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SHATTERED SYMMETRY : group theory from the eightfold way to the periodic table.
Symmetry and its breaking is at the heart of our understanding of matter. The book tells the tale of two constituents of matter quarks and atoms from a common symmetry perspective.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
OXFORD :
OXFORD University Press,
2017.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Half Title page; Title page; Copyright page; Dedication; Contents; List of Figures; List of Tables; Preface; PART ONE SPACE SYMMETRIES; 1 A primer on symmetry; 1.1 THE TRAGIC LIFE OF ÉVARISTE GALOIS; 1.1.1 Entrance exams; 1.1.2 Publish or perish; 1.1.3 Galois' mathematical testament; 1.2 THE CONCEPT OF SYMMETRY; 1.2.1 Symmetry defined; 1.2.2 The symmetries of a triangle; 1.2.3 Quantifying symmetry; 1.2.4 Discrete and continuous symmetries; 1.2.5 Multiplying symmetries; 2 The elements of group theory; 2.1 MATHEMATICAL DEFINITION; 2.2 THE ABSTRACT AND THE CONCRETE; 2.3 ABELIAN GROUPS.
- 2.4 EXAMPLES OF GROUPS2.5 SUBGROUPS; 2.6 SYMMETRY BREAKING; 2.7 ISOMORPHISMS AND HOMOMORPHISMS; 2.8 HISTORICAL INTERLUDE; 2.8.1 Évariste Galois; 2.8.2 The French school; 2.8.3 Sir Arthur Cayley; 3 The axial rotation group; 3.1 ACTIVE VERSUS PASSIVE VIEW OF SYMMETRY; 3.2 ROTATION OPERATORS; 3.3 THE AXIAL ROTATION GROUP; 3.4 TRANSFORMATIONS OF COORDINATES; 3.5 TRANSFORMATIONS OF COORDINATE FUNCTIONS; 3.6 MATRIX REPRESENTATIONS; 3.6.1 Matrix representation of coordinate operators R; 3.6.2 Matrix representation of function operators \hat{R}; 3.7 THE ORTHOGONAL GROUP O(2).
- 3.7.1 Symmetry and invariance3.7.2 Proper and improper rotation matrices; 3.7.3 Orthogonal groups: O(2) and SO(2); 4 The SO(2) group; 4.1 INFINITE CONTINUOUS GROUPS; 4.1.1 The nature of infinite continuous groups; 4.1.2 Parameters of continuous groups; 4.1.3 Examples of continuous groups; 4.1.4 The composition functions; 4.2 LIE GROUPS; 4.2.1 Definition; 4.2.2 Parameter space; 4.2.3 Connectedness and compactness; 4.3 THE INFINITESIMAL GENERATOR; 4.3.1 Matrix form of the SO(2) generator; 4.3.2 Operator form of the SO(2) generator; 4.4 ANGULAR MOMENTUM; 4.4.1 Classical mechanical picture.
- 4.4.2 Quantum mechanical picture4.5 SO(2) SYMMETRY AND AROMATIC MOLECULES; 4.5.1 The particle on a ring model; 4.5.2 The shell perspective; 4.5.3 Aromatic molecules; 5 The SO(3) group; 5.1 THE SPHERICAL ROTATION GROUP; 5.2 THE ORTHOGONAL GROUP IN THREE DIMENSIONS; 5.2.1 Rotation matrices; 5.2.2 The orthogonal group O(3); 5.2.3 The special orthogonal group SO(3); 5.3 ROTATIONS AND SO(3); 5.3.1 Orthogonality and skew-symmetry; 5.3.2 The matrix representing an infinitesimal rotation; 5.3.3 The exponential map; 5.3.4 The Euler parameterization; 5.4 THE so(3) LIE ALGEBRA.
- 5.4.1 The so(3) generators5.4.2 Operator form of the SO(3) generators; 5.5 ROTATIONS IN QUANTUM MECHANICS; 5.5.1 Angular momentum as the generator of rotations; 5.5.2 The rotation operator; 5.6 ANGULAR MOMENTUM; 5.6.1 The angular momentum algebra; 5.6.2 Casimir invariants; 5.6.3 The eigenvalue problem; 5.6.4 Dirac's ladder operator method; 5.7 APPLICATION: PARTICLE ON A SPHERE; 5.7.1 Spherical components of the Hamiltonian; 5.7.2 The flooded planet model and Buckminsterfullerene; 5.8 EPILOGUE; 6 Scholium I; 6.1 SYMMETRY IN QUANTUM MECHANICS; 6.1.1 State vector transformations.