Applied Group Theory

Applied Group Theory

This text introduces advanced undergraduates and graduate students to key applications of group theory.

Author: George H. Duffey

Publisher: Courier Corporation

ISBN: 9780486783147

Category: Science

Page: 384

View: 635

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.
Categories: Science

Applied Group Theory

Applied Group Theory

This book is intended to be suitable for final-year students and fresh postgraduate students in physics. Physicists and researcher workers will also find this book extremely useful.

Author: Arthur P. Cracknell

Publisher: Elsevier

ISBN: 9781483149387

Category: Science

Page: 430

View: 289

Selected Readings in Physics: Applied Group Theory provides information pertinent to the fundamental aspects of applied group theory. This book discusses the properties of symmetry of a system in quantum mechanics. Organized into two parts encompassing nine chapters, this book begins with an overview of the problem of elastic vibrations of a symmetric structure. This text then examines the numbers, degeneracies, and symmetries of the normal modes of vibration. Other chapters consider the conditions under which a polyatomic molecule can have a stable equilibrium configuration when its electronic state has orbital degeneracy. This book discusses as well the effect of an electric field having a given symmetry upon an atom. The final chapter deals with the symmetry of crystals with a magnetic moment. This book is intended to be suitable for final-year students and fresh postgraduate students in physics. Physicists and researcher workers will also find this book extremely useful.
Categories: Science

Group Theory Applied to Chemistry

Group Theory Applied to Chemistry

Chemists are used to the operational definition of symmetry, which crystallographers introduced long before the advent of quantum mechanics.

Author: Arnout Jozef Ceulemans

Publisher: Springer Science & Business Media

ISBN: 9789400768635

Category: Science

Page: 269

View: 556

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.
Categories: Science

Symmetries in Physics

Symmetries in Physics

Emphasis is placed on the theory of group representations and on the powerful method of projection operators. The excercises are intended to stimulate readers to apply the techniques demonstrated in the text.

Author: Wolfgang Ludwig

Publisher: Springer Science & Business Media

ISBN: 9783642799778

Category: Science

Page: 473

View: 518

Symmetries in Physics presents the fundamental theories of symmetry, together with many examples of applications taken from several different branches of physics. Emphasis is placed on the theory of group representations and on the powerful method of projection operators. The excercises are intended to stimulate readers to apply the techniques demonstrated in the text.
Categories: Science

Elements of Group Theory for Physicists

Elements of Group Theory for Physicists

This Is A Valuable Book For Senior Students And Researchers In Physics And Physical Chemistry.

Author: A. W. Joshi

Publisher: New Age International

ISBN: 812240975X

Category: Group theory

Page: 305

View: 701

The Mathematical Study Of Group Theory Was Initiated In The Early Nineteenth Century By Such Mathematicians As Gauss, Cauchy, Abel, Hamilton, Galois, Cayley, And Many Others. However, The Advantages Of Group Theory In Physics Were Not Recognized Till 1925 When It Was Applied For Formal Study Of Theoretical Foundations Of Quantum Mechanics, Atomic Structures And Spectra By, To Name A Few, H A Bethe, E P Wigner, Etc. It Has Now Become Indispensable In Several Branches Of Physics And Physical Chemistry.Dr. Joshi Develops The Mathematics Of Group Theory And Then Goes On To Present Its Applications To Quantum Mechanics, Crystallography, And Solid State Physics. For Proper Comprehension Of Representation Theory, He Has Covered Thoroughly Such Diverse But Relevant Topics As Hilbert Spaces, Function Spaces, Operators, And Direct Sum And Product Of Matrices. He Often Proceeds From The Particular To The General So That The Beginning Student Does Not Have An Impression That Group Theory Is Merely A Branch Of Abstract Mathematics. Various Concepts Have Been Explained Consistently By The Use Of The C4V. Besides, It Contains An Improved And More General Proof Of The Schurs First Lemma And An Interpretation Of The Orthogonality Theorem In The Language Of Vector Spaces (Chapter 3).Throughout The Text The Author Gives Attention To Details And Avoids Complicated Notation. This Is A Valuable Book For Senior Students And Researchers In Physics And Physical Chemistry. A Thorough Understanding Of The Methodology And Results Contained In This Book Will Provide The Reader Sound Theoretical Foundations For Advanced Study Of Quantum Mechanics, Solid State Physics And Atomic And Particle Physics To Help Students A Flow-Chart Explaining Step By Step The Method Of Determining A Parallel-Running Example Illustrating The Procedure In Full Details Have Been Included. An Appendix On Mappings And Functions Has Also Been Added.
Categories: Group theory

Applications of Group Theory in Physics and Mathematical Physics

Applications of Group Theory in Physics and Mathematical 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: MoshŽ Flato

Publisher: American Mathematical Soc.

ISBN: 0821896865

Category: Science

Page: 420

View: 172

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.
Categories: Science

Group Theoretic Methods in Mechanics and Applied Mathematics

Group Theoretic Methods in Mechanics and Applied Mathematics

as presented by Pontryagin, then the group-theoretic analysis of differential
equations as described by Ovsiannikov or Olver is an applied field. Nevertheless,
its fundamental role in the theory of differential equations itself is indisputable.

Author: D.M. Klimov

Publisher: CRC Press

ISBN: 9781482265224

Category: Mathematics

Page: 240

View: 665

Group analysis of differential equations has applications to various problems in nonlinear mechanics and physics. For the first time, this book gives the systematic group analysis of main postulates of classical and relativistic mechanics. The consistent presentation of Lie group theory is illustrated by plentiful examples. Symmetries and conservat
Categories: Mathematics

Group Theory and Its Application to Physical Problems

Group Theory and Its Application to Physical Problems

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: Morton Hamermesh

Publisher: Courier Corporation

ISBN: 9780486140391

Category: Science

Page: 544

View: 638

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.
Categories: Science

An Introduction to Tensors and Group Theory for Physicists

An Introduction to Tensors and Group Theory for Physicists

Part I of the text begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to classical and quantum physics through the use of tensor products.

Author: Nadir Jeevanjee

Publisher: Springer Science & Business Media

ISBN: 9780817647148

Category: Science

Page: 242

View: 128

An Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory. Advanced undergraduate and graduate students in physics and applied mathematics will find clarity and insight into the subject in this textbook.
Categories: Science

Linear Algebra and Group Theory for Physicists and Engineers

Linear Algebra and Group Theory for Physicists and Engineers

This text is ideal for undergraduates majoring in engineering, physics, chemistry, computer science, or applied mathematics. It is mostly self-contained—readers should only be familiar with elementary calculus.

Author: Yair Shapira

Publisher: Springer

ISBN: 9783030178567

Category: Mathematics

Page: 441

View: 227

This textbook demonstrates the strong interconnections between linear algebra and group theory by presenting them simultaneously, a pedagogical strategy ideal for an interdisciplinary audience. Being approached together at the same time, these two topics complete one another, allowing students to attain a deeper understanding of both subjects. The opening chapters introduce linear algebra with applications to mechanics and statistics, followed by group theory with applications to projective geometry. Then, high-order finite elements are presented to design a regular mesh and assemble the stiffness and mass matrices in advanced applications in quantum chemistry and general relativity. This text is ideal for undergraduates majoring in engineering, physics, chemistry, computer science, or applied mathematics. It is mostly self-contained—readers should only be familiar with elementary calculus. There are numerous exercises, with hints or full solutions provided. A series of roadmaps are also provided to help instructors choose the optimal teaching approach for their discipline.
Categories: Mathematics

Group Theory

Group Theory

The text is recommended for physicists and mathematicians who are interested in the application of group theory to quantum mechanics.

Author: Eugene Wigner

Publisher: Elsevier

ISBN: 9780323152785

Category: Mathematics

Page: 386

View: 877

Group Theory: And Its Application To The Quantum Mechanics Of Atomic Spectra aims to describe the application of group theoretical methods to problems of quantum mechanics with specific reference to atomic spectra. Chapters 1 to 3 discuss the elements of linear vector theory, while Chapters 4 to 6 deal more specifically with the rudiments of quantum mechanics itself. Chapters 7 to 16 discuss the abstract group theory, invariant subgroups, and the general theory of representations. These chapters are mathematical, although much of the material covered should be familiar from an elementary course in quantum theory. Chapters 17 to 23 are specifically concerned with atomic spectra, as is Chapter 25. The remaining chapters discuss topics such as the recoupling (Racah) coefficients, the time inversion operation, and the classical interpretations of the coefficients. The text is recommended for physicists and mathematicians who are interested in the application of group theory to quantum mechanics. Those who are only interested in mathematics can choose to focus on the parts more devoted to that particular area of the subject.
Categories: Mathematics

Group Theory and Physics

Group Theory and Physics

A cohesive and well-motivated introduction to group theory and its application to physics.

Author: S. Sternberg

Publisher: Cambridge University Press

ISBN: 0521558859

Category: Mathematics

Page: 429

View: 385

A cohesive and well-motivated introduction to group theory and its application to physics.
Categories: Mathematics

Group Theory in Chemistry and Spectroscopy

Group Theory in Chemistry and Spectroscopy

This handbook on group theory is geared toward chemists and experimental physicists who use spectroscopy and require knowledge of the electronic structures of the materials they investigate.

Author: Boris S. Tsukerblat

Publisher: Courier Corporation

ISBN: 9780486450353

Category: Science

Page: 448

View: 205

This handbook on group theory is geared toward chemists and experimental physicists who use spectroscopy and require knowledge of the electronic structures of the materials they investigate. Accessible to undergraduate students, it takes an elementary approach to many of the key concepts. Rather than the deductive method common to books on mathematics and theoretical physics, the present volume introduces fundamental concepts with simple examples, relating them to specific chemical and physical problems. The text is centered on detailed analysis of examples. Since neither chemists nor spectroscopists require theorem proofs, very few appear here. Instead, the focus remains on the principal conclusions, their meaning, and their use. In keeping with the text's practical bias, the main results of group theory are presented in all sections as procedures, making possible their systematic and step-by-step-application. Each chapter contains problems that develop practical skill and provide a valuable supplement to the text.
Categories: Science

Group Theory in a Nutshell for Physicists

Group Theory in a Nutshell for Physicists

He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study.

Author: A. Zee

Publisher: Princeton University Press

ISBN: 9781400881185

Category: Science

Page: 632

View: 283

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)
Categories: Science

Group Theory in Solid State Physics and Photonics

Group Theory in Solid State Physics and 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.

Author: Wolfram Hergert

Publisher: John Wiley & Sons

ISBN: 9783527413003

Category: Science

Page: 360

View: 959

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.
Categories: Science

Group Theory

Group Theory

The text and problem sets have proved a useful springboard for the application of the basic material presented here to topics in semiconductor physics, and the physics of carbon-based nanostructures.

Author: Mildred S. Dresselhaus

Publisher: Springer Science & Business Media

ISBN: 9783540328971

Category: Science

Page: 582

View: 958

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.
Categories: Science

Group Theory with Applications in Chemical Physics

Group Theory with Applications in Chemical Physics

This book provides a rigorous account on the fundamentals and applications of Group Theory to chemical physics.

Author: Patrick Jacobs

Publisher: Cambridge University Press

ISBN: 0521642507

Category: Mathematics

Page: 485

View: 646

This book provides a rigorous account on the fundamentals and applications of Group Theory to chemical physics.
Categories: Mathematics