Symmetry rules
Subtitle: how science and nature are founded on symmetry
By: by Joseph Rosen
Series: The frontiers collection; Frontiers collection
Publisher: Springer
Published: 2008
Place of publication: Berlin; London
Language: eng
Number of pages: 304
ISBN-13: 9783540759720; 9783540759737
Subjects: Symmetry; Symmetrie
Description: 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.
Notes: Includes index.

Includes bibliographical references (p. [289]-295) and index.
Table of contents: title: 1; title: The Concept of Symmetry -- 1 -- 1.1; title: The Essence of Symmetry -- 1 -- 1.2; title: Symmetry Implies Asymmetry -- 8 -- 1.3; title: Analogy and Classification Are Symmetry -- 10 -- 2; title: Science Is Founded on Symmetry -- 17 -- 2.1; title: Science -- 17 -- 2.2; title: Reduction Is Symmetry -- 20 -- 2.2.1; title: Reduction to Observer and Observed -- 22 -- 2.2.2; title: Reduction to Quasi-Isolated System and Environment -- 25 -- 2.2.3; title: Reduction to Initial State and Evolution -- 26 -- 2.3; title: Reproducibility Is Symmetry -- 29 -- 2.4; title: Predictability Is Symmetry -- 32 -- 2.5; title: Analogy in Science -- 35 -- 2.6; title: Symmetry at the Foundation of Science -- 37 -- 3; title: Symmetry in Physics -- 39 -- 3.1; title: Symmetry of Evolution -- 40 -- 3.2; title: Symmetry of States -- 44 -- 3.3; title: Reference Frame -- 49 -- 3.4; title: Global, Inertial, and Local Reference Frames -- 53 -- 3.5; title: Gauge Transformation -- 55 -- 3.6; title: Gauge Symmetry -- 58 -- 3.7; title: Symmetry and Conservation -- 65 -- 3.7.1; title: Conservation of Energy -- 66 -- 3.7.2; title: Conservation of Linear Momentum -- 67 -- 3.7.3; title: Conservation of Angular Momentum -- 68 -- 3.8; title: Symmetry at the Foundation of Physics -- 70 -- 3.9; title: Symmetry at the Foundation of Quantum Theory -- 71 -- 3.9.1; title: Association of a Hilbert Space with a Physical System -- 71 -- 3.9.2; title: Correspondence of Observables to Hermitian Operators -- 73 -- 3.9.3; title: Complete Set of Compatible Observables -- 74 -- 3.9.4; title: Heisenberg Commutation Relations -- 75 -- 3.9.5; title: Operators for Canonical Variables -- 75 -- 3.9.6; title: A Measurement Result Is an Eigenvalue -- 75 -- 3.9.7; title: Expectation Values and Probabilities -- 76 -- 3.9.8; title: The Hamiltonian Operator -- 76 -- 3.9.9; title: Planck's Constant as a Parameter -- 77 -- 3.9.10; title: The Correspondence Principle -- 77 -- 4; title: The Symmetry Principle -- 81 -- 4.1; title: Causal Relation -- 81 -- 4.2; title: Equivalence Relation, Equivalence Class -- 86 -- 4.3; title: The Equivalence Principle -- 89 -- 4.4; title: The Symmetry Principle -- 97 -- 4.5; title: Cause and Effect in Quantum Systems -- 102 -- 5; title: Application of Symmetry -- 107 -- 5.1; title: Minimalistic Use of the Symmetry Principle -- 107 -- 5.2; title: Maximalistic Use of the Symmetry Principle -- 125 -- 6; title: Approximate Symmetry, Spontaneous Symmetry Breaking -- 131 -- 6.1; title: Approximate Symmetry -- 131 -- 6.2; title: Spontaneous Symmetry Breaking -- 135 -- 7; title: Cosmic Considerations -- 141 -- 7.1; title: Symmetry of the Laws of Nature -- 141 -- 7.2; title: Symmetry of the Universe -- 144 -- 7.3; title: No Cosmic Symmetry Breaking or Restoration -- 147 -- 7.4; title: The Quantum Era and The Beginning -- 155 -- 8; title: The Mathematics of Symmetry: Group Theory -- 161 -- 8.1; title: Group -- 161 -- 8.2; title: Mapping -- 176 -- 8.3; title: Isomorphism -- 180 -- 8.4; title: Homomorphism -- 186 -- 8.5; title: Subgroup -- 192 -- 9; title: Group Theory Continued -- 195 -- 9.1; title: Conjugacy, Invariant Subgroup, Kernel -- 195 -- 9.2; title: Coset Decomposition -- 203 -- 9.3; title: Factor Group -- 207 -- 9.4; title: Anatomy of Homomorphism -- 209 -- 9.5; title: Generator -- 215 -- 9.6; title: Direct Product -- 217 -- 9.7; title: Permutation, Symmetric Group -- 220 -- 9.8; title: Cayley's Theorem -- 224 -- 10; title: The Formalism of Symmetry -- 227 -- 10.1; title: System, State -- 227 -- 10.2; title: Transformation, Transformation Group -- 229 -- 10.3; title: Transformations in Space, Time, and Space-Time -- 236 -- 10.4; title: State Equivalence -- 240 -- 10.5; title: Symmetry Transformation, Symmetry Group -- 243 -- 10.6; title: Approximate Symmetry Transformation -- 251 -- 10.7; title: Quantification of Symmetry -- 253 -- 10.8; title: Quantum Systems -- 255 -- 11; title: Symmetry in Processes -- 261 -- 11.1; title: Symmetry of the Laws of Nature -- 261 -- 11.2; title: Symmetry of Initial and Final States, the General Symmetry Evolution Principle -- 270 -- 11.3; title: The Special Symmetry Evolution Principle and Entropy -- 274 -- 12; title: Summary of Principles -- 283 -- 12.1; title: Symmetry and Asymmetry -- 283 -- 12.2; title: Symmetry Implies Asymmetry -- 283 -- 12.3; title: No Exact Symmetry of the Universe -- 284 -- 12.4; title: Cosmological Implications -- 285 -- 12.5; title: The Equivalence Principle -- 285 -- 12.6; title: The Symmetry Principle -- 285 -- 12.7; title: The Equivalence Principle for Processes -- 286 -- 12.8; title: The Symmetry Principle for Processes -- 286 -- 12.9; title: The General Symmetry Evolution Principle -- 286 -- 12.10; title: The Special Symmetry Evolution Principle-- 286.