Symmetry rules how science and nature are founded on symmetry / [Texte imprimé] :
by Joseph Rosen
- Berlin ; London : Springer, 2008
- 1 vol. (XIV-304 p.) : ill., couv. ill. ; 24 cm
- The frontiers collection .
- The Frontiers Collection (Springer, Berlin) .
Bibliogr. p. [289]-295
The Concept of Symmetry The Essence of Symmetry Symmetry Implies Asymmetry Analogy and Classification Are Symmetry Science Is Founded on Symmetry Science Reduction Is Symmetry Reduction to Observer and Observed Reduction to Quasi-Isolated System and Environment Reduction to Initial State and Evolution Reproducibility Is Symmetry Predictability Is Symmetry Analogy in Science Symmetry at the Foundation of Science Symmetry in Physics Symmetry of Evolution Symmetry of States Reference Frame Global, Inertial, and Local Reference Frames Gauge Transformation Gauge Symmetry Symmetry and Conservation Conservation of Energy Conservation of Linear Momentum Conservation of Angular Momentum Symmetry at the Foundation of Physics Symmetry at the Foundation of Quantum Theory Association of a Hilbert Space with a Physical System Correspondence of Observables to Hermitian Operators Complete Set of Compatible Observables Heisenberg Commutation Relations Operators for Canonical Variables A Measurement Result Is an Eigenvalue Expectation Values and Probabilities The Hamiltonian Operator Planck's Constant as a Parameter The Correspondence Principle The Symmetry Principle Causal Relation Equivalence Relation, Equivalence Class The Equivalence Principle The Symmetry Principle Cause and Effect in Quantum Systems Application of Symmetry Minimalistic Use of the Symmetry Principle Maximalistic Use of the Symmetry Principle Approximate Symmetry, Spontaneous Symmetry Breaking Approximate Symmetry Spontaneous Symmetry Breaking Cosmic Considerations Symmetry of the Laws of Nature Symmetry of the Universe No Cosmic Symmetry Breaking or Restoration The Quantum Era and The Beginning The Mathematics of Symmetry: Group Theory Group Mapping Isomorphism Homomorphism Subgroup Group Theory Continued Conjugacy, Invariant Subgroup, Kernel Coset Decomposition Factor Group Anatomy of Homomorphism Generator Direct Product Permutation, Symmetric Group Cayley's Theorem The Formalism of Symmetry System, State Transformation, Transformation Group Transformations in Space, Time, and Space-Time State Equivalence Symmetry Transformation, Symmetry Group Approximate Symmetry Transformation Quantification of Symmetry Quantum Systems Symmetry in Processes Symmetry of the Laws of Nature Symmetry of Initial and Final States, the General Symmetry Evolution Principle The Special Symmetry Evolution Principle and Entropy Summary of Principles Symmetry and Asymmetry Symmetry Implies Asymmetry No Exact Symmetry of the Universe Cosmological Implications The Equivalence Principle The Symmetry Principle The Equivalence Principle for Processes The Symmetry Principle for Processes The General Symmetry Evolution Principle The Special Symmetry Evolution Principle 1 1 -- 1.1 1 -- 1.2 8 -- 1.3 10 -- 2 17 -- 2.1 17 -- 2.2 20 -- 2.2.1 22 -- 2.2.2 25 -- 2.2.3 26 -- 2.3 29 -- 2.4 32 -- 2.5 35 -- 2.6 37 -- 3 39 -- 3.1 40 -- 3.2 44 -- 3.3 49 -- 3.4 53 -- 3.5 55 -- 3.6 58 -- 3.7 65 -- 3.7.1 66 -- 3.7.2 67 -- 3.7.3 68 -- 3.8 70 -- 3.9 71 -- 3.9.1 71 -- 3.9.2 73 -- 3.9.3 74 -- 3.9.4 75 -- 3.9.5 75 -- 3.9.6 75 -- 3.9.7 76 -- 3.9.8 76 -- 3.9.9 77 -- 3.9.10 77 -- 4 81 -- 4.1 81 -- 4.2 86 -- 4.3 89 -- 4.4 97 -- 4.5 102 -- 5 107 -- 5.1 107 -- 5.2 125 -- 6 131 -- 6.1 131 -- 6.2 135 -- 7 141 -- 7.1 141 -- 7.2 144 -- 7.3 147 -- 7.4 155 -- 8 161 -- 8.1 161 -- 8.2 176 -- 8.3 180 -- 8.4 186 -- 8.5 192 -- 9 195 -- 9.1 195 -- 9.2 203 -- 9.3 207 -- 9.4 209 -- 9.5 215 -- 9.6 217 -- 9.7 220 -- 9.8 224 -- 10 227 -- 10.1 227 -- 10.2 229 -- 10.3 236 -- 10.4 240 -- 10.5 243 -- 10.6 251 -- 10.7 253 -- 10.8 255 -- 11 261 -- 11.1 261 -- 11.2 270 -- 11.3 274 -- 12 283 -- 12.1 283 -- 12.2 283 -- 12.3 284 -- 12.4 285 -- 12.5 285 -- 12.6 285 -- 12.7 286 -- 12.8 286 -- 12.9 286 -- 12.10 286.
Modern theoretical physics suggests that symmetry is a, if not the, foundational principle of nature. Emphasizing the concepts, this book introduces symmetry and its applications. It is shown that the universe cannot possess exact symmetry, which is a principle of fundamental significance.