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Group Theoretic Methods In Mechanics And Applied Mathematics
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Book Synopsis Group-Theoretic Methods in Mechanics and Applied Mathematics by : D.M. Klimov
Download or read book Group-Theoretic Methods in Mechanics and Applied Mathematics written by D.M. Klimov and published by CRC Press. This book was released on 2014-04-21 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Modern Group Theoretical Methods in Physics by : J. Bertrand
Download or read book Modern Group Theoretical Methods in Physics written by J. Bertrand and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of a meeting that brought together friends and colleagues of Guy Rideau at the Université Denis Diderot (Paris, France) in January 1995. It contains original results as well as review papers covering important domains of mathematical physics, such as modern statistical mechanics, field theory, and quantum groups. The emphasis is on geometrical approaches. Several papers are devoted to the study of symmetry groups, including applications to nonlinear differential equations, and deformation of structures, in particular deformation-quantization and quantum groups. The richness of the field of mathematical physics is demonstrated with topics ranging from pure mathematics to up-to-date applications such as imaging and neuronal models. Audience: Researchers in mathematical physics.
Book Synopsis Group Theoretical Methods in Physics by : G.S Pogosyan
Download or read book Group Theoretical Methods in Physics written by G.S Pogosyan and published by CRC Press. This book was released on 2005-05-01 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry is permeating our understanding of nature: Group theoretical methods of intrinsic interest to mathematics have expanded their applications from physics to chemistry and biology. The ICGTMP Colloquia maintain the communication among the many branches into which this endeavor has bloomed. Lie group and representation theory, special functions, foundations of quantum mechanics, and elementary particle, nuclear, atomic, and molecular physics are among the traditional subjects. More recent areas include supersymmetry, superstrings and quantum gravity, integrability, nonlinear systems and quantum chaos, semigroups, time asymmetry and resonances, condensed matter, and statistical physics. Topics such as linear and nonlinear optics, quantum computing, discrete systems, and signal analysis have only in the last few years become part of the group theorists' turf. In Group Theoretical Methods in Physics, readers will find both review contributions that distill the state of the art in a broad field, and articles pointed to specific problems, in many cases, preceding their formal publication in the journal literature.
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.
Book Synopsis Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics by : N.H. Ibragimov
Download or read book Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics written by N.H. Ibragimov and published by Springer Science & Business Media. This book was released on 2011-06-27 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the occasion of the 150th anniversary of Sophus Lie, an International Work shop "Modern Group Analysis: advanced analytical and computational methods in mathematical physics" has been organized in Acireale (Catania, Sicily, October 27 31, 1992). The Workshop was aimed to enlighten the present state ofthis rapidly expanding branch of applied mathematics. Main topics of the Conference were: • classical Lie groups applied for constructing invariant solutions and conservation laws; • conditional (partial) symmetries; • Backlund transformations; • approximate symmetries; • group analysis of finite-difference equations; • problems of group classification; • software packages in group analysis. The success of the Workshop was due to the participation of many experts in Group Analysis from different countries. This book consists of selected papers presented at the Workshop. We would like to thank the Scientific Committee for the generous support of recommending invited lectures and selecting the papers for this volume, as well as the members of the Organizing Committee for their help. The Workshop was made possible by the financial support of several sponsors that are listed below. It is also a pleasure to thank our colleague Enrico Gregorio for his invaluable help of this volume.
Book Synopsis Nonlinear Mechanics, Groups and Symmetry by : Yuri A. Mitropolsky
Download or read book Nonlinear Mechanics, Groups and Symmetry written by Yuri A. Mitropolsky and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique monograph deals with the development of asymptotic methods of perturbation theory, making wide use of group- theoretical techniques. Various assumptions about specific group properties are investigated, and are shown to lead to modifications of existing methods, such as the Bogoliubov averaging method and the Poincaré--Birkhoff normal form, as well as to the formulation of new ones. The development of normalization techniques of Lie groups is also treated. The wealth of examples demonstrates how these new group theoretical techniques can be applied to analyze specific problems. This book will be of interest to researchers and graduate students in the field of pure and applied mathematics, mechanics, physics, engineering, and biosciences.
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.
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.
Book Synopsis An Introduction to Tensors and Group Theory for Physicists by : Nadir Jeevanjee
Download or read book An Introduction to Tensors and Group Theory for Physicists written by Nadir Jeevanjee and published by Birkhäuser. This book was released on 2015-03-11 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics. Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects this formulation to the component formalism of physics calculations. New pedagogical features, such as new illustrations, tables, and boxed sections, as well as additional “invitation” sections that provide accessible introductions to new material, offer increased visual engagement, clarity, and motivation for students. Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Examples and exercises are provided in each chapter for good practice in applying the presented material and techniques. Prerequisites for this text include the standard lower-division mathematics and physics courses, though extensive references are provided for the motivated student who has not yet had these. Advanced undergraduate and beginning graduate students in physics and applied mathematics will find this textbook to be a clear, concise, and engaging introduction to tensors and groups. Reviews of the First Edition “[P]hysicist Nadir Jeevanjee has produced a masterly book that will help other physicists understand those subjects [tensors and groups] as mathematicians understand them... From the first pages, Jeevanjee shows amazing skill in finding fresh, compelling words to bring forward the insight that animates the modern mathematical view...[W]ith compelling force and clarity, he provides many carefully worked-out examples and well-chosen specific problems... Jeevanjee’s clear and forceful writing presents familiar cases with a freshness that will draw in and reassure even a fearful student. [This] is a masterpiece of exposition and explanation that would win credit for even a seasoned author.” —Physics Today "Jeevanjee’s [text] is a valuable piece of work on several counts, including its express pedagogical service rendered to fledgling physicists and the fact that it does indeed give pure mathematicians a way to come to terms with what physicists are saying with the same words we use, but with an ostensibly different meaning. The book is very easy to read, very user-friendly, full of examples...and exercises, and will do the job the author wants it to do with style.” —MAA Reviews
Book Synopsis Symmetries and Groups in Contemporary Physics by : Chengming Bai
Download or read book Symmetries and Groups in Contemporary Physics written by Chengming Bai and published by World Scientific. This book was released on 2013-07-26 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on developments in the field of group theory in its broadest sense and is of interest to theoretical and experimental physicists, mathematicians, and scientists in related disciplines who are interested in the latest methods and applications. In an increasingly ultra-specialized world, this volume will demonstrate the interchange of ideas and methods in theoretical and mathematical physics. Contents:The Wigner MedalThe Hermann Weyl PrizePlenary SessionParallel Sessions:Nonlinear SciencesQuantum AlgebrasSuperintegrable HamiltoniansApplications in BiologyQuantum Information and Representation TheoryFinite Quantum Systems and Combinatorial PhysicsSymmetries in String Theory and SupergravityLoop Quantum GravityTensor and Group Field Theories for Quantum GravityConformal Field TheoriesSupersymmetry and Quantum GroupsApplications in Particle and Nuclear PhysicsGeneral Quantum Mechanics and Its Mathematical Methods Involving Group TheoryPoster Session Readership: Researchers and specialists in group theory and its applications to mathematics, physics and other fields in natural science. Keywords:Symmetries;Group Theory;Quantum Physics;Coherent States;Quantum Information;Nonlinear Physics;Supersymmetry;Quantum Gravity;Strings;Conformal Fields;Tensor Fields;Mathematical Biology;Particle Physics;Quantum Algebras;Foundations Of Quantum Mechanics;Combinatorial PhysicsKey Features:Wide range of topics in theoretical and mathematical physicsContains the most recent developments in innovative fields like quantum information, physics and biology, quantum gravity (e.g., strings, loop, tensor fields approaches), combinatorial physicsCross-sectional view of these developments given by prominent specialists, be they promising young scientists (e.g. Gurau, Chiribella, etc.) or confirmed researchers (e.g., Lewandowski, Batchelor, Wang, Murakami, Busch, etc.)
Book Synopsis Applications of Lie Groups to Differential Equations by : Peter J. Olver
Download or read book Applications of Lie Groups to Differential Equations written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.
Book Synopsis Group Theoretical Methods in Physics by : Robert Shar
Download or read book Group Theoretical Methods in Physics written by Robert Shar and published by Elsevier. This book was released on 2012-12-02 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group Theoretical Methods in Physics: Proceedings of the Fifth International Colloquium provides information pertinent to the fundamental aspects of group theoretical methods in physics. This book provides a variety of topics, including nuclear collective motion, complex Riemannian geometry, quantum mechanics, and relativistic symmetry. Organized into six parts encompassing 64 chapters, this book begins with an overview of the theories of nuclear quadrupole dynamics. This text then examines the conventional approach in the determination of superstructures. Other chapters consider the Hamiltonian formalism and how it is applied to the KdV equation and to a slight variant of the KdV equation. This book discusses as well the significant differential equations of mathematical physics that are integrable Hamiltonian systems, including the equations governing self-induced transparency and the motion of particles under an inverse square potential. The final chapter deals with the decomposition of the tensor product of two irreducible representations of the symmetric group into a direct sum of irreducible representations. This book is a valuable resource for physicists.
Author :Mildred S. Dresselhaus Publisher :Springer Science & Business Media ISBN 13 :3540328998 Total Pages :576 pages Book Rating :4.5/5 (43 download)
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.
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:
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.
Book Synopsis Group Theoretical Methods in Physics by : G.S Pogosyan
Download or read book Group Theoretical Methods in Physics written by G.S Pogosyan and published by CRC Press. This book was released on 2005-05-01 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry is permeating our understanding of nature: Group theoretical methods of intrinsic interest to mathematics have expanded their applications from physics to chemistry and biology. The ICGTMP Colloquia maintain the communication among the many branches into which this endeavor has bloomed. Lie group and representation theory, special function
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 1989-01-01 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A remarkably intelligible survey . . . well organized, well written and very clear throughout." — Mathematical Reviews This excellent text, long considered one of the best-written, most skillful expositions of group theory and its physical applications, is directed primarily to advanced undergraduate and graduate students in physics, especially quantum physics. No knowledge of group theory is assumed, but the reader is expected to be familiar with quantum mechanics. And while much of the book concerns theory, readers will nevertheless find a large number of physical applications in the fields of crystallography, molecular theory, and atomic and nuclear physics. The first seven chapters of the book are concerned with finite groups, focusing on the central role of the symmetric group. This section concludes with a chapter dealing with the problem of determining group characters, as it discusses Young tableaux, Yamanouchi symbols, and the method of Hund. The remaining five chapters discuss continuous groups, particularly Lie groups, with the final chapter devoted to the ray representation of Lie groups. The author, Professor Emeritus of Physics at the University of Minnesota, has included a generous selection of problems. They are inserted throughout the text at the place where they naturally arise, making the book ideal for self-study as well as for classroom assignment. 77 illustrations. "A very welcome addition to [the] literature. . . . I would warmly recommend the book to all serious students of Group Theory as applied to Physics." — Contemporary Physics. Index. Bibliography. Problems. Tables.
