| The Concept of Symmetry | p. 1 |
| The Essence of Symmetry | p. 1 |
| Symmetry Implies Asymmetry | p. 8 |
| Analogy and Classification Are Symmetry | p. 10 |
| Summary | p. 15 |
| Science Is Founded on Symmetry | p. 17 |
| Science | p. 17 |
| Reduction Is Symmetry | p. 20 |
| Reduction to Observer and Observed | p. 22 |
| Reduction to Quasi-Isolated System and Environment | p. 25 |
| Reduction to Initial State and Evolution | p. 26 |
| Reproducibility Is Symmetry | p. 29 |
| Predictability Is Symmetry | p. 32 |
| Analogy in Science | p. 35 |
| Symmetry at the Foundation of Science | p. 37 |
| Summary | p. 38 |
| Symmetry in Physics | p. 39 |
| Symmetry of Evolution | p. 40 |
| Symmetry of States | p. 44 |
| Reference Frame | p. 49 |
| Global, Inertial, and Local Reference Frames | p. 53 |
| Gauge Transformation | p. 55 |
| Gauge Symmetry | p. 58 |
| Symmetry and Conservation | p. 65 |
| Conservation of Energy | p. 66 |
| Conservation of Linear Momentum | p. 67 |
| Conservation of Angular Momentum | p. 68 |
| Symmetry at the Foundation of Physics | p. 70 |
| Symmetry at the Foundation of Quantum Theory | p. 71 |
| Association of a Hilbert Space with a Physical System | p. 71 |
| Correspondence of Observables to Hermitian Operators | p. 73 |
| Complete Set of Compatible Observables | p. 74 |
| Heisenberg Commutation Relations | p. 75 |
| Operators for Canonical Variables | p. 75 |
| A Measurement Result Is an Eigenvalue | p. 75 |
| Expectation Values and Probabilities | p. 76 |
| The Hamiltonian Operator | p. 76 |
| Planck's Constant as a Parameter | p. 77 |
| The Correspondence Principle | p. 77 |
| Summary | p. 77 |
| The Symmetry Principle | p. 81 |
| Causal Relation | p. 81 |
| Equivalence Relation, Equivalence Class | p. 86 |
| The Equivalence Principle | p. 89 |
| The Symmetry Principle | p. 97 |
| Cause and Effect in Quantum Systems | p. 102 |
| Summary | p. 104 |
| Application of Symmetry | p. 107 |
| Minimalistic Use of the Symmetry Principle | p. 107 |
| Maximalistic Use of the Symmetry Principle | p. 125 |
| Summary | p. 130 |
| Approximate Symmetry, Spontaneous Symmetry Breaking | p. 131 |
| Approximate Symmetry | p. 131 |
| Spontaneous Symmetry Breaking | p. 135 |
| Summary | p. 140 |
| Cosmic Considerations | p. 141 |
| Symmetry of the Laws of Nature | p. 141 |
| Symmetry of the Universe | p. 144 |
| No Cosmic Symmetry Breaking or Restoration | p. 147 |
| The Quantum Era and The Beginning | p. 155 |
| Summary | p. 159 |
| The Mathematics of Symmetry: Group Theory | p. 161 |
| Group | p. 161 |
| Mapping | p. 176 |
| Isomorphism | p. 180 |
| Homomorphism | p. 186 |
| Subgroup | p. 192 |
| Summary | p. 194 |
| Group Theory Continued | p. 195 |
| Conjugacy, Invariant Subgroup, Kernel | p. 195 |
| Coset Decomposition | p. 203 |
| Factor Group | p. 207 |
| Anatomy of Homomorphism | p. 209 |
| Generator | p. 215 |
| Direct Product | p. 217 |
| Permutation, Symmetric Group | p. 220 |
| Cayley's Theorem | p. 224 |
| Summary | p. 226 |
| The Formalism of Symmetry | p. 227 |
| System, State | p. 227 |
| Transformation, Transformation Group | p. 229 |
| Transformations in Space, Time, and Space-Time | p. 236 |
| State Equivalence | p. 240 |
| Symmetry Transformation, Symmetry Group | p. 243 |
| Approximate Symmetry Transformation | p. 251 |
| Quantification of Symmetry | p. 253 |
| Quantum Systems | p. 255 |
| Summary | p. 258 |
| Symmetry in Processes | p. 261 |
| Symmetry of the Laws of Nature | p. 261 |
| Symmetry of Initial and Final States, the General Symmetry Evolution Principle | p. 270 |
| The Special Symmetry Evolution Principle and Entropy | p. 274 |
| Summary | p. 280 |
| Summary of Principles | p. 283 |
| Symmetry and Asymmetry | p. 283 |
| Symmetry Implies Asymmetry | p. 283 |
| No Exact Symmetry of the Universe | p. 284 |
| Cosmological Implications | p. 285 |
| The Equivalence Principle | p. 285 |
| The Symmetry Principle | p. 285 |
| The Equivalence Principle for Processes | p. 286 |
| The Symmetry Principle for Processes | p. 286 |
| The General Symmetry Evolution Principle | p. 286 |
| The Special Symmetry Evolution Principle | p. 286 |
| References | p. 289 |
| Further Reading | p. 293 |
| Index | p. 297 |
| Table of Contents provided by Ingram. All Rights Reserved. |