Symmetry: An Introduction to Group Theory and Its Applications (Dover Books on Physics) by Roy McWeeny (PDF)

Description

The crucial significance of symmetry to the development of group theory and in the fields of physics and chemistry cannot be overstated, and this well-organized volume provides an excellent introduction to the topic.The text develops the elementary ideas of both group theory and representation theory in a progressive and thorough fashion, leading students to a point from which they can proceed easily to more elaborate applications. The finite groups describing the symmetry of regular polyhedral and of repeating patterns are emphasized, and geometric illustrations of all main processes appear here — including more than 100 fully worked examples.Designed to be read at a variety of levels and to allow students to focus on any of the main fields of application, this volume is geared toward advanced undergraduate and graduate physics and chemistry students with the requisite mathematical background.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I can see why this book has positive reviews for its presentation. A good teacher starts with what the students understand, the intuitions they have developed, a common point of understanding and then motivates then to take a journey from this point to areas and topics that the student does not know nor understand … yet. The author starts with counting and uses informal presentations and examples to present concepts of Linear Algebra, Abstract Algebra, Group Theory, and Representation Theory, always anchored in the physical reality of understanding Symmetry of physical things such as atoms, molecules, and crystals. I must say having worked with several other text books on group theory and many presentations on application to chemistry and crystallography the journey here is not unpleasant, though the informality has sort of tap down my urges to calculate things since most things have yet to be formally defined through chapter 3.But by the end of chapter 3 I already know I am in a room of no exit. The material covered in Chapter 3 is quite astonishing. Instead of dealing initially with point symmetries, the author starts with space symmetries that include point rotations and reflections as well as translations, with a taste of representation theory, a embryonic character table, and a smidge of unitary transforms, we are covering all the generators for all point symmetries of degree 1, 2, 3, 4, and 6 as well as polyhedron groups T and O. This leads to an excellent presentation of crystal groups, which I have not seen so concisely presented before, and a proof that this is all that is necessary to understand to apply to physical symmetries that include translation (I.e. crystallography). The presentation of Icosahedron symmetries and the introduction of quasi-cyrstals resulting from these symmetries is not included which breaks from the conventional wisdom presented here. For someone who wants or needs to come up to speed on typical applications of group theory to chemistry and physics this may not be so bad. But I am currently focused on polyhedral symmetries and their representations, this another dead end.I actually appreciate that the book explains well the conventional wisdom that permeates the development and its applications in chemistry and crystallography, though most of the actual concepts and theorems have yet to be defined and discussed. This leads me to my initial point, I have been lead to this point by my intuitive understanding – I believe that I understand what the author is presenting but it is not clear yet that I can do anything with that understanding. I will have to see as I proceed through the book if I will discovery actionable knowledge. . I have some time before I receive my next text book on group theory.

⭐The author states in the preface that this book was written to serve readers at a variety of levels. In fact this rather short book is almost three books in one.The first two chapters provide an introduction to groups, vector spaces, and lattices. The material here is elementary, but the author is to be commended both for clear explanations as well as excellent notation. My only complaint is that the notation is useful to read, but not really to write as it relies on different typefaces.The next two chapters dig into translation groups, point groups, and space groups in three dimensions. Chapter 5 focuses on the theory of irreducible representations, and in many ways forms the core of the book. The material in these chapters is definitely more challenging than the material in the first two chapters.The final three chapters are devoted to applications. Chapter 6 covers applications to algebraic forms particularly as applied to vibrational modes as encountered in spectroscopy. Chapter 7 focuses on applications to functions and operators. Finally, chapter 8 is devoted to tensors and tensor operators. These three chapters are the most advanced in the book, and each is successively more advanced than the preceding one. These chapters will serve more advanced readers.Early on the author introduces the group which comes to be known as C_3v. This groups is used as an example throughout the book and comes fully to life in chapter 6 where it is used to analyze the vibrational modes of the ammonia molecule. I really appreciated the continuity of and the elaboration on this one example as a unifying thread in the text.The entire book contains copious tables and figures which are extremely helpful. In particular, chapters 3 and 4 contain detailed tables of the groups considered as well as their representations. The book has no exercises, but does offer a nice collection of suggestions for further reading at the end of each chapter. Finally, this book has remarkably few errors which is actually somewhat surprising just given the level of detail in some sections such as the group tables mentioned above.Sure to be useful in particular to students of quantum chemistry and spectroscopy, this book is excellent and repays multiple readings, but I’d recommend the prospective reader bring a background in linear algebra and some quantum chemistry.

⭐I wanted to learn about symmetry for use in understanding the quantum understanding of the periodic table. The orbital groups, labeled with the letters S, P, D, and F seem to involve symmetry. They are often said to be solutions to the Schrodinger equation. However this book gives a mathematical description of symmetry groups and a geometric way of thinking about including and excluding various possibilities as solutions. The pragmatics seem very powerful.This book is designed for mathematicians. Since I am not and I am only interested in learning and teaching about the periodic table, I skipped over the mathematical notation’s and was able to extract principles of group theory and symmetry as it pertains to the periodic table. Therefore I found the book very valuable.

⭐Los textos sobre la materia acostumbran a ser una especie de libros de leyes donde te vienen a enumerar las propiedades, ecuaciones, etc, demostrándotelas desde un punto de vista puramente formal, sin conexión alguna con la realidad. Este libro es un prodigio de dicáctica, sin perder la profundidad necesaria, y está lleno de ideas, de ideas normales escritas con palabras normales en inglés. Si alguna persona está buscando un libro que le explique bien que es la Teoría de Grupos pienso que éste es el texto. Para su lectura es necesaria una base mínima en álgebra y en las cuestiones básicas de las matemáticas.

⭐Not found.

⭐very pleased with every thing

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