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Author: Mark A. Armstrong Publisher: Springer Science & Business Media ISBN: 1475740344 Category : Mathematics Languages : en Pages : 197
Book Description
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.
Author: Yvette Kosmann-Schwarzbach Publisher: Springer Science & Business Media ISBN: 0387788662 Category : Mathematics Languages : en Pages : 207
Book Description
- Combines material from many areas of mathematics, including algebra, geometry, and analysis, so students see connections between these areas - Applies material to physics so students appreciate the applications of abstract mathematics - Assumes only linear algebra and calculus, making an advanced subject accessible to undergraduates - Includes 142 exercises, many with hints or complete solutions, so text may be used in the classroom or for self study
Author: Mark A. Armstrong Publisher: Springer Science & Business Media ISBN: 1475740344 Category : Mathematics Languages : en Pages : 197
Book Description
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.
Author: Alexey P Isaev Publisher: World Scientific ISBN: 9813236876 Category : Science Languages : en Pages : 475
Book Description
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.
Author: Giovanni Costa Publisher: Springer ISBN: 3642154824 Category : Science Languages : en Pages : 300
Book Description
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.
Author: Virendra P. Sinha Publisher: Springer Science & Business Media ISBN: 9048194342 Category : Technology & Engineering Languages : en Pages : 164
Book Description
Symmetries and Groups in Signal Processing: An Introduction deals with the subject of symmetry, and with its place and role in modern signal processing. In the sciences, symmetry considerations and related group theoretic techniques have had a place of central importance since the early twenties. In engineering, however, a matching recognition of their power is a relatively recent development. Despite that, the related literature, in the form of journal papers and research monographs, has grown enormously. A proper understanding of the concepts that have emerged in the process requires a mathematical background that goes beyond what is traditionally covered in an engineering undergraduate curriculum. Admittedly, there is a wide selection of excellent introductory textbooks on the subject of symmetry and group theory. But they are all primarily addressed to students of the sciences and mathematics, or to students of courses in mathematics. Addressed to students with an engineering background, this book is meant to help bridge the gap.
Author: Alexey P Isaev Publisher: World Scientific ISBN: 9811217424 Category : Science Languages : en Pages : 615
Book Description
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: Nathan Carter Publisher: American Mathematical Soc. ISBN: 1470464330 Category : Education Languages : en Pages : 295
Book Description
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
Author: Milan Damnjanovic Publisher: Springer ISBN: 3642111726 Category : Science Languages : en Pages : 201
Book Description
Over last decades low-dimensional materials are in focus of physics and chemistry as well as of material and other natural sciences. Like Vitaly Ginzburg has foreseen 30 years ago, low dimensionality offers physical phenomena and properties unseen in three-dimensional world. To see how thin ?lms and monomolecular layers realize such a prediction it suf?ces only to observe intensity of research devoted to recently synthesized graphene. Still, quasi-one-dimensional compounds are over long period established as the origin of the most important and most interesting discoveries of material science and solid state physics. To mention only deoxyribonucleic acid, the most important molecule in nature, and diversity of nanotubes and nanowires, the cornerstones of the present and future nanotechnology. Line groups, describing symmetry of quasi-one-dimensional materials, offer the deepest insight to their characteristic properties. Underlying many of the laws, they are very useful, but far from simple. This book is intended to explain them, their properties, and their most common applications. In particular, it is important to understand that the line groups are much wider class of symmetries than the well-known rod groups. While the latter describe only translationally periodical objects, line groups include symmetries of incommensurate periodical structures.
Author: David W. Farmer Publisher: American Mathematical Soc. ISBN: 0821804502 Category : Mathematics Languages : en Pages : 112
Book Description
Mathematics is discovered by looking at examples, noticing patterns, making conjectures, and testing those conjectures. Once discovered, the final results get organized and put in textbooks. The details and the excitement of the discovery are lost. This book introduces the reader to the excitement of the original discovery. By means of a wide variety of tasks, readers are led to find interesting examples, notice patterns, devise rules to explain the patterns, and discover mathematics for themselves. The subject studied here is the mathematics behind the idea of symmetry, but the methods and ideas apply to all of mathematics. The only prerequisites are enthusiasm and a knowledge of basic high-school math. The book is only a guide. It will start you off in the right direction and bring you back if you stray too far. The excitement and the discovery are left to you.
Author: Yvette Kosmann-Schwarzbach Publisher: Springer Nature ISBN: 3030943607 Category : Mathematics Languages : en Pages : 266
Book Description
- Combines material from many areas of mathematics, including algebra, geometry, and analysis, so students see connections between these areas - Applies material to physics so students appreciate the applications of abstract mathematics - Assumes only linear algebra and calculus, making an advanced subject accessible to undergraduates - Includes 142 exercises, many with hints or complete solutions, so text may be used in the classroom or for self study
Author: Mark A. Armstrong
Author: Yvette Kosmann-Schwarzbach
Author: Mark A. Armstrong
Author: Alexey P Isaev
Author: Giovanni Costa
Author: Virendra P. Sinha
Author: Alexey P Isaev
Author: Nathan Carter
Author: Milan Damnjanovic
Author: David W. Farmer
Author: Yvette Kosmann-Schwarzbach