduction of RepresentationsExceptional Lie AlgebrasApplications to the Construction of Orthonormal Bases of StatesSpacetime Symmetries and Their RepresentationsKinematical AlgebrasSymmetries in Particles Physics
Readership: Graduate students, researchers and academicians interested in group theory and quantum fields.
Key Features:Presents alternative methods and algorithms for practical computations, as well as detailed nontrivial examples considered in applications in the current literature, like exceptional Lie algebras and octonionsIncludes a detailed analysis of relevant physical equations in the context of infinite dimensional representationsStudies kinematical groups as a physically based illustration of abstract notions like contractions and proyective representations