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Author : M. Hamermesh
Publisher : Unknown
Page : 128 pages
File Size : 45,9 Mb
Release : 1964
Category : Electronic
ISBN : OCLC:841407509
Author : Leopoldo Maximo Falicov
Publisher : Unknown
Page : 230 pages
File Size : 51,5 Mb
Release : 1966
Category : Fisica matematica
ISBN : 0226235408
Author : Teturo Inui,Yukito Tanabe,Yositaka Onodera
Publisher : Springer Science & Business Media
Page : 409 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642800214
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 : Mildred S. Dresselhaus,Gene Dresselhaus,Ado Jorio
Publisher : Springer Science & Business Media
Page : 576 pages
File Size : 41,8 Mb
Release : 2007-12-18
Category : Science
ISBN : 9783540328995
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 : Morton Hamermesh
Publisher : Courier Corporation
Page : 548 pages
File Size : 44,9 Mb
Release : 2012-04-26
Category : Science
ISBN : 9780486140391
One of the best-written, most skillful expositions of group theory and its physical applications, directed primarily to advanced undergraduate and graduate students in physics, especially quantum physics. With problems.
Author : Leopoldo Maximo Falicov
Publisher : Unknown
Page : 242 pages
File Size : 40,9 Mb
Release : 1966
Category : Mathematics
ISBN : UOM:39015004508936
Author : R. McWeeny
Publisher : Elsevier
Page : 262 pages
File Size : 45,6 Mb
Release : 2013-09-03
Category : Mathematics
ISBN : 9781483226248
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 : Traubenberg M Rausch De,Strursberg R Campoamor
Publisher : World Scientific
Page : 760 pages
File Size : 46,7 Mb
Release : 2018-09-19
Category : Science
ISBN : 9789813273627
This 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 : Petre P. Teodorescu,Nicolae-A.P. Nicorovici
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 50,7 Mb
Release : 2004-04-30
Category : Mathematics
ISBN : 9781402020476
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 : Mosh Flato,Paul Sally,Gregg Zuckerman
Publisher : American Mathematical Soc.
Page : 436 pages
File Size : 54,7 Mb
Release : 1985-12-31
Category : Science
ISBN : 0821896865
The past decade has seen a renewal in the close ties between mathematics and physics. The Chicago Summer Seminar on Applications of Group Theory in Physics and Mathematical Physics, held in July, 1982, was organized to bring together a broad spectrum of scientists from theoretical physics, mathematical physics, and various branches of pure and applied mathematics in order to promote interaction and an exchange of ideas and results in areas of common interest. This volume contains the papers submitted by speakers at the Seminar. The reader will find several groups of articles varying from the most abstract aspects of mathematics to a concrete phenomenological description of some models applicable to particle physics. The papers have been divided into four categories corresponding to the principal topics covered at the Seminar. This is only a rough division, and some papers overlap two or more of these categories.
Author : Ernest M. Loebl
Publisher : Academic Press
Page : 326 pages
File Size : 46,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483263786
Group Theory and its Applications, Volume II covers the two broad areas of applications of group theory, namely, all atomic and molecular phenomena, as well as all aspects of nuclear structure and elementary particle theory. This volume contains five chapters and begins with the representation and tensor operators of the unitary groups. The next chapter describes wave equations, both Schrödinger’s and Dirac’s for a wide variety of potentials. These topics are followed by discussions of the applications of dynamical groups in dealing with bound-state problems of atomic and molecular physics. A chapter explores the connection between the physical constants of motion and the unitary group of the Hamiltonian, the symmetry adaptation with respect to arbitrary finite groups, and the Dixon method for computing irreducible characters without the occurrence of numerical errors. The last chapter deals with the study of the extension, representation, and applications of Galilei group. This book will prove useful to mathematicians, practicing engineers, and physicists.
Author : S. Bhagavantam,T. Venkatarayudu
Publisher : Academic Press
Page : 294 pages
File Size : 53,9 Mb
Release : 2016-01-21
Category : Science
ISBN : 9781483275987
Theory of Groups and Its Application to Physical Problems is an introductory study of the theory of groups for persons with no easy access to an orthodox mathematical treatise on the subject. The aim is to provide an understanding of the method of applying group theory to various problems and appreciate the advantages thereof. It is hoped that this account of the theory of groups will serve a real need for physicists interested in the subject. The book opens with a discussion of the concept of groups. This is followed by separate chapters on the one-dimensional and two-dimensional lattices, some properties of groups, matrix groups, and the wave equation and its properties. Subsequent chapters deal with vibrations of a dynamical system, vibrational Raman effect and infrared absorption, molecular structure and normal modes, three-dimensional lattices, Raman and infrared spectra of crystals, crystal symmetry and physical properties, rotation groups, and applications to problems of atomic spectra.
Author : Patrick W. M. Jacobs
Publisher : Cambridge University Press
Page : 520 pages
File Size : 46,6 Mb
Release : 2005-10-18
Category : Mathematics
ISBN : 0521642507
This book provides a rigorous account on the fundamentals and applications of Group Theory to chemical physics.
Author : John F. Cornwell
Publisher : Academic Press
Page : 361 pages
File Size : 49,7 Mb
Release : 1997-07-11
Category : Science
ISBN : 9780080532660
This book, an abridgment of Volumes I and II of the highly respected Group Theory in Physics, presents a carefully constructed introduction to group theory and its applications in physics. The book provides anintroduction to and description of the most important basic ideas and the role that they play in physical problems. The clearly written text contains many pertinent examples that illustrate the topics, even for those with no background in group theory.This work presents important mathematical developments to theoretical physicists in a form that is easy to comprehend and appreciate. Finite groups, Lie groups, Lie algebras, semi-simple Lie algebras, crystallographic point groups and crystallographic space groups, electronic energy bands in solids, atomic physics, symmetry schemes for fundamental particles, and quantum mechanics are all covered in this compact new edition. Covers both group theory and the theory of Lie algebras Includes studies of solid state physics, atomic physics, and fundamental particle physics Contains a comprehensive index Provides extensive examples
Author : Young Suh Kim,M. Noz
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400945586
Special relativity and quantum mechanics, formulated early in the twentieth century, are the two most important scientific languages and are likely to remain so for many years to come. In the 1920's, when quantum mechanics was developed, the most pressing theoretical problem was how to make it consistent with special relativity. In the 1980's, this is still the most pressing problem. The only difference is that the situation is more urgent now than before, because of the significant quantity of experimental data which need to be explained in terms of both quantum mechanics and special relativity. In unifying the concepts and algorithms of quantum mechanics and special relativity, it is important to realize that the underlying scientific language for both disciplines is that of group theory. The role of group theory in quantum mechanics is well known. The same is true for special relativity. Therefore, the most effective approach to the problem of unifying these two important theories is to develop a group theory which can accommodate both special relativity and quantum mechanics. As is well known, Eugene P. Wigner is one of the pioneers in developing group theoretical approaches to relativistic quantum mechanics. His 1939 paper on the inhomogeneous Lorentz group laid the foundation for this important research line. It is generally agreed that this paper was somewhat ahead of its time in 1939, and that contemporary physicists must continue to make real efforts to appreciate fully the content of this classic work.
