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A First Course on Symmetry, Special Relativity and Quantum Mechanics: The Foundations of Physics (2021) (Paperback)
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$770.00
購買後立即進貨, 約需 18-25 天
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商品簡介 |
| 1 Introduction 91.1 The goal of physics . . . . . . . . . . . . . . . . . . . . . . . . 91.2 The connection between physics and mathematics . . . . . . . 101.3 Paradigm shifts . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4 The Correspondence Principle . . . . . . . . . . . . . . . . . . 162 Symmetry and Physics 172.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 172.2 What is Symmetry? . . . . . . . . . . . . . . . . . . . . . . . . 172.3 Role of Symmetry in Physics . . . . . . . . . . . . . . . . . . . 182.3.1 Symmetry as a guiding principle . . . . . . . . . . . . . 182.3.2 Symmetry and Conserved Quantities: Noether's Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.3 Symmetry as a tool for simplifying problems . . . . . . 192.4 Symmetries were made to be broken . . . . . . . . . . . . . . 202.4.1 Spacetime symmetries . . . . . . . . . . . . . . . . . . 202.4.2 Parity violation . . . . . . . . . . . . . . . . . . . . . . 212.4.3 Spontaneously broken symmetries . . . . . . . . . . . . 242.4.4 Variational calculations: Lifeguards and light rays . . . 273 Formal Aspects of Symmetry 303.1 Learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . 303.2 Symmetries and Operations . . . . . . . . . . . . . . . . . . . 303.2.1 Denition of a symmetry operation . . . . . . . . . . . 303.2.2 Rules obeyed by symmetry operations . . . . . . . . . 323.2.3 Multiplication tables . . . . . . . . . . . . . . . . . . . 353.2.4 Symmetry and group theory . . . . . . . . . . . . . . . 363.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3.1 The identity operation . . . . . . . . . . . . . . . . . . 373.3.2 Permutations of two identical objects . . . . . . . . . . 373.3.3 Permutations of three identical objects . . . . . . . . . 383.3.4 Rotations of regular polygons . . . . . . . . . . . . . . 393.4 Continuous vs discrete symmetries . . . . . . . . . . . . . . . 403.5 Symmetries and Conserved Quantities: Noether's Theorem . . . . . . . . . . . . . . . . . . . . . . . . 413.6 Supplementary: Variational Mechanics and the Proof of Noether'sTheorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.6.1 Variational Mechanics: Principle of Least Action . . . . 423.6.2 Euler-Lagrange Equations . . . . . . . . . . . . . . . . 473.6.3 Proof of Noether's Theorem . . . . . . . . . . . . . . . 484 Symmetries and Linear Transformations 524.1 Learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . 524.2 Review of Vectors . . . . . . . . . . . . . . . . . . . . . . . . . 534.2.1 Coordinate free denitions . . . . . . . . . . . . . . . . 534.2.2 Cartesian Coordinates . . . . . . . . . . . . . . . . . . 584.2.3 Vector operations in component form . . . . . . . . . . 594.2.4 Position vector . . . . . . . . . . . . . . . . . . . . . . 604.2.5 Dierentiation of vectors: velocity and acceleration . . 624.3 Linear Transformations . . . . . . . . . . . . . . . . . . . . . . 634.3.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . 634.3.2 Translations . . . . . . . . . . . . . . . . . . . . . . . . 644.3.3 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . 664.3.4 Reections . . . . . . . . . . . . . . . . . . . . . . . . . 674.4 Linear Transformations and matrices . . . . . . . . . . . . . . 684.4.1 Linear transformations as matrices . . . . . . . . . . . 684.4.2 Identity Transformation and Inverses . . |
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