Applications Of The Theory Of Groups In Mechanics And Physics

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Applications of the Theory of Groups in Mechanics and Physics

Author : Petre P. Teodorescu
Publisher : Springer Science & Business Media
ISBN 13 : 1402020473
Total Pages : 455 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Applications of the Theory of Groups in Mechanics and Physics by : Petre P. Teodorescu

Download or read book Applications of the Theory of Groups in Mechanics and Physics written by Petre P. Teodorescu and published by Springer Science & Business Media. This book was released on 2004-04-30 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Group Theory and Its Applications in Physics

Author : Teturo Inui
Publisher : Springer Science & Business Media
ISBN 13 : 3642800211
Total Pages : 409 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Group Theory and Its Applications in Physics by : Teturo Inui

Download or read book Group Theory and Its Applications in Physics written by Teturo Inui and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Group Theory and Its Application to Physical Problems

Author : M. Hamermesh
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (841 download)

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Book Synopsis Group Theory and Its Application to Physical Problems by : M. Hamermesh

Download or read book Group Theory and Its Application to Physical Problems written by M. Hamermesh and published by . This book was released on 1964 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Applications of Group Theory in Quantum Mechanics

Author : M. I. Petrashen
Publisher : Courier Corporation
ISBN 13 : 0486172724
Total Pages : 338 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Applications of Group Theory in Quantum Mechanics by : M. I. Petrashen

Download or read book Applications of Group Theory in Quantum Mechanics written by M. I. Petrashen and published by Courier Corporation. This book was released on 2013-01-03 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared toward postgraduate students, theoretical physicists, and researchers, this advanced text explores the role of modern group-theoretical methods in quantum theory. The authors based their text on a physics course they taught at a prominent Soviet university. Readers will find it a lucid guide to group theory and matrix representations that develops concepts to the level required for applications. The text's main focus rests upon point and space groups, with applications to electronic and vibrational states. Additional topics include continuous rotation groups, permutation groups, and Lorentz groups. A number of problems involve studies of the symmetry properties of the Schroedinger wave function, as well as the explanation of "additional" degeneracy in the Coulomb field and certain subjects in solid-state physics. The text concludes with an instructive account of problems related to the conditions for relativistic invariance in quantum theory.

Theory and Applications of the Poincaré Group

Author : Young Suh Kim
Publisher : Springer Science & Business Media
ISBN 13 : 9400945582
Total Pages : 346 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Theory and Applications of the Poincaré Group by : Young Suh Kim

Download or read book Theory and Applications of the Poincaré Group written by Young Suh Kim and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Applications of the Theory of Groups in Mechanics and Physics

Author : Petre P. Teodorescu
Publisher : Springer Science & Business Media
ISBN 13 : 9781402020469
Total Pages : 466 pages
Book Rating : 4.0/5 (24 download)

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Book Synopsis Applications of the Theory of Groups in Mechanics and Physics by : Petre P. Teodorescu

Download or read book Applications of the Theory of Groups in Mechanics and Physics written by Petre P. Teodorescu and published by Springer Science & Business Media. This book was released on 2004-04-30 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics

Author : D.H. Sattinger
Publisher : Springer Science & Business Media
ISBN 13 : 1475719108
Total Pages : 218 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics by : D.H. Sattinger

Download or read book Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics written by D.H. Sattinger and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselves to the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.

Group Theory

Author : Eugene P. Wigner
Publisher : Elsevier
ISBN 13 : 1483275760
Total Pages : 384 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Group Theory by : Eugene P. Wigner

Download or read book Group Theory written by Eugene P. Wigner and published by Elsevier. This book was released on 2013-09-03 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Applications of Group Theory in Physics and Mathematical Physics

Author : Mosh Flato
Publisher : American Mathematical Soc.
ISBN 13 : 9780821896860
Total Pages : 436 pages
Book Rating : 4.8/5 (968 download)

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Book Synopsis Applications of Group Theory in Physics and Mathematical Physics by : Mosh Flato

Download or read book Applications of Group Theory in Physics and Mathematical Physics written by Mosh Flato and published by American Mathematical Soc.. This book was released on 1985-12-31 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Theory of Groups and Quantum Mechanics

Author : Hermann Weyl
Publisher : Courier Corporation
ISBN 13 : 9780486602691
Total Pages : 468 pages
Book Rating : 4.6/5 (26 download)

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Book Synopsis The Theory of Groups and Quantum Mechanics by : Hermann Weyl

Download or read book The Theory of Groups and Quantum Mechanics written by Hermann Weyl and published by Courier Corporation. This book was released on 1950-01-01 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves — rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric transformations.

Group Theory

Author : Mildred S. Dresselhaus
Publisher : Springer Science & Business Media
ISBN 13 : 3540328998
Total Pages : 576 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Group Theory by : Mildred S. Dresselhaus

Download or read book Group Theory written by Mildred S. Dresselhaus and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Group Theory and Its Application to Physical Problems

Author : Morton Hamermesh
Publisher : Courier Corporation
ISBN 13 : 0486140393
Total Pages : 548 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Group Theory and Its Application to Physical Problems by : Morton Hamermesh

Download or read book Group Theory and Its Application to Physical Problems written by Morton Hamermesh and published by Courier Corporation. This book was released on 2012-04-26 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Group Theory in Quantum Mechanics

Author : Volker Heine
Publisher : Courier Corporation
ISBN 13 : 0486174336
Total Pages : 634 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Group Theory in Quantum Mechanics by : Volker Heine

Download or read book Group Theory in Quantum Mechanics written by Volker Heine and published by Courier Corporation. This book was released on 2013-02-21 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared toward research students in physics and chemistry, this text introduces the three main uses of group theory in quantum mechanics: (1) to label energy levels and the corresponding eigenstates; (2) to discuss qualitatively the splitting of energy levels, starting from an approximate Hamiltonian and adding correction terms; and (3) to aid in the evaluation of matrix elements of all kinds. "The theme," states author Volker Heine, "is to show how all this is achieved by considering the symmetry properties of the Hamiltonian and the way in which these symmetries are reflected in the wave functions." Early chapters cover symmetry transformations, the quantum theory of a free atom, and the representations of finite groups. Subsequent chapters address the structure and vibrations of molecules, solid state physics, nuclear physics, and relativistic quantum mechanics. A previous course in quantum theory is necessary, but the relevant matrix algebra appears in an appendix. A series of examples of varying levels of difficulty follows each chapter. They include simple drills related to preceding material as well as extensions of theory and further applications. The text is enhanced with 46 illustrations and 12 helpful appendixes.

Group Theory and Quantum Mechanics

Author : Michael Tinkham
Publisher : Courier Corporation
ISBN 13 : 0486131661
Total Pages : 354 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Group Theory and Quantum Mechanics by : Michael Tinkham

Download or read book Group Theory and Quantum Mechanics written by Michael Tinkham and published by Courier Corporation. This book was released on 2012-04-20 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text develops the aspects of group theory most relevant to physics and chemistry (such as the theory of representations) and illustrates their applications to quantum mechanics. The first five chapters focus chiefly on the introduction of methods, illustrated by physical examples, and the final three chapters offer a systematic treatment of the quantum theory of atoms, molecules, and solids. The formal theory of finite groups and their representation is developed in Chapters 1 through 4 and illustrated by examples from the crystallographic point groups basic to solid-state and molecular theory. Chapter 5 is devoted to the theory of systems with full rotational symmetry, Chapter 6 to the systematic presentation of atomic structure, and Chapter 7 to molecular quantum mechanics. Chapter 8, which deals with solid-state physics, treats electronic energy band theory and magnetic crystal symmetry. A compact and worthwhile compilation of the scattered material on standard methods, this volume presumes a basic understanding of quantum theory.

Group Theory in Physics

Author : John F. Cornwell
Publisher : Academic Press
ISBN 13 : 0080532667
Total Pages : 361 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Group Theory in Physics by : John F. Cornwell

Download or read book Group Theory in Physics written by John F. Cornwell and published by Academic Press. This book was released on 1997-07-11 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Group Theory In Physics: A Practitioner's Guide

Author : Traubenberg M Rausch De
Publisher : World Scientific
ISBN 13 : 9813273623
Total Pages : 760 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Group Theory In Physics: A Practitioner's Guide by : Traubenberg M Rausch De

Download or read book Group Theory In Physics: A Practitioner's Guide written by Traubenberg M Rausch De and published by World Scientific. This book was released on 2018-09-19 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Group Theory with Applications

Author : Gerald Burns
Publisher : Academic Press
ISBN 13 : 1483191494
Total Pages : 446 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Introduction to Group Theory with Applications by : Gerald Burns

Download or read book Introduction to Group Theory with Applications written by Gerald Burns and published by Academic Press. This book was released on 2014-05-10 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Group Theory with Applications covers the basic principles, concepts, mathematical proofs, and applications of group theory. This book is divided into 13 chapters and begins with discussions of the elementary topics related to the subject, including symmetry operations and group concepts. The succeeding chapters deal with the properties of matrix representations of finite groups, the vibrations of molecular and crystals, vibrational wave function, selection rules, and molecular approximations. These topics are followed by reviews of the basic of quantum mechanics, crystal field theory, atomic physics, hybrid functions, and molecular orbital theory. The last chapters describe the symmetry of crystal lattices, the band theory of solids, and the full rotation group. This book will be of value to undergraduate mathematics and physics students.