Groups, Representations and Physics

Author: H.F Jones

Publisher: CRC Press

ISBN: 9781420050295

Category: Mathematics

Page: 340

View: 7187

Illustrating the fascinating interplay between physics and mathematics, Groups, Representations and Physics, Second Edition provides a solid foundation in the theory of groups, particularly group representations. For this new, fully revised edition, the author has enhanced the book's usefulness and widened its appeal by adding a chapter on the Cartan-Dynkin treatment of Lie algebras. This treatment, a generalization of the method of raising and lowering operators used for the rotation group, leads to a systematic classification of Lie algebras and enables one to enumerate and construct their irreducible representations. Taking an approach that allows physics students to recognize the power and elegance of the abstract, axiomatic method, the book focuses on chapters that develop the formalism, followed by chapters that deal with the physical applications. It also illustrates formal mathematical definitions and proofs with numerous concrete examples.

Theory of Group Representations and Applications

Author: Asim Orhan Barut,Ryszard R?czka

Publisher: World Scientific

ISBN: 9789971502171

Category: Mathematics

Page: 717

View: 5823

Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.

Group Theory and Physics

Author: S. Sternberg

Publisher: Cambridge University Press

ISBN: 9780521558853

Category: Mathematics

Page: 429

View: 6954

This book is an introduction to group theory and its application to physics. The author considers the physical applications and develops mathematical theory in a presentation that is unusually cohesive and well-motivated. The book discusses many modern topics including molecular vibrations, homogeneous vector bundles, compact groups and Lie groups, and there is much discussion of the group SU(n) and its representations, which is of great significance in elementary particle physics. The author also considers applications to solid-state physics. This is an essential resource for senior undergraduates and researchers in physics and applied mathematics.

Group Representations, Ergodic Theory, and Mathematical Physics

A Tribute to George W. Mackey : AMS Special Session Honoring the Memory of George W. Mackey, January 7-8, 2007, New Orleans, Louisiana

Author: Robert S. Doran,Calvin C. Moore,Robert J. Zimmer

Publisher: American Mathematical Soc.

ISBN: 0821842250

Category: Mathematics

Page: 446

View: 9006

George Mackey was an extraordinary mathematician of great power and vision. His profound contributions to representation theory, harmonic analysis, ergodic theory, and mathematical physics left a rich legacy for researchers that continues today. This book is based on lectures presented at an AMS special session held in January 2007 in New Orleans dedicated to his memory. The papers, written especially for this volume by internationally-known mathematicians and mathematical physicists, range from expository and historical surveys to original high-level research articles. The influence of Mackey's fundamental ideas is apparent throughout. The introductory article contains recollections from former students, friends, colleagues, and family as well as a biography describing his distinguished career as a mathematician at Harvard, where he held the Landon D. Clay Professorship of Mathematics. Topics examined here include recent results on induced representations, virtual groups, the Mackey Machine and crossed products, representations of Baumslag-Solitar groups, the Radon transform and the heat equation, groupoids in the study of wavelets, and quantum theory. The in-depth historical surveys of Mackey's work on representation theory, ergodic theory, and physics, together with recent developments inspired by his fundamental work will be of considerable interest to both graduate students and researchers alike.

Group Theory in Physics

An Introduction to Symmetry Principles, Group Representations, and Special Functions in Classical and Quantum Physics

Author: Wu-Ki Tung

Publisher: World Scientific Publishing Company

ISBN: 981310404X

Category: Representations of groups

Page: 336

View: 7348

An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems. Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry. Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained. A set of problems and solutions has been published in a separate booklet. Request Inspection Copy

Group Theory and Quantum Mechanics

Author: Michael Tinkham

Publisher: Courier Corporation

ISBN: 0486131661

Category: Science

Page: 352

View: 6885

Graduate-level text develops group theory relevant to physics and chemistry and illustrates their applications to quantum mechanics, with systematic treatment of quantum theory of atoms, molecules, solids. 1964 edition.

Quantum Theory, Groups and Representations

An Introduction

Author: Peter Woit

Publisher: Springer

ISBN: 3319646125

Category: Science

Page: 668

View: 551

This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.

Representations and Invariants of the Classical Groups

Author: Roe Goodman,Nolan R. Wallach

Publisher: Cambridge University Press

ISBN: 9780521663489

Category: Mathematics

Page: 703

View: 2614

Presents an updated version of Weyl's invariant theory of the classical groups, together with many of the important recent developments.

Group Theory and Its Application to Physical Problems

Author: Morton Hamermesh

Publisher: Courier Corporation

ISBN: 0486140393

Category: Science

Page: 544

View: 4890

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

A Physicist's Survey

Author: Pierre Ramond

Publisher: Cambridge University Press

ISBN: 113948964X

Category: Science

Page: N.A

View: 8761

Group theory has long been an important computational tool for physicists, but, with the advent of the Standard Model, it has become a powerful conceptual tool as well. This book introduces physicists to many of the fascinating mathematical aspects of group theory, and mathematicians to its physics applications. Designed for advanced undergraduate and graduate students, this book gives a comprehensive overview of the main aspects of both finite and continuous group theory, with an emphasis on applications to fundamental physics. Finite groups are extensively discussed, highlighting their irreducible representations and invariants. Lie algebras, and to a lesser extent Kac–Moody algebras, are treated in detail, including Dynkin diagrams. Special emphasis is given to their representations and embeddings. The group theory underlying the Standard Model is discussed, along with its importance in model building. Applications of group theory to the classification of elementary particles are treated in detail.

Symmetry, Groups, and Representations in Physics

Author: Dimitri D. Vvedensky,Timothy S. Evans

Publisher: N.A

ISBN: 9781786340153


Page: 350

View: 6168

This book is an introduction to symmetry in physics based on discrete and continuous groups. No knowledge of algebra is assumed and the book is suitable for both beginning and advanced graduate students. In fact, at Imperial College, the notes on which this book is based have been thoroughly tested in the classroom by two lecturers with quite different backgrounds (condensed matter theory and field theory) to classes composed of third- and fourth-year undergraduate students as well as students from the MSc in Quantum Fields and Fundamental Forces program. Abundant exercises, all with detailed solutions that are available in a separate instructor's manual, are included to illustrate the concepts introduced in the main text, to extend some of the main results, and to introduce new ideas. One of the main themes in the book is the application of group theory to physical problems.

Lie Groups, Lie Algebras, and Representations

An Elementary Introduction

Author: Brian Hall,Brian C.. Hall

Publisher: Springer Science & Business Media

ISBN: 9780387401225

Category: Mathematics

Page: 351

View: 3231

This book addresses Lie groups, Lie algebras, and representation theory. The author restricts attention to matrix Lie groups and Lie algebras. This approach keeps the discussion concrete, allows the reader to get to the heart of the subject quickly, and covers all of the most interesting examples.From the reviews:"Sure to become a standard textbook for graduate students in mathematics and physics with little or no prior exposure to Lie theory." --L'Enseignement Mathematique

Representations of Finite and Compact Groups

Author: Barry Simon

Publisher: American Mathematical Soc.

ISBN: 0821804537

Category: Mathematics

Page: 266

View: 5987

Barry Simon, I.B.M. Professor of Mathematics and Theoretical Physics at the California Institute of Technology, is the author of several books, including such classics as ""Methods of Mathematical Physics"" (with M. Reed) and ""Functional Integration and Quantum Physics"". This new book, based on courses given at Princeton, Caltech, ETH-Zurich, and other universities, is an introductory textbook on representation theory.According to the author, 'Two facets distinguish my approach. First, this book is relatively elementary, and second, while the bulk of the books on the subject is written from the point of view of an algebraist or a geometer, this book is written with an analytical flavor'. The exposition in the book centers around the study of representation of certain concrete classes of groups, including permutation groups and compact semi simple Lie groups. It culminates in the complete proof of the Weyl character formula for representations of compact Lie groups and the Frobenius formula for characters of permutation groups. Extremely well tailored both for a one-year course in representation theory and for independent study, this book is an excellent introduction to the subject which, according to the author, is unique in having 'so much innate beauty so close to the surface'.

Quantum Theory, Groups, Fields and Particles

Author: A. O. Barut,P. Barut

Publisher: Springer Science & Business Media

ISBN: 9781402003240

Category: Mathematics

Page: 334

View: 6699

Symmetry and Dynamics have played, sometimes dualistic, sometimes complimentary, but always a very essential role in the physicist's description and conception of Nature. These are again the basic underlying themes of the present volume. It collects self-contained introductory contributions on some of the recent developments both in mathematical concepts and in physical applications which are becoming very important in current research. So we see in this volume, on the one hand, differential geometry, group representations, topology and algebras and on the other hand, particle equations, particle dynamics and particle interactions. Specifically, this book contains a complete exposition of the theory of deformations of symplectic algebras and quantization, expository material on topology and geometry in physics, and group representations. On the more physical side, we have studies on the concept of particles, on conformal spinors of Cartan, on gauge and supersymmetric field theories, and on relativistic theory of particle interactions and the theory of magnetic resonances. The contributions collected here were originally delivered at two Meetings in Turkey, at Blacksea University in Trabzon and at the University of Bosphorus in Istanbul. But they have been thoroughly revised, updated and extended for this volume. It is a pleasure for me to acknowledge the support of UNESCO, the support and hospitality of Blacksea and Bosphorus Universities for these two memorable Meetings in Mathematical Physics, and to thank the Contributors for their effort and care in preparing this work.

Group Theory with Applications in Chemical Physics

Author: Patrick W. M. Jacobs

Publisher: Cambridge University Press

ISBN: 9780521642507

Category: Mathematics

Page: 485

View: 8240

Group Theory is an indispensable mathematical tool in many branches of chemistry and physics. This book provides a self-contained and rigorous account on the fundamentals and applications of the subject to chemical physics, assuming no prior knowledge of group theory. The first half of the book focuses on elementary topics, such as molecular and crystal symmetry, whilst the latter half is more advanced in nature. Discussions on more complex material such as space groups, projective representations, magnetic crystals and spinor bases, often omitted from introductory texts, are expertly dealt with. With the inclusion of numerous exercises and worked examples, this book will appeal to advanced undergraduates and beginning graduate students studying physical sciences and is an ideal text for use on a two-semester course.

Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics

Proceedings of a Conference in Honor of George W. Mackey

Author: Calvin C. Moore

Publisher: Springer Science & Business Media

ISBN: 1461247225

Category: Mathematics

Page: 278

View: 8541

The Mathematical Sciences Research Institute sponsored a three day conference, May 21-23, 1984 to honor Professor George W. Mackey. The title of the conference, Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics, reflects the interests in science that have characterized Professor wide ranging Mackey's work. The conference provided an opportunity for his students, friends and colleagues to honor him and his contributions. The conference was attended by over one hundred people and the participants included five mathematical generations Professor Mackey's mathematical father, Marshall Stone, many mathematical children, grandchildren, and at least one mathematical great-grandchild. This volume is a compendium of the scientific papers presented at the conference plus some additional papers contributed after the conference. The far ranging scope of the various articles is a further indication of the large number of fields that have been affected by Professor Mackey's work. Calvin C. Moore Berkeley, CA Feb, 1986 Table of Contents Preface vi i Ambiguity Functions and Group L. Auslander and Representations R. Tolimieri Kirillov Orbits and Direct Integral Lawrence Corwin 11 Decompositions on Certain Quotient Spaces Some Homotopy and Shape Calculations Edward G. Effors and 69 for C*-Algebras Jerome Kaminker 121 Small Unitary Representations of Roger Howe Classical Groups Dual Vector Spaces Irving Kaplansky 151 Exponential Decay of Correlation Calvin C. Moore 163 Coefficients for Geodesic Flows Lattices in U(n. I) G. D. Mostow Induced Bundles and Nonlinear Irving E. Segal 199 Wave equations Compact Ahelian Aut.

Group Theory in Physics

An Introduction

Author: John F. Cornwell

Publisher: Academic Press

ISBN: 9780080532660

Category: Science

Page: 349

View: 5923

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