| Description |
1 online resource |
| Series |
Chapman & Hall/CRC press monographs and research notes in mathematics |
| Contents |
Cover; Half Title; Title Page; Copyright Page; Dedication; Contents; Author Biography; Preface; Plan of the Book; List of Figures; Part I: Spin; 1 Physical Space; 1.1 Modeling space; 1.2 Real linear operators and matrix groups; 1.3 SO(3) is the group of rotations; 2 Spinor Space; 2.1 Angular momentum in classical mechanics; 2.2 Modeling spin; 2.3 Complex linear operators and matrix groups; 2.4 The geometry of SU(2); 2.4.1 The tangent space to the circle U(1) = S(sup[1]); 2.4.2 The tangent space to the sphere SU(2) =S(sup[3]); 2.4.3 The exponential of a matrix |
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2.4.4 SU(2) is the universal cover of SO(3)2.5 Back to spinor space; 3 Observables and Uncertainty; 3.1 Spin observables; 3.2 The Lie algebra su(2); 3.3 Commutation relations and uncertainty; 3.4 Some related Lie algebras; 3.4.1 Warmup: The Lie algebra u(1); 3.4.2 The Lie algebra sl(sub[2])(C); 3.4.3 The Lie algebra u(2); 3.4.4 The Lie algebra gl(sub[2])(C); 4 Dynamics; 4.1 Time-independent external fields; 4.2 Time-dependent external fields; 4.3 The energy-time uncertainty principle; 4.3.1 Conserved quantities; 5 Higher Spin; 5.1 Group representations; 5.2 Representations of SU(2) |
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5.3 Lie algebra representations5.4 Representations of su(2)(sub[C]) = sl(sub[2])(C); 5.5 Spin-s particles; 5.6 Representations of SO(3); 5.6.1 The so(3)-action; 5.6.2 Comments about analysis; 6 Multiple Particles; 6.1 Tensor products of representations; 6.2 The Clebsch-Gordan problem; 6.3 Identical particles-spin only; Part: II Position & Momentum; 7 A One-Dimensional World; 7.1 Position; 7.2 Momentum; 7.3 The Heisenberg Lie algebra and Lie group; 7.3.1 The meaning of the Heisenberg group action; 7.4 Time-evolution; 7.4.1 The free particle; 7.4.2 The infinite square well |
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7.4.3 The simple harmonic oscillator8 A Three-Dimensional World; 8.1 Position; 8.2 Linear momentum; 8.2.1 The Heisenberg group H(sub[3]) and its algebra h(sub[3]); 8.3 Angular momentum; 8.4 The Lie group G =H(sub[3) [omitted] SO(3) and its Lie algebra g; 8.5 Time-evolution; 8.5.1 The free particle; 8.5.2 The three-dimensional harmonic oscillator; 8.5.3 Central potentials; 8.5.4 The infinite spherical well; 8.6 Two-particle systems; 8.6.1 The Coulomb potential; 8.7 Particles with spin; 8.7.1 The hydrogen atom; 8.8 Identical particles; 9 Toward a Relativistic Theory; 9.1 Galilean relativity |
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9.2 Special relativity9.3 SL(sub[2])(C) is the universal cover of SO(sup[+]) (1, 3); 9.4 The Dirac equation; Appendix A: Appendices; A.1 Linear algebra; A.1.1 Vector spaces and linear transformations; A.1.2 Inner product spaces and adjoints; A.2 Multivariable calculus; A.3 Analysis; A.3.1 Hilbert spaces and adjoints; A.3.2 Some big theorems; A.4 Solutions to selected exercises; Bibliography; Index |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Symmetry (Physics)
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Quantum theory.
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SCIENCE -- Energy.
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SCIENCE -- Mechanics -- General.
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SCIENCE -- Physics -- General.
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Quantum theory
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Symmetry (Physics)
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| Form |
Electronic book
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| ISBN |
9781498701174 |
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1498701175 |
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