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: Victor G. Kac; Peter J. Olver; Pavel Winternitz; T Название: Symmetries, Differential Equations and Applications ISBN: 3030131769 ISBN-13(EAN): 9783030131760 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Based on the third International Conference on Symmetries, Differential Equations and Applications (SDEA-III), this proceedings volume highlights recent important advances and trends in the applications of Lie groups, including a broad area of topics in interdisciplinary studies, ranging from mathematical physics to financial mathematics. The selected and peer-reviewed contributions gathered here cover Lie theory and symmetry methods in differential equations, Lie algebras and Lie pseudogroups, super-symmetry and super-integrability, representation theory of Lie algebras, classification problems, conservation laws, and geometrical methods.
The SDEA III, held in honour of the Centenary of Noether’s Theorem, proven by the prominent German mathematician Emmy Noether, at Istanbul Technical University in August 2017 provided a productive forum for academic researchers, both junior and senior, and students to discuss and share the latest developments in the theory and applications of Lie symmetry groups.This work has an interdisciplinary appeal and will be a valuable read for researchers in mathematics, mechanics, physics, engineering, medicine and finance.
Based on the third International Conference on Symmetries, Differential Equations and Applications (SDEA-III), this proceedings volume highlights recent important advances and trends in the applications of Lie groups, including a broad area of topics in interdisciplinary studies, ranging from mathematical physics to financial mathematics. The selected and peer-reviewed contributions gathered here cover Lie theory and symmetry methods in differential equations, Lie algebras and Lie pseudogroups, super-symmetry and super-integrability, representation theory of Lie algebras, classification problems, conservation laws, and geometrical methods.
The SDEA III, held in honour of the Centenary of Noether’s Theorem, proven by the prominent German mathematician Emmy Noether, at Istanbul Technical University in August 2017 provided a productive forum for academic researchers, both junior and senior, and students to discuss and share the latest developments in the theory and applications of Lie symmetry groups.This work has an interdisciplinary appeal and will be a valuable read for researchers in mathematics, mechanics, physics, engineering, medicine and finance.
Автор: Kurt Sundermeyer Название: Symmetries in Fundamental Physics ISBN: 3319065807 ISBN-13(EAN): 9783319065809 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. Given this pivotal role of symmetries it is thus not surprising that current research in fundamental physics is to a great degree motivated and inspired by considerations of symmetry.
Автор: Kurt Sundermeyer Название: Symmetries in Fundamental Physics ISBN: 3319342649 ISBN-13(EAN): 9783319342641 Издательство: Springer Рейтинг: Цена: 19589.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. Given this pivotal role of symmetries it is thus not surprising that current research in fundamental physics is to a great degree motivated and inspired by considerations of symmetry.
Автор: Julius Wess; Evgeny A. Ivanov Название: Supersymmetries and Quantum Symmetries ISBN: 3662142082 ISBN-13(EAN): 9783662142080 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is a collection of papers in honour of Victor I. Ogievetsky. It contains reviews on supersymmetry and supergravity, dualities, integrable systems, W (super)algebras and quantum symmetries. The reader will also find reprints of some of Ogievetsky`s pioneering work on supersymmetry.
Автор: A. Faessler; T.S. Kosmas; G.K. Leontaris Название: Symmetries in Intermediate and High Energy Physics ISBN: 3642085997 ISBN-13(EAN): 9783642085994 Издательство: Springer Рейтинг: Цена: 40389.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book contains comprehensive reviews of modern topics in nuclear physics, particle physics, astrophysics and cosmology.
Автор: Uwe Franz; Guillaume Aubrun; Adam Skalski; Roland Название: Quantum Symmetries ISBN: 3319632051 ISBN-13(EAN): 9783319632056 Издательство: Springer Рейтинг: Цена: 4890.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems. A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics.
Автор: Alejandro Frank; Kurt B. Wolf Название: Symmetries in Physics ISBN: 3642772862 ISBN-13(EAN): 9783642772863 Издательство: Springer Рейтинг: Цена: 16979.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This volume gives a broad overview of symmetry methods applied to molecular and nuclear physics, particle physics, decay processes and phase space dynamics. The thoroughly edited contributions should be of interest not only to scientists but also to those that want to see how symmetry considerations are put to work in twentieth century physics.
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.
Описание: The formulation involves some vector (or analogous higher symmetry) coupling of the intrinsic algebra with the n-dimensional oscillator algebra, leading to matrix representations and Wigner coefficients of the higher symmetry algebra expressed in terms of simple calculable functions and recoupling coefficients for the simpler intrinsic algebra.
Автор: Bruno Gruber; Takaharu Otsuka Название: Symmetries in Science VII ISBN: 1461362857 ISBN-13(EAN): 9781461362852 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Proceedings of a symposium held in Nakajo, Niigata, Japan, August 28-31, 1992
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