Applied Group Theory
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| Author | : Arthur P. Cracknell |
| Publisher | : Elsevier |
| Total Pages | : 433 |
| Release | : 2016-06-03 |
| Genre | : Science |
| ISBN | : 1483182479 |
Applied Group Theory covers group theory and its applications and is designed to cater undergraduate students. This text is comprised of two parts; the first of which discusses topics such as symmetry; crystallographic groups; vibrations in molecules and solids; and electronic states in atoms, molecules, and solids. This book then explains in the second part topics including the elastic characteristic vibrations of symmetrical systems; theory of Brillouin zones and symmetry properties of wave functions in crystals; and magnetic symmetry of crystals. This text also gives hints to solutions of the exercises provided in each discussion. This selection will be invaluable to undergraduate students of mathematics who are in need of reference materials in group theory that are understandable to them. Mathematics instructors will also find this book helpful.
| Author | : George H. Duffey |
| Publisher | : Courier Corporation |
| Total Pages | : 387 |
| Release | : 2015-02-18 |
| Genre | : Science |
| ISBN | : 0486783146 |
This text introduces advanced undergraduates and graduate students to key applications of group theory. Topics include the nature of symmetry operations; applications to vibrating systems, continuum mechanics, and quantum structures; permutation, continuous, and rotation groups; and physical Lie algebras. Each chapter concludes with a concise review, discussion questions, problems, and references. 1992 edition.
| Author | : Mildred S. Dresselhaus |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 576 |
| Release | : 2007-12-18 |
| Genre | : Science |
| ISBN | : 3540328998 |
This concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters.
| Author | : Teturo Inui |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 409 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642800211 |
This book has been written to introduce readers to group theory and its ap plications in atomic physics, molecular physics, and solid-state physics. The first Japanese edition was published in 1976. The present English edi tion has been translated by the authors from the revised and enlarged edition of 1980. In translation, slight modifications have been made in. Chaps. 8 and 14 to update and condense the contents, together with some minor additions and improvements throughout the volume. The authors cordially thank Professor J. L. Birman and Professor M. Car dona, who encouraged them to prepare the English translation. Tokyo, January 1990 T. Inui . Y. Tanabe Y. Onodera Preface to the Japanese Edition As the title shows, this book has been prepared as a textbook to introduce readers to the applications of group theory in several fields of physics. Group theory is, in a nutshell, the mathematics of symmetry. It has three main areas of application in modern physics. The first originates from early studies of crystal morphology and constitutes a framework for classical crystal physics. The analysis of the symmetry of tensors representing macroscopic physical properties (such as elastic constants) belongs to this category. The sec ond area was enunciated by E. Wigner (1926) as a powerful means of handling quantum-mechanical problems and was first applied in this sense to the analysis of atomic spectra. Soon, H.
| Author | : Arnout Jozef Ceulemans |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 276 |
| Release | : 2013-09-03 |
| Genre | : Science |
| ISBN | : 940076863X |
Chemists are used to the operational definition of symmetry, which crystallographers introduced long before the advent of quantum mechanics. The ball-and-stick models of molecules naturally exhibit the symmetrical properties of macroscopic objects. However, the practitioner of quantum chemistry and molecular modeling is not concerned with balls and sticks, but with subatomic particles: nuclei and electrons. This textbook introduces the subtle metaphors which relate our macroscopic understanding of symmetry to the molecular world. It gradually explains how bodily rotations and reflections, which leave all inter-particle distances unaltered, affect the study of molecular phenomena that depend only on these internal distances. It helps readers to acquire the skills to make use of the mathematical tools of group theory for whatever chemical problems they are confronted with in the course of their own research.
| Author | : R. McWeeny |
| Publisher | : Elsevier |
| Total Pages | : 263 |
| Release | : 2013-09-03 |
| Genre | : Mathematics |
| ISBN | : 1483226247 |
Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.
| Author | : Nathan Carter |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 295 |
| Release | : 2021-06-08 |
| Genre | : Education |
| ISBN | : 1470464330 |
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
| Author | : Patrick W. M. Jacobs |
| Publisher | : Cambridge University Press |
| Total Pages | : 520 |
| Release | : 2005-10-18 |
| Genre | : Mathematics |
| ISBN | : 9780521642507 |
This book provides a rigorous account on the fundamentals and applications of Group Theory to chemical physics.
| Author | : Wolfram Hergert |
| Publisher | : John Wiley & Sons |
| Total Pages | : 387 |
| Release | : 2018-08-20 |
| Genre | : Science |
| ISBN | : 352741133X |
While group theory and its application to solid state physics is well established, this textbook raises two completely new aspects. First, it provides a better understanding by focusing on problem solving and making extensive use of Mathematica tools to visualize the concepts. Second, it offers a new tool for the photonics community by transferring the concepts of group theory and its application to photonic crystals. Clearly divided into three parts, the first provides the basics of group theory. Even at this stage, the authors go beyond the widely used standard examples to show the broad field of applications. Part II is devoted to applications in condensed matter physics, i.e. the electronic structure of materials. Combining the application of the computer algebra system Mathematica with pen and paper derivations leads to a better and faster understanding. The exhaustive discussion shows that the basics of group theory can also be applied to a totally different field, as seen in Part III. Here, photonic applications are discussed in parallel to the electronic case, with the focus on photonic crystals in two and three dimensions, as well as being partially expanded to other problems in the field of photonics. The authors have developed Mathematica package GTPack which is available for download from the book's homepage. Analytic considerations, numerical calculations and visualization are carried out using the same software. While the use of the Mathematica tools are demonstrated on elementary examples, they can equally be applied to more complicated tasks resulting from the reader's own research.
| Author | : A. Zee |
| Publisher | : Princeton University Press |
| Total Pages | : 632 |
| Release | : 2016-03-29 |
| Genre | : Science |
| ISBN | : 1400881188 |
A concise, modern textbook on group theory written especially for physicists Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-contained textbook on the subject written especially for physicists. Group Theory in a Nutshell for Physicists fills this gap, providing a user-friendly and classroom-tested text that focuses on those aspects of group theory physicists most need to know. From the basic intuitive notion of a group, A. Zee takes readers all the way up to how theories based on gauge groups could unify three of the four fundamental forces. He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study. Provides physicists with a modern and accessible introduction to group theory Covers applications to various areas of physics, including field theory, particle physics, relativity, and much more Topics include finite group and character tables; real, pseudoreal, and complex representations; Weyl, Dirac, and Majorana equations; the expanding universe and group theory; grand unification; and much more The essential textbook for students and an invaluable resource for researchers Features a brief, self-contained treatment of linear algebra An online illustration package is available to professors Solutions manual (available only to professors)
