E-book
Symmetry Rules [electronic resource] : How Science and Nature are founded on Symmetry / by Joe Rosen.
Record details
- ISBN: 9783540759737
- Physical Description: online resource.
- Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
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| Subject: | Physics. Aesthetics. Group theory. Mathematical physics. Physics. Mathematical Methods in Physics. Group Theory and Generalizations. Aesthetics. |
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Electronic resources
| 1 | ||
| The Concept of Symmetry -- 1 -- 1.1 | ||
| The Essence of Symmetry -- 1 -- 1.2 | ||
| Symmetry Implies Asymmetry -- 8 -- 1.3 | ||
| Analogy and Classification Are Symmetry -- 10 -- 2 | ||
| Science Is Founded on Symmetry -- 17 -- 2.1 | ||
| Science -- 17 -- 2.2 | ||
| Reduction Is Symmetry -- 20 -- 2.2.1 | ||
| Reduction to Observer and Observed -- 22 -- 2.2.2 | ||
| Reduction to Quasi-Isolated System and Environment -- 25 -- 2.2.3 | ||
| Reduction to Initial State and Evolution -- 26 -- 2.3 | ||
| Reproducibility Is Symmetry -- 29 -- 2.4 | ||
| Predictability Is Symmetry -- 32 -- 2.5 | ||
| Analogy in Science -- 35 -- 2.6 | ||
| Symmetry at the Foundation of Science -- 37 -- 3 | ||
| Symmetry in Physics -- 39 -- 3.1 | ||
| Symmetry of Evolution -- 40 -- 3.2 | ||
| Symmetry of States -- 44 -- 3.3 | ||
| Reference Frame -- 49 -- 3.4 | ||
| Global, Inertial, and Local Reference Frames -- 53 -- 3.5 | ||
| Gauge Transformation -- 55 -- 3.6 | ||
| Gauge Symmetry -- 58 -- 3.7 | ||
| Symmetry and Conservation -- 65 -- 3.7.1 | ||
| Conservation of Energy -- 66 -- 3.7.2 | ||
| Conservation of Linear Momentum -- 67 -- 3.7.3 | ||
| Conservation of Angular Momentum -- 68 -- 3.8 | ||
| Symmetry at the Foundation of Physics -- 70 -- 3.9 | ||
| Symmetry at the Foundation of Quantum Theory -- 71 -- 3.9.1 | ||
| Association of a Hilbert Space with a Physical System -- 71 -- 3.9.2 | ||
| Correspondence of Observables to Hermitian Operators -- 73 -- 3.9.3 | ||
| Complete Set of Compatible Observables -- 74 -- 3.9.4 | ||
| Heisenberg Commutation Relations -- 75 -- 3.9.5 | ||
| Operators for Canonical Variables -- 75 -- 3.9.6 | ||
| A Measurement Result Is an Eigenvalue -- 75 -- 3.9.7 | ||
| Expectation Values and Probabilities -- 76 -- 3.9.8 | ||
| The Hamiltonian Operator -- 76 -- 3.9.9 | ||
| Planck's Constant as a Parameter -- 77 -- 3.9.10 | ||
| The Correspondence Principle -- 77 -- 4 | ||
| The Symmetry Principle -- 81 -- 4.1 | ||
| Causal Relation -- 81 -- 4.2 | ||
| Equivalence Relation, Equivalence Class -- 86 -- 4.3 | ||
| The Equivalence Principle -- 89 -- 4.4 | ||
| The Symmetry Principle -- 97 -- 4.5 | ||
| Cause and Effect in Quantum Systems -- 102 -- 5 | ||
| Application of Symmetry -- 107 -- 5.1 | ||
| Minimalistic Use of the Symmetry Principle -- 107 -- 5.2 | ||
| Maximalistic Use of the Symmetry Principle -- 125 -- 6 | ||
| Approximate Symmetry, Spontaneous Symmetry Breaking -- 131 -- 6.1 | ||
| Approximate Symmetry -- 131 -- 6.2 | ||
| Spontaneous Symmetry Breaking -- 135 -- 7 | ||
| Cosmic Considerations -- 141 -- 7.1 | ||
| Symmetry of the Laws of Nature -- 141 -- 7.2 | ||
| Symmetry of the Universe -- 144 -- 7.3 | ||
| No Cosmic Symmetry Breaking or Restoration -- 147 -- 7.4 | ||
| The Quantum Era and The Beginning -- 155 -- 8 | ||
| The Mathematics of Symmetry: Group Theory -- 161 -- 8.1 | ||
| Group -- 161 -- 8.2 | ||
| Mapping -- 176 -- 8.3 | ||
| Isomorphism -- 180 -- 8.4 | ||
| Homomorphism -- 186 -- 8.5 | ||
| Subgroup -- 192 -- 9 | ||
| Group Theory Continued -- 195 -- 9.1 | ||
| Conjugacy, Invariant Subgroup, Kernel -- 195 -- 9.2 | ||
| Coset Decomposition -- 203 -- 9.3 | ||
| Factor Group -- 207 -- 9.4 | ||
| Anatomy of Homomorphism -- 209 -- 9.5 | ||
| Generator -- 215 -- 9.6 | ||
| Direct Product -- 217 -- 9.7 | ||
| Permutation, Symmetric Group -- 220 -- 9.8 | ||
| Cayley's Theorem -- 224 -- 10 | ||
| The Formalism of Symmetry -- 227 -- 10.1 | ||
| System, State -- 227 -- 10.2 | ||
| Transformation, Transformation Group -- 229 -- 10.3 | ||
| Transformations in Space, Time, and Space-Time -- 236 -- 10.4 | ||
| State Equivalence -- 240 -- 10.5 | ||
| Symmetry Transformation, Symmetry Group -- 243 -- 10.6 | ||
| Approximate Symmetry Transformation -- 251 -- 10.7 | ||
| Quantification of Symmetry -- 253 -- 10.8 | ||
| Quantum Systems -- 255 -- 11 | ||
| Symmetry in Processes -- 261 -- 11.1 | ||
| Symmetry of the Laws of Nature -- 261 -- 11.2 | ||
| Symmetry of Initial and Final States, the General Symmetry Evolution Principle -- 270 -- 11.3 | ||
| The Special Symmetry Evolution Principle and Entropy -- 274 -- 12 | ||
| Summary of Principles -- 283 -- 12.1 | ||
| Symmetry and Asymmetry -- 283 -- 12.2 | ||
| Symmetry Implies Asymmetry -- 283 -- 12.3 | ||
| No Exact Symmetry of the Universe -- 284 -- 12.4 | ||
| Cosmological Implications -- 285 -- 12.5 | ||
| The Equivalence Principle -- 285 -- 12.6 | ||
| The Symmetry Principle -- 285 -- 12.7 | ||
| The Equivalence Principle for Processes -- 286 -- 12.8 | ||
| The Symmetry Principle for Processes -- 286 -- 12.9 | ||
| The General Symmetry Evolution Principle -- 286 -- 12.10 | ||
| The Special Symmetry Evolution Principle-- 286. |
