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Author : Susann Vihma
Publisher : Unknown
Page : 224 pages
File Size : 51,8 Mb
Release : 1995
Category : Aesthetics
ISBN : UOM:39015064762985
Author : H. E. Moses
Publisher : Unknown
Page : 52 pages
File Size : 47,5 Mb
Release : 1969
Category : Conformal mapping
ISBN : UOM:39015095296789
The factors of the direct product and the representations which appear in the expansion are expressed in terms of a particular momentum representation called 'the standard helicity representation' which enables one to use a uniform notation for all masses, whether real, zero, or imaginary. The earlier portions of the present paper summarizes the properties of these representations.
Author : H.F Jones
Publisher : CRC Press
Page : 348 pages
File Size : 45,5 Mb
Release : 2020-07-14
Category : Mathematics
ISBN : 142005029X
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.
Author : Alberto Ibort,Miguel A. Rodriguez
Publisher : CRC Press
Page : 242 pages
File Size : 51,6 Mb
Release : 2019-10-28
Category : Mathematics
ISBN : 9781351869560
This book offers an introduction to the theory of groupoids and their representations encompassing the standard theory of groups. Using a categorical language, developed from simple examples, the theory of finite groupoids is shown to knit neatly with that of groups and their structure as well as that of their representations is described. The book comprises numerous examples and applications, including well-known games and puzzles, databases and physics applications. Key concepts have been presented using only basic notions so that it can be used both by students and researchers interested in the subject. Category theory is the natural language that is being used to develop the theory of groupoids. However, categorical presentations of mathematical subjects tend to become highly abstract very fast and out of reach of many potential users. To avoid this, foundations of the theory, starting with simple examples, have been developed and used to study the structure of finite groups and groupoids. The appropriate language and notions from category theory have been developed for students of mathematics and theoretical physics. The book presents the theory on the same level as the ordinary and elementary theories of finite groups and their representations, and provides a unified picture of the same. The structure of the algebra of finite groupoids is analysed, along with the classical theory of characters of their representations. Unnecessary complications in the formal presentation of the subject are avoided. The book offers an introduction to the language of category theory in the concrete setting of finite sets. It also shows how this perspective provides a common ground for various problems and applications, ranging from combinatorics, the topology of graphs, structure of databases and quantum physics.
Author : Anatoli Klimyk,Konrad Schmüdgen
Publisher : Springer Science & Business Media
Page : 568 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642608964
This book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.
Author : F. L. Williams
Publisher : Springer
Page : 139 pages
File Size : 46,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540378655
Author : Brian C. Hall
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 50,5 Mb
Release : 2003-08-07
Category : Mathematics
ISBN : 0387401229
This book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics. Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it a useful addition to the literature. First, it treats Lie groups (not just Lie alge bras) in a way that minimizes the amount of manifold theory needed. Thus, I neither assume a prior course on differentiable manifolds nor provide a con densed such course in the beginning chapters. Second, this book provides a gentle introduction to the machinery of semi simple groups and Lie algebras by treating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory. The standard books on Lie theory begin immediately with the general case: a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. This approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time.
Author : A Barut,R Raczka
Publisher : World Scientific Publishing Company
Page : 740 pages
File Size : 52,6 Mb
Release : 1986-11-01
Category : Mathematics
ISBN : 9789813103870
The material collected in this book originated from lectures given by authors over many years in Warsaw, Trieste, Schladming, Istanbul, Goteborg and Boulder. There is no other comparable book on group representations, neither in mathematical nor in physical literature and it is hoped that this book will prove to be useful in many areas of research. It is highly recommended as a textbook for an advanced course in mathematical physics on Lie algebras, Lie groups and their representations. Request Inspection Copy
Author : E.B. Vinberg
Publisher : Springer Science & Business Media
Page : 160 pages
File Size : 55,7 Mb
Release : 1989-06-01
Category : Mathematics
ISBN : 3764322888
This book gives an exposition of the fundamentals of the theory of linear representations of finite and compact groups, as well as elements of the the ory of linear representations of Lie groups. As an application we derive the Laplace spherical functions. The book is based on lectures that I delivered in the framework of the experimental program at the Mathematics-Mechanics Faculty of Moscow State University and at the Faculty of Professional Skill Improvement. My aim has been to give as simple and detailed an account as possible of the problems considered. The book therefore makes no claim to completeness. Also, it can in no way give a representative picture of the modern state of the field under study as does, for example, the monograph of A. A. Kirillov [3]. For a more complete acquaintance with the theory of representations of finite groups we recommend the book of C. W. Curtis and I. Reiner [2], and for the theory of representations of Lie groups, that of M. A. Naimark [6]. Introduction The theory of linear representations of groups is one of the most widely ap plied branches of algebra. Practically every time that groups are encountered, their linear representations play an important role. In the theory of groups itself, linear representations are an irreplaceable source of examples and a tool for investigating groups. In the introduction we discuss some examples and en route we introduce a number of notions of representation theory. O.
Author : Alexey P Isaev,Valery A Rubakov
Publisher : World Scientific
Page : 615 pages
File Size : 51,6 Mb
Release : 2020-07-16
Category : Science
ISBN : 9789811217425
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.
Author : EUJIN. SELF PEI (JAMES ANDREW.),James Andrew Self
Publisher : CRC Press
Page : 232 pages
File Size : 43,7 Mb
Release : 2021-11-19
Category : Electronic
ISBN : 036763001X
This book extends understanding of the design process by exploring design representation types and examining them as theoretical constructs. It shows how fidelity and ambiguity inform the creative act of design, and considers design thinking through the lens of design representation. Design thinking is a method that has the potential to stimulate and enhance creativity. This book enhances understanding of what constitutes design thinking, why it is used and how it can be applied in practice to explore and develop ideas. The book positions a particular type of thinking through design representations, exploring this from its roots in design history, to the types of thinking in action associated with contemporary design practice. A taxonomy of design representations as a scaffold to express design intent, is applied to real world case studies. Product Design and the Role of Representation will be of interest to those working in or studying product development, engineering design and additive manufacturing. "This book responds to the expression 'all you always wanted to know about design representation but didn't know where to ask'. Indeed, the book is a thematic guide to design representation, and the amount of information about design representations it holds is phenomenal." Professor Gabriela Goldschmidt Technion - Israel Institute of Technology
Author : Graham J. Leuschke,Frauke Bleher,Ralf Schiffler,Dan Zacharia
Publisher : American Mathematical Soc.
Page : 296 pages
File Size : 50,9 Mb
Release : 2018
Category : Algebra
ISBN : 9781470435769
This volume contains the proceedings of the 17th Workshop and International Conference on Representations of Algebras (ICRA 2016), held from August 10-19, 2016, at Syracuse University, Syracuse, NY. Included are three survey articles based on short courses in the areas of commutative algebraic groups, modular group representation theory, and thick tensor ideals of bounded derived categories. Other articles represent contributions to areas in and related to representation theory, such as noncommutative resolutions, twisted commutative algebras, and upper cluster algebras.
Author : Anonim
Publisher : Unknown
Page : 436 pages
File Size : 49,7 Mb
Release : 1983
Category : Administrative law
ISBN : OSU:32437121416107
Special edition of the Federal Register, containing a codification of documents of general applicability and future effect ... with ancillaries.
Author : Wu-Ki Tung
Publisher : World Scientific Publishing Company
Page : 336 pages
File Size : 44,9 Mb
Release : 1985-08-31
Category : Representations of groups
ISBN : 9789813104044
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
Author : Stanley Burris,Ralph McKenzie
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 48,6 Mb
Release : 1981
Category : Mathematics
ISBN : 9780821822463
