Rosen J. Symmetry in Science. An Introduction to the General Theory 1995

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Rosen J. Symmetry in Science. An Introduction to the General Theory 1995

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Textbook in PDF format Symmetry in Science: An Introduction to the General Theory by Joseph Rosen posits that everyone has some idea of what symmetry is. We recognize the bilateral symmetry of the human body, of the bodies of many other animals, and of numerous objects in our environment. We consider a-scalene triangle to be completely lacking in symmetry, while we see symmetry in an isosceles triangle and even more symmetry in an equilateral triangle. That is only for starters. Any reader of this book can easily point out many more kinds and examples of symmetry. In science, of course, our recognition and utilization of symmetry is often more sophisticated, sometimes very much more. But what symmetry actually boils down to in the final analysis is that the situation possesses the possibility of a change that leaves some aspect of the situation unchanged. A bilaterally symmetric body can be reflected through its midplane, through the (imaginary) plane separating the body's two similar halves. Think of a two-sided mirror positioned in that plane. Such a reflection is a change. Yet the reflected body looks the same as the original one; it coincides with the original: the reflected right- and left-hands, paws, or hooves coincide, respectively, with the original left and right ones, and similarly with the feet, ears, and so on. Symmetry plays an essential role in science - not only in crystallography and quantum theory, where its role has long been explicitly recognized, but also in condensed-matter physics, thermodynamics, chemistry, biology, and others. This text discusses the concept of symmetry and its application to many areas of science. While it includes a detailed introduction to the theory of groups, which forms the mathematical apparatus for describing symmetries, it also includes a much more general discussion of the nature of symmetry and its role in science. Many problems serve to sharpen the reader's understanding, and an extensive bibliography concludes the book. Contents Preface What Is Symmetry? The Mathematics of Symmetry: Group Theory The Group Concept Mapping Isomorphism Equivalence Relation Homomorphism Subgroup Summary of Chapter Two Group Theory Continued Conjugacy, Equivalence Class, Invariant Subgroup, Kernel Coset Decomposition Factor Group Anatomy of Homomorphism Generators Direct Product Permutations, Symmetric Groups Cycles, Transpositions, Alternating Groups Cayley's Theorem Summary of Chapter Three Symmetry: The Formalism System, State Transformations, Transformation Group Transformations in Space, Time, and Space-Time State Equivalence Symmetry Transformations, Symmetry Group Quantification of Symmetry Quantum Systems Summary of Chapter Four Application of Symmetry Causal Relation The Equivalence Principle The Symmetry Principle Minimalistic Use of the Symmetry Principle Maximalistic Use of the Symmetry Principle Quantum Systems Summary of Chapter Five Approximate Symmetry and Spontaneous Symmetry Breaking Approximate Symmetry Spontaneous Symmetry Breaking Summary of Chapter Six Symmetry in Processes, Conservation, and Cosmic Considerations Symmetry of the Laws of Nature Symmetry of Initial and Final States, the General Symmetry Evolution Principle The Special Symmetry Evolution Principle and Entropy Conservation Cosmic Considerations Summary of Chapter Seven Symmetry: The Concept The Essence of Symmetry How Is Change? Symmetry of the Universe Analogy as Symmetry Summary of Chapter Eight Symmetry in Science Science Reduction as Symmetry Observer and Observed Quasi-Isolated System and Surroundings Initial State and Evolution Reproducibility as Symmetry Predictability as Symmetry Symmetry at the Foundation of Science Summary of Chapter Nine More Symmetry in Science Analogy in Science Symmetry of Evolution Symmetry of States Summary of Chapter Ten Summary of Principles Onward Bibliography Index