||Number of Pages
||Mohammad Saleem, Muhammad Rafique
||GROUP THEORY FOR HIGH ENERGY PHYSICISTS
Author: Mohammad Saleem, Muhammad Rafique
Description: The book introduces the concept of a group and the characteristics that are imperative for developing group theory as applied to high energy physics. With a focus on continuous groups, the text analyzes the root structure of important groups and obtains the weights of various representations of these groups.
Table of Content: * Elements of Group Theory * Definition of a Group * Some Characteristics of Group Elements * Permutation Groups * Multiplication Table Subgroups * Power of an Element of a Group * Cyclic Groups * Cosets * Conjugate Elements and Conjugate Classes * Conjugate Subgroups * Normal Subgroups * Centre of a Group * Factor Group * Mapping * Homomorphism * Kernel * Isomorphism * Direct Product of Groups * Direct Product of Subgroups* Group Representations * Linear Vector Spaces * Linearly Independent Vectors * Basic Vectors * Operators * Unitary and Hilbert Vector Spaces * Matrix Representative of a Linear Operator * Change of Basis and Matrix Representative of a Linear Operator * Group Representations * Equivalent and Unitary Representations * Reducible and Irreducible Representations * Complex Conjugate and Adjoint Representations * Construction of Representations by Addition * Analysis of Representations * Irreducible Invariant Subspaces* Matrix Representations and Invariant Subspaces * Product Representations * Continuous Groups * Definition of a Continuous Group * Groups of Linear Transformations * Order of a Group of Transformations * Lie Groups * Generators of Lie Groups * Real Orthogonal Group in 2 Dimensions: O(2) * Generators of SU (2) * Generators of SU (3) * Generators and Parameterisation of a Group * Matrix Representatives of Generators * Structure Constants * Rank of a Lie Group * Lie Algebras * Commutation Relations between the Generators of a Semi-Simple Lie Group * Properties of the Roots * Structure Constants Náâ* Classification of Simple Groups * Roots of SU (2) * Roots of SU (3) * Numerical Values of Structure Constants of SU (3) * Weights of a Representation * Computation of the Highest Weight of any Irreducible Representation of SU (3) * Dimension of any Irreducible Representation of SU (n) * Computation of Weights of an Irreducible Representation of SU (3) * Weights of the Irreducible Representation D8 (1,1) of SU(3) * Weight Diagrams * Decomposition of a Product of Two Irreducible Representations * Symmetry, Lie Groups, and Physics * Symmetry * Casimir Operators * Symmetry Group and Unitary Symmetry * Symmetry and Physics * Group Theory and Elementary Particles