Symmetry Representation Theory And Its Applications
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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.
Symmetry
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Author : Roger E. Howe
language : en
Publisher:
Release Date : 2015-01-31
Symmetry written by Roger E. Howe and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-31 with categories.
Symmetries And Laplacians
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Author : David Gurarie
language : en
Publisher: Courier Corporation
Release Date : 2007-12-21
Symmetries And Laplacians written by David Gurarie and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-21 with Mathematics categories.
Designed as an introduction to harmonic analysis and group representations, this book examines concepts, ideas, results, and techniques related to symmetry groups and Laplacians. Its exposition is based largely on examples and applications of general theory, covering a wide range of topics rather than delving deeply into any particular area. Author David Gurarie, a Professor of Mathematics at Case Western Reserve University, focuses on discrete or continuous geometrical objects and structures, such as regular graphs, lattices, and symmetric Riemannian manifolds. Starting with the basics of representation theory, Professor Gurarie discusses commutative harmonic analysis, representations of compact and finite groups, Lie groups, and the Heisenberg group and semidirect products. Among numerous applications included are integrable hamiltonian systems, geodesic flows on symmetric spaces, and the spectral theory of the Hydrogen atom (Schrodinger operator with Coulomb potential) explicated by its Runge-Lenz symmetry. Three helpful appendixes include supplemental information, and the text concludes with references, a list of frequently used notations, and an index.
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.
Symmetry Representations And Invariants
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Author : Roe Goodman
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-30
Symmetry Representations And Invariants written by Roe Goodman 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 2009-07-30 with Mathematics categories.
Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete arguments now given in the general case. Key Features of Symmetry, Representations, and Invariants: (1) Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus; (2) Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux); (3) Self-contained chapters, appendices, comprehensive bibliography; (4) More than 350 exercises (most with detailed hints for solutions) further explore main concepts; (5) Serves as an excellent main text for a one-year course in Lie group theory; (6) Benefits physicists as well as mathematicians as a reference work.
Asymptotic Representation Theory Of The Symmetric Group And Its Applications In Analysis
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Author : Sergei Vasilʹevich Kerov
language : en
Publisher:
Release Date : 2003
Asymptotic Representation Theory Of The Symmetric Group And Its Applications In Analysis written by Sergei Vasilʹevich Kerov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Representations of groups categories.
Asymptotic representation theory of symmetric groups deals with two types of problems: asymptotic properties of representations of symmetric groups of large order and representations of the limiting object, i.e., the infinite symmetric group. The author contributed significantly in the development of problems of both types, and his book presents an account of these contributions, as well as those of other researchers. Among the problems of the first type, the author discusses the properties of the distribution of the normalized cycle length in a random permutation, and the limiting shape of a.
Quantum Theory And Symmetries With Lie Theory And Its Applications In Physics Volume 1
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Author : Vladimir Dobrev
language : en
Publisher: Springer
Release Date : 2018-11-28
Quantum Theory And Symmetries With Lie Theory And Its Applications In Physics Volume 1 written by Vladimir Dobrev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-28 with Mathematics categories.
This book is the first volume of proceedings from the joint conference X International Symposium “Quantum Theory and Symmetries” (QTS-X) and XII International Workshop “Lie Theory and Its Applications in Physics” (LT-XII), held on 19–25 June 2017 in Varna, Bulgaria. The QTS series was founded on the core principle that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium at the forefront of theoretical and mathematical physics. The LT series covers the whole field of Lie theory in its widest sense, together with its applications in many areas of physics. As an interface between mathematics and physics, the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In dividing the material between the two volumes, the Editor has sought to select papers that are more oriented toward mathematics for the first volume, and those focusing more on physics for the second. However, this division is relative, since many papers are equally suitable for either volume. The topics addressed in this volume represent the latest trends in the fields covered by the joint conferences: representation theory, integrability, entanglement, quantum groups, number theory, conformal geometry, quantum affine superalgebras, noncommutative geometry. Further, they present various mathematical results: on minuscule modules, symmetry breaking operators, Kashiwara crystals, meta-conformal invariance, the superintegrable Zernike system.
The Representation Theory Of The Symmetric Group
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Author : James
language : en
Publisher: Cambridge University Press
Release Date : 2009-03-19
The Representation Theory Of The Symmetric Group written by James and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-19 with Mathematics categories.
The Representation Theory of the Symmetric Group provides an account of both the ordinary and modular representation theory of the symmetric groups. The range of applications of this theory is vast, varying from theoretical physics, through combinatories to the study of polynomial identity algebras; and new uses are still being found.
Lie Theory And Its Applications In Physics
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Author : Vladimir Dobrev
language : en
Publisher: Springer Nature
Release Date : 2020-10-15
Lie Theory And Its Applications In Physics written by Vladimir Dobrev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-15 with Science categories.
This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2019. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field. The topics covered in this volume from the workshop represent the most modern trends in the field : Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.
Symmetry Representation Theory And Its Applications
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Author : Roger Howe
language : en
Publisher: Springer
Release Date : 2015-01-04
Symmetry Representation Theory And Its Applications written by Roger Howe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-04 with Mathematics categories.
Nolan Wallach's mathematical research is remarkable in both its breadth and depth. His contributions to many fields include representation theory, harmonic analysis, algebraic geometry, combinatorics, number theory, differential equations, Riemannian geometry, ring theory, and quantum information theory. The touchstone and unifying thread running through all his work is the idea of symmetry. This volume is a collection of invited articles that pay tribute to Wallach's ideas, and show symmetry at work in a large variety of areas. The articles, predominantly expository, are written by distinguished mathematicians and contain sufficient preliminary material to reach the widest possible audiences. Graduate students, mathematicians, and physicists interested in representation theory and its applications will find many gems in this volume that have not appeared in print elsewhere. Contributors: D. Barbasch, K. Baur, O. Bucicovschi, B. Casselman, D. Ciubotaru, M. Colarusso, P. Delorme, T. Enright, W.T. Gan, A Garsia, G. Gour, B. Gross, J. Haglund, G. Han, P. Harris, J. Hong, R. Howe, M. Hunziker, B. Kostant, H. Kraft, D. Meyer, R. Miatello, L. Ni, G. Schwarz, L. Small, D. Vogan, N. Wallach, J. Wolf, G. Xin, O. Yacobi.