Theory Of Groups And Symmetries
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Theory Of Groups And Symmetries Representations Of Groups And Lie Algebras Applications
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Author : Alexey P Isaev
language : en
Publisher: World Scientific
Release Date : 2020-07-16
Theory Of Groups And Symmetries Representations Of Groups And Lie Algebras Applications written by Alexey P Isaev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-16 with Science categories.
This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras.The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed.Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C[Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed.Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.
Theory Of Groups And Symmetries Finite Groups Lie Groups And Lie Algebras
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Author : Rubakov Valery A
language : en
Publisher: World Scientific
Release Date : 2018-03-21
Theory Of Groups And Symmetries Finite Groups Lie Groups And Lie Algebras written by Rubakov Valery A and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-21 with Science categories.
The book presents the main approaches in study of algebraic structures of symmetries in models of theoretical and mathematical physics, namely groups and Lie algebras and their deformations. It covers the commonly encountered quantum groups (including Yangians). The second main goal of the book is to present a differential geometry of coset spaces that is actively used in investigations of models of quantum field theory, gravity and statistical physics. The third goal is to explain the main ideas about the theory of conformal symmetries, which is the basis of the AdS/CFT correspondence. The theory of groups and symmetries is an important part of theoretical physics. In elementary particle physics, cosmology and related fields, the key role is played by Lie groups and algebras corresponding to continuous symmetries. For example, relativistic physics is based on the Lorentz and Poincare groups, and the modern theory of elementary particles — the Standard Model — is based on gauge (local) symmetry with the gauge group SU(3) x SU(2) x U(1). This book presents constructions and results of a general nature, along with numerous concrete examples that have direct applications in modern theoretical and mathematical physics. Contents: Preface Groups and Transformations Lie Groups Lie Algebras Representations of Groups and Lie Algebras Compact Lie Algebras Root Systems and Classification of Simple Lie Algebras Homogeneous Spaces and their Geometry Solutions to Selected Problems Selected Bibliography References Index Readership: Graduate students and researchers in theoretical physics and mathematical physics. Keywords: Lie Groups;Lie Algebras;Representation Theory;Conformal Symmetries;Yangians;Coset Spaces;Differential Geometry;Casimir Operators;Root Systems;AdS Spaces;Lobachevskian GeometryReview:0
Symmetry
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Author : R. McWeeny
language : en
Publisher: Elsevier
Release Date : 2013-09-03
Symmetry written by R. McWeeny and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-03 with Mathematics categories.
Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.
Groups And Symmetry
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Author : Mark A. Armstrong
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Groups And Symmetry written by Mark A. Armstrong 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 2013-03-14 with Mathematics categories.
This is a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal style, the material is divided into short sections, each of which deals with an important result or a new idea. Includes more than 300 exercises and approximately 60 illustrations.
Theory Of Groups And Symmetries
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Author : Alexey P. Isaev
language : en
Publisher:
Release Date : 2018
Theory Of Groups And Symmetries written by Alexey P. Isaev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
The book presents the main approaches in study of algebraic structures of symmetries in models of theoretical and mathematical physics, namely groups and Lie algebras and their deformations. It covers the commonly encountered quantum groups (including Yangians). The second main goal of the book is to present a differential geometry of coset spaces that is actively used in investigations of models of quantum field theory, gravity and statistical physics. The third goal is to explain the main ideas about the theory of conformal symmetries, which is the basis of the AdS/CFT correspondence.The theory of groups and symmetries is an important part of theoretical physics. In elementary particle physics, cosmology and related fields, the key role is played by Lie groups and algebras corresponding to continuous symmetries. For example, relativistic physics is based on the Lorentz and Poincare groups, and the modern theory of elementary particles &mdash, the Standard Model &mdash, is based on gauge (local) symmetry with the gauge group SU(3) x SU(2) x U(1). This book presents constructions and results of a general nature, along with numerous concrete examples that have direct applications in modern theoretical and mathematical physics.
Groups And Symmetry
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Author : Bijan Davvaz
language : en
Publisher: Springer Nature
Release Date : 2021-11-17
Groups And Symmetry written by Bijan Davvaz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-17 with Mathematics categories.
This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. This is the second book of the set of two books on groups theory. Topics on linear transformation and linear groups, group actions on sets, Sylow’s theorem, simple groups, products of groups, normal series, free groups, platonic solids, Frieze and wallpaper symmetry groups and characters of groups have been discussed in depth. Covering all major topics, this book is targeted to advanced undergraduate students of mathematics with no prerequisite knowledge of the discussed topics. Each section ends with a set of worked-out problems and supplementary exercises to challenge the knowledge and ability of the reader.
Group Theory In Physics A Practitioner S Guide
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Author : Traubenberg M Rausch De
language : en
Publisher: World Scientific
Release Date : 2018-09-19
Group Theory In Physics A Practitioner S Guide written by Traubenberg M Rausch De and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-19 with Science categories.
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.
Groups And Symmetries
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Author : Yvette Kosmann-Schwarzbach
language : en
Publisher:
Release Date : 2022
Groups And Symmetries written by Yvette Kosmann-Schwarzbach and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
Groups and Symmetries: From Finite Groups to Lie Groups presents an introduction to the theory of group representations and its applications in quantum mechanics. Accessible to advanced undergraduates in mathematics and physics as well as beginning graduate students, the text deals with the theory of representations of finite groups, compact groups, linear Lie groups and their Lie algebras, concisely and in one volume. Prerequisites include calculus and linear algebra. This new edition contains an additional chapter that deals with Clifford algebras, spin groups, and the theory of spinors, as well as new sections entitled "Topics in history" comprising notes on the history of the material treated within each chapter. (Taken together, they constitute an account of the development of the theory of groups from its inception in the 18th century to the mid-20th.) References for additional resources and further study are provided in each chapter. All chapters end with exercises of varying degree of difficulty, some of which introduce new definitions and results. The text concludes with a collection of problems with complete solutions making it ideal for both course work and independent study. Key Topics include: Brisk review of the basic definitions of group theory, with examples Representation theory of finite groups: character theory Representations of compact groups using the Haar measure Lie algebras and linear Lie groups Detailed study of SO(3) and SU(2), and their representations Spherical harmonics Representations of SU(3), roots and weights, with quark theory as a consequence of the mathematical properties of this symmetry group Spin groups and spinors.
Symmetries And Group Theory In Particle Physics
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Author : Giovanni Costa
language : en
Publisher: Springer
Release Date : 2012-02-03
Symmetries And Group Theory In Particle Physics written by Giovanni Costa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-03 with Science categories.
Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is an introduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of the Minkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standard model of particle physics. This book, based on several courses given by the authors, addresses advanced graduate students and non-specialist researchers wishing to enter active research in the field, and having a working knowledge of classical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures.
The Theory Of Groups And Quantum Mechanics
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Author : Hermann Weyl
language : en
Publisher: Courier Corporation
Release Date : 1950-01-01
The Theory Of Groups And Quantum Mechanics written by Hermann Weyl and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1950-01-01 with Mathematics categories.
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.