Theory Of Group Representations And Applications
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Theory Of Group Representations And Applications
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Author : Asim Orhan Barut
language : en
Publisher: World Scientific
Release Date : 1986
Theory Of Group Representations And Applications written by Asim Orhan Barut and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.
Representation Theory Of Finite Groups
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Author : Benjamin Steinberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-23
Representation Theory Of Finite Groups written by Benjamin Steinberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-23 with Mathematics categories.
This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.
Introduction To The Theory Of Banach Representations Of Groups
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Author : Yurii I. Lyubich
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Introduction To The Theory Of Banach Representations Of Groups written by Yurii I. Lyubich and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Social Science categories.
The theory of group representations plays an important roie in modern mathematics and its applica~ions to natural sciences. In the compulsory university curriculum it is included as a branch of algebra, dealing with representations of finite groups (see, for example, the textbook of A. I. Kostrikin [25]). The representation theory for compact, locally compact Abelian, and Lie groups is co vered in graduate courses, concentrated around functional analysis. The author of the present boo~ has lectured for many years on functional analysis at Khar'kov University. He subsequently con tinued these lectures in the form of a graduate course on the theory of group representations, in which special attention was devoted to a retrospective exposition of operator theory and harmo nic analysis of functions from the standpoint of representation theory. In this approach it was natural to consider not only uni tary, but also Banach representations, and not only representations of groups, but also of semigroups.
Group And Representation Theory
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Author : Ioannis John Demetrius Vergados
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-12-29
Group And Representation Theory written by Ioannis John Demetrius Vergados and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-29 with Science categories.
This volume goes beyond the understanding of symmetries and exploits them in the study of the behavior of both classical and quantum physical systems. Thus it is important to study the symmetries described by continuous (Lie) groups of transformations. We then discuss how we get operators that form a Lie algebra. Of particular interest to physics is the representation of the elements of the algebra and the group in terms of matrices and, in particular, the irreducible representations. These representations can be identified with physical observables.This leads to the study of the classical Lie algebras, associated with unitary, unimodular, orthogonal and symplectic transformations. We also discuss some special algebras in some detail. The discussion proceeds along the lines of the Cartan-Weyl theory via the root vectors and root diagrams and, in particular, the Dynkin representation of the roots. Thus the representations are expressed in terms of weights, which are generated by the application of the elements of the algebra on uniquely specified highest weight states. Alternatively these representations can be described in terms of tensors labeled by the Young tableaux associated with the discrete symmetry Sn. The connection between the Young tableaux and the Dynkin weights is also discussed. It is also shown that in many physical systems the quantum numbers needed to specify the physical states involve not only the highest symmetry but also a number of sub-symmetries contained in them. This leads to the study of the role of subalgebras and in particular the possible maximal subalgebras. In many applications the physical system can be considered as composed of subsystems obeying a given symmetry. In such cases the reduction of the Kronecker product of irreducible representations of classical and special algebras becomes relevant and is discussed in some detail. The method of obtaining the relevant Clebsch-Gordan (C-G) coefficients for such algebras is discussed and some relevant algorithms are provided. In some simple cases suitable numerical tables of C-G are also included.The above exposition contains many examples, both as illustrations of the main ideas as well as well motivated applications. To this end two appendices of 51 pages — 11 tables in Appendix A, summarizing the material discussed in the main text and 39 tables in Appendix B containing results of more sophisticated examples are supplied. Reference to the tables is given in the main text and a guide to the appropriate section of the main text is given in the tables.
Representation Theory Of Finite Groups
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Author : Martin Burrow
language : en
Publisher: Courier Corporation
Release Date : 2014-05-05
Representation Theory Of Finite Groups written by Martin Burrow and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-05 with Mathematics categories.
DIVConcise, graduate-level exposition covers representation theory of rings with identity, representation theory of finite groups, more. Exercises. Appendix. 1965 edition. /div
Groups Representations And Physics
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Author : H.F Jones
language : en
Publisher: CRC Press
Release Date : 2020-07-14
Groups Representations And Physics written by H.F Jones and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-14 with Mathematics categories.
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.
Applications Of Finite Groups
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Author : J. S. Lomont
language : en
Publisher: Academic Press
Release Date : 2014-05-12
Applications Of Finite Groups written by J. S. Lomont and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Applications of Finite Groups focuses on the applications of finite groups to problems of physics, including representation theory, crystals, wave equations, and nuclear and molecular structures. The book first elaborates on matrices, groups, and representations. Topics include abstract properties, applications, matrix groups, key theorem of representation theory, properties of character tables, simply reducible groups, tensors and invariants, and representations generated by functions. The text then examines applications and subgroups and representations, as well as subduced and induced representations, fermion annihilation and creation operators, crystallographic point groups, proportionality tensors in crystals, and nonrelativistic wave equations. The publication takes a look at space group representations and energy bands, symmetric groups, and applications. Topics include molecular and nuclear structures, multiplet splitting in crystalline electric fields, construction of irreducible representations of the symmetric groups, and reality of representations. The manuscript is a dependable source of data for physicists and researchers interested in the applications of finite groups.
Group Theory
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Author : Mildred S. Dresselhaus
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-13
Group Theory written by Mildred S. Dresselhaus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-13 with Science categories.
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 Representation Theory For Physicists 2nd Edition
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Author : Jialun Ping
language : en
Publisher: World Scientific Publishing Company
Release Date : 2002-08-15
Group Representation Theory For Physicists 2nd Edition written by Jialun Ping and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-15 with Science categories.
This book introduces systematically the eigenfunction method, a new approach to the group representation theory which was developed by the authors in the 1970's and 1980's in accordance with the concept and method used in quantum mechanics. It covers the applications of the group theory in various branches of physics and quantum chemistry, especially nuclear and molecular physics. Extensive tables and computational methods are presented.Group Representation Theory for Physicists may serve as a handbook for researchers doing group theory calculations. It is also a good reference book and textbook for undergraduate and graduate students who intend to use group theory in their future research careers.
Group Theory In Physics
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Author : Wu-Ki Tung
language : en
Publisher: World Scientific
Release Date : 1985
Group Theory In Physics written by Wu-Ki Tung and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Science categories.
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.