Saleem / Rafique Group Theory for High Energy Physicists

1. Auflage 2012
ISBN: 978-1-4665-1064-7
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 230 Seiten

Although group theory has played a significant role in the development of various disciplines of physics, there are few recent books that start from the beginning and then build on to consider applications of group theory from the point of view of high energy physicists. Group Theory for High Energy Physicists fills that role. It presents groups, especially Lie groups, and their characteristics in a way that is easily comprehensible to physicists.

The book first introduces the concept of a group and the characteristics that are imperative for developing group theory as applied to high energy physics. It then describes group representations since matrix representations of a group are often more convenient to deal with than the abstract group itself. 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. It also explains how symmetry principles associated with group theoretical techniques can be used to interpret experimental results and make predictions.

This concise, gentle introduction is accessible to undergraduate and graduate students in physics and mathematics as well as researchers in high energy physics. It shows how to apply group theory to solve high energy physics problems.

Zielgruppe

Graduate students and scientists in particle/high energy physics.

Autoren/Hrsg.

Saleem, Mohammad

Rafique, Muhammad

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Quantenphysik Teilchenphysik
• Naturwissenschaften Physik Quantenphysik Hochenergiephysik
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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 Naß
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
Appendices
Index

Über Autor(innen)

Dr. Mohammad Saleem is a professor emeritus at the University of the Punjab and a professor at the Institute for Basic Research in Florida. He has written more than 150 research papers on high energy physics and is an editor of the Hadronic Journal.
Dr. Muhammad Rafique was a professor of applied mathematics at University of the Punjab.