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Group theory in physics [[electronic resource] ] : an introduction / / J.F. Cornwell
| Group theory in physics [[electronic resource] ] : an introduction / / J.F. Cornwell |
| Autore | Cornwell J. F |
| Pubbl/distr/stampa | San Diego, : Academic Press, c1997 |
| Descrizione fisica | 1 online resource (361 p.) |
| Disciplina | 530.1522 |
| Collana | Techniques of physics |
| Soggetto topico |
Group theory
Mathematical physics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-46682-4
9786611466824 0-08-053266-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910458584503321 |
Cornwell J. F
|
||
| San Diego, : Academic Press, c1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Group theory in physics [[electronic resource] ] : an introduction / / J.F. Cornwell
| Group theory in physics [[electronic resource] ] : an introduction / / J.F. Cornwell |
| Autore | Cornwell J. F |
| Pubbl/distr/stampa | San Diego, : Academic Press, c1997 |
| Descrizione fisica | 1 online resource (361 p.) |
| Disciplina | 530.1522 |
| Collana | Techniques of physics |
| Soggetto topico |
Group theory
Mathematical physics |
| ISBN |
1-281-46682-4
9786611466824 0-08-053266-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910784533003321 |
|
Cornwell J. F
|
||
| San Diego, : Academic Press, c1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Group theory in physics [[electronic resource] ] : an introduction / / J.F. Cornwell
| Group theory in physics [[electronic resource] ] : an introduction / / J.F. Cornwell |
| Autore | Cornwell J. F |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | San Diego, : Academic Press, c1997 |
| Descrizione fisica | 1 online resource (361 p.) |
| Disciplina | 530.1522 |
| Collana | Techniques of physics |
| Soggetto topico |
Group theory
Mathematical physics |
| ISBN |
1-281-46682-4
9786611466824 0-08-053266-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910827536303321 |
|
Cornwell J. F
|
||
| San Diego, : Academic Press, c1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||