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.
Автор: G?len Aktas; Cihan Saclioglu; Meral Serdaroglu Название: Strings and Symmetries ISBN: 3662140322 ISBN-13(EAN): 9783662140321 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The topics in this volume constitute a fitting tribute by distinguished physicists and mathematicians. They cover strings, conformal field theories, W and Virasoro algebras, topological field theory, quantum groups, vertex and Hopf algebras, and non-commutative geometry.
Автор: Claus M?ller Название: Analysis of Spherical Symmetries in Euclidean Spaces ISBN: 1461268273 ISBN-13(EAN): 9781461268277 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This self-contained book offers a new and direct approach to the theories of special functions with emphasis on spherical symmetry in Euclidean spaces of arbitrary dimensions.
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.
Автор: Bruno Gruber; Michael Ramek Название: Symmetries in Science IX ISBN: 1461377153 ISBN-13(EAN): 9781461377153 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Proceedings of a symposium held in Bregenz, Austria, August 6-10, 1996
Автор: A.M. Vinogradov Название: Symmetries of Partial Differential Equations ISBN: 9401073708 ISBN-13(EAN): 9789401073707 Издательство: Springer Рейтинг: Цена: 278580.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Higher symmetries, conservation laws, partial differential equations, infinitely prolonged equations, generating functions. More exactly, we will focus our attention on the main conceptual points as well as on the problem of how to find all higher symmetries and conservation laws for a given system of partial differential equations.
Автор: Kenji Iohara; Sophie Morier-Genoud; Bertrand R?my Название: Symmetries, Integrable Systems and Representations ISBN: 1447148622 ISBN-13(EAN): 9781447148623 Издательство: Springer Рейтинг: Цена: 139750.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This volume is the result of two international workshops; Infinite Analysis 11 - Frontier of Integrability - held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Universit Claude Bernard Lyon 1, France in December 13th to 16th, 2011.
Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions.
Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.
Автор: Bruno Gruber; L.C. Biedenharn; H.D. D?bner Название: Symmetries in Science V ISBN: 1461366437 ISBN-13(EAN): 9781461366430 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Proceedings of a symposium held in Landesbildungszentrum Schloss Hofen, Lochau, Vorarlberg, Austria, July 30-August 3, 1990
Автор: Bruno Gruber Название: Symmetries in Science VIII ISBN: 1461357837 ISBN-13(EAN): 9781461357834 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Decio Levi; Rapha?l Rebelo; Pavel Winternitz Название: Symmetries and Integrability of Difference Equations ISBN: 3319566652 ISBN-13(EAN): 9783319566658 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations.
Автор: Heinrich Saller Название: Operational Symmetries ISBN: 3319586637 ISBN-13(EAN): 9783319586632 Издательство: Springer Рейтинг: Цена: 116450.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book describes the endeavour to relate the particle spectrum with representations of operational electroweak spacetime, in analogy to the atomic spectrum as characterizing representations of hyperbolic space.
Автор: Ulrich Mosel Название: Fields, Symmetries, and Quarks ISBN: 3540652353 ISBN-13(EAN): 9783540652359 Издательство: Springer Рейтинг: Цена: 69650.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Written at an introductory level, this text covers elements of quantum field theory, symmetries, gauge field theories, and the phenomenology of hadrons, with emphasis on topics relevant to high-energy and nuclear physics.
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