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Author: Teturo Inui
Publisher: Springer Science & Business Media
ISBN: 3642800211
Category : Science
Languages : en
Pages : 409
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Book Description
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: Teturo Inui
Publisher: Springer Science & Business Media
ISBN: 3642800211
Category : Science
Languages : en
Pages : 409
Get Book Here
Book Description
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: R. McWeeny
Publisher: Elsevier
ISBN: 1483226247
Category : Mathematics
Languages : en
Pages : 263
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Book Description
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: Morton Hamermesh
Publisher:
ISBN:
Category : Group theory
Languages : en
Pages : 0
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Book Description
Author: R Campoamor Strursberg
Publisher: World Scientific
ISBN: 9813273623
Category : Science
Languages : en
Pages : 759
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Book Description
'The book contains a lot of examples, a lot of non-standard material which is not included in many other books. At the same time the authors manage to avoid numerous cumbersome calculations … It is a great achievement that the authors found a balance.'zbMATHThis book presents the study of symmetry groups in Physics from a practical perspective, i.e. emphasising the explicit methods and algorithms useful for the practitioner and profusely illustrating by examples.The first half reviews the algebraic, geometrical and topological notions underlying the theory of Lie groups, with a review of the representation theory of finite groups. The topic of Lie algebras is revisited from the perspective of realizations, useful for explicit computations within these groups. The second half is devoted to applications in physics, divided into three main parts — the first deals with space-time symmetries, the Wigner method for representations and applications to relativistic wave equations. The study of kinematical algebras and groups illustrates the properties and capabilities of the notions of contractions, central extensions and projective representations. Gauge symmetries and symmetries in Particle Physics are studied in the context of the Standard Model, finishing with a discussion on Grand-Unified Theories.
Author: Mildred S. Dresselhaus
Publisher: Springer Science & Business Media
ISBN: 3540328998
Category : Science
Languages : en
Pages : 576
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Book Description
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: Petre P. Teodorescu
Publisher: Springer Science & Business Media
ISBN: 9781402020469
Category : Mathematics
Languages : en
Pages : 466
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Book Description
The notion of group is fundamental in our days, not only in mathematics, but also in classical mechanics, electromagnetism, theory of relativity, quantum mechanics, theory of elementary particles, etc. This notion has developed during a century and this development is connected with the names of great mathematicians as E. Galois, A. L. Cauchy, C. F. Gauss, W. R. Hamilton, C. Jordan, S. Lie, E. Cartan, H. Weyl, E. Wigner, and of many others. In mathematics, as in other sciences, the simple and fertile ideas make their way with difficulty and slowly; however, this long history would have been of a minor interest, had the notion of group remained connected only with rather restricted domains of mathematics, those in which it occurred at the beginning. But at present, groups have invaded almost all mathematical disciplines, mechanics, the largest part of physics, of chemistry, etc. We may say, without exaggeration, that this is the most important idea that occurred in mathematics since the invention of infinitesimal calculus; indeed, the notion of group expresses, in a precise and operational form, the vague and universal ideas of regularity and symmetry. The notion of group led to a profound understanding of the character of the laws which govern natural phenomena, permitting to formulate new laws, correcting certain inadequate formulations and providing unitary and non contradictory formulations for the investigated phenomena.
Author: Patrick W. M. Jacobs
Publisher: Cambridge University Press
ISBN: 9780521642507
Category : Mathematics
Languages : en
Pages : 520
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Book Description
This book provides a rigorous account on the fundamentals and applications of Group Theory to chemical physics.
Author: Eugene P. Wigner
Publisher: Elsevier
ISBN: 1483275760
Category : Science
Languages : en
Pages : 385
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Book Description
Group Theory and its Application to the Quantum Mechanics of Atomic Spectra describes the applications of group theoretical methods to problems of quantum mechanics with particular reference to atomic spectra. The manuscript first takes a look at vectors and matrices, generalizations, and principal axis transformation. Topics include principal axis transformation for unitary and Hermitian matrices; unitary matrices and the scalar product; linear independence of vectors; and real orthogonal and symmetric matrices. The publication also ponders on the elements of quantum mechanics, perturbation theory, and transformation theory and the bases for the statistical interpretation of quantum mechanics. The book discusses abstract group theory and invariant subgroups, including theorems of finite groups, factor group, and isomorphism and homomorphism. The text also reviews the algebra of representation theory, rotation groups, three-dimensional pure rotation group, and characteristics of atomic spectra. Discussions focus on eigenvalues and quantum numbers, spherical harmonics, and representations of the unitary group. The manuscript is a valuable reference for readers interested in the applications of group theoretical methods.
Author: Zhong-qi Ma
Publisher: World Scientific
ISBN: 9813277408
Category : Science
Languages : en
Pages : 656
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Book Description
This textbook explains the fundamental concepts and techniques of group theory by making use of language familiar to physicists. Calculation methods in the context of physics are emphasized. New materials drawn from the teaching and research experience of the author are included. The generalized Gel'fand's method is presented to calculate the matrices of irreducible representations of the simple Lie algebra and its Clebsch-Gordan coefficients. This book is for graduate students and young researchers in physics, especially theoretical physics. It is also for graduate students in theoretical chemistry.
Author: Grigoriĭ I︠A︡kovlevich Li︠u︡barskiĭ
Publisher: Reader's Digest Young Families
ISBN:
Category : Mathematics
Languages : en
Pages : 392
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Book Description
Elements of the theory of groups -- Some specific groups -- The theory of group representations -- Operations with group representations -- Representations of certain groups -- Small oscillations of symmetrical systems -- Second order phase transitions -- Crystals -- Infinite groups -- Representations of the rotation groups in two and three dimensions and of the full orthogonal group -- Clebsch-Gordon and Racah coefficients -- The Schrödinger equation -- Equations invariant under the Euclidean group of motions in space -- Absorption and Raman scattering of light -- Representations of the Lorentz group -- Relativistically invariant equations -- Nuclear reactions.
