Group theory in physics [[electronic resource] ] : an introduction / / J.F. Cornwell

• Record Nr.: UNINA9910458584503321
• Autore: Cornwell J. F
• Pubbl/distr/stampa: San Diego, : Academic Press, c1997
• ISBN: 1-281-46682-4; 9786611466824; 0-08-053266-7
• Descrizione fisica: 1 online resource (361 p.)
• Collana: Techniques of physics ; ; 7
• Disciplina: 530.1522
• Soggetti: Group theory; Mathematical physics; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Front Cover; Group Theory in Physics: An Introduction; Copyright Page; Contents; Preface; Chapter 1. The Basic Framework; 1. The concept of a group; 2. Groups of coordinate transformations; 3. The group of the Schrödinger equation; 4. The role of matrix representations; Chapter 2. The Structure of Groups; 1. Some elementary considerations; 2. Classes; 3. Invariant subgroups; 4. Cosets; 5. Factor groups; 6. Homomorphic and isomorphic mappings; 7. Direct products and semi-direct products of groups; Chapter 3. Lie Groups; 1. Definition of a linear Lie group; 2. The connected components of a linear Lie group3. The concept of compactness for linear Lie; 4. Invariant integration; Chapter 4. Representations of Groups - Principal Ideas; 1. Definitions; 2. Equivalent representations; 3. Unitary representations; 4. Reducible and irreducible representations; 5. Schur's Lemmas and the orthogonality theorem for matrix representations; 6. Characters; Chapter 5. Representations of Groups - Developments; 1. Projection operators; 2. Direct product representations; 3. The Wigner-Eckart Theorem for groups of coordinate transfor-mations in IR3; 4. The Wigner-Eckart Theorem generalized5. Representations of direct ; product groups; 6. Irreducible representations of finite Abelian groups; 7. Induced representations; Chapter 6. Group Theory in Quantum Mechanical Calculations; 1. The solution of the Schrödinger equation; 2. Transition probabilities and selection rules; 3. Time-independent perturbation theory; Chapter 7. Crystallographic Space Groups; 1. The Bravais lattices; 2. The cyclic boundary conditions; 3. Irreducible representations of the group T of pure primitive translations and Bloch's Theorem; 4. Brillouin zones; 5. Electronic energy bands6. Survey of the crystallographic space groups; 7. Irreducible representations of symmorphic space groups; 8. Consequences of the fundamental theorems; Chapter 8. The Role of Lie Algebras; 1. ""Local"" and ""global"" aspects of Lie groups; 2. The matrix exponential function; 3. One-parameter subgroups; 4. Lie algebras; 5. The real Lie algebras that correspond to general linear Lie groups; Chapter 9. The Relationships between Lie Groups and Lie Algebras Explored; 1. Introduction; 2. Subalgebras of Lie algebras; 3. Homomorphic and isomorphic mappings of Lie algebras; 4. Representations of Lie algebras5. The adjoint representations of Lie algebras and linear Lie groups; 6. Direct sum of Lie algebras; Chapter 10. The Three-dimensional Rotation Groups; 1. Some properties reviewed; 2. The class structures of SU(2) and SO(3); 3. Irreducible representations of the Lie algebras su(2) and so(3); 4. Representations of the Lie groups SU(2), SO(3) and O(3); 5. Direct products of irreducible representations and the Clebsch-Gordan coefficients; 6. Applications to atomic physics; Chapter 11. The Structure of Semi-simple Lie Algebras; 1. An outline of the presentation; 2. The Killing form and Cartan's criterion
• Sommario/riassunto: This book, an abridgment of Volumes I and II of the highly respected Group Theory in Physics, presents a carefully constructed introduction to group theory and its applications in physics. The book provides anintroduction to and description of the most important basic ideas and the role that they play in physical problems. The clearly written text contains many pertinent examples that illustrate the topics, even for those with no background in group theory.This work presents important mathematical developments to theoretical physicists in a form that is easy to comprehend and apprec