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: Boris Kruglikov; Valentin Lychagin; Eldar Straume Название: Differential Equations - Geometry, Symmetries and Integrability ISBN: 3642269338 ISBN-13(EAN): 9783642269332 Издательство: Springer Рейтинг: Цена: 23058.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book contains papers presented at the Abel Symposium 2008, which focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. It presents a modern approach to this classical subject.
Автор: Boris Kruglikov; Valentin Lychagin; Eldar Straume Название: Differential Equations - Geometry, Symmetries and Integrability ISBN: 3642008720 ISBN-13(EAN): 9783642008726 Издательство: Springer Рейтинг: Цена: 23058.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The Abel Symposium 2008 focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. This title consists of original contributions and overview lectures of the participants of the Symposium. It includes papers that present the modern approach to this classical subject.
Описание: This three-week summer program considered the symmetries preserving various natural geometric structures. The articles in the first part are expository but all contain significant new material. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.
Описание: This is a detailed exposition of algebraic and geometrical aspects related to the theory of symmetries and recursion operators for nonlinear partial differential equations (PDE), both in classical and in super, or graded, versions.
Автор: A.M. Vinogradov Название: Symmetries of Partial Differential Equations ISBN: 9401073708 ISBN-13(EAN): 9789401073707 Издательство: Springer Рейтинг: Цена: 41787.00 р. 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.
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: 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.
Автор: Mitra Parthasarathi Название: Symmetries and Symmetry Breaking in Field Theory ISBN: 1466581042 ISBN-13(EAN): 9781466581043 Издательство: Taylor&Francis Рейтинг: Цена: 16843.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Many courses on modern quantum field theory focus on the formulation and application of field theory, leaving topics related to symmetry underdeveloped. This leads to students often having an incomplete understanding of symmetries. Filling this gap, Symmetries and Symmetry Breaking in Field Theory sheds light on various aspects of symmetry in field theory.
The book presents a broad selection of important topics, including constraint theory, generalized Pauli-Villars regularization, the measure approach to anomalies, zeta function regularization, and anomalous gauge theories. The author explains how some classical symmetries are broken by anomalies and how other symmetries of the theory are spontaneously broken. He discusses all of the ideas in as simple a way as possible.
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: Berghofer, Philipp (universitat Graz, Austria) Francois, Jordan (universite De Mons, Belgium) Friederich, Simon (rijksuniversiteit Groningen, The Neth Название: Gauge symmetries, symmetry breaking, and gauge-invariant approaches ISBN: 1009197223 ISBN-13(EAN): 9781009197229 Издательство: Cambridge Academ Рейтинг: Цена: 2693.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or whether they can be eliminated. It is also unclear whether they are merely an auxiliary tool to simplify (and possibly localize) calculations or whether they contain independent information. Therefore their status, both in physics and philosophy of physics, remains to be fully clarified. This Element reviews the current state of affairs on both the philosophy and the physics side. In particular, it focuses on the circumstances in which the restriction of gauge theories to gauge invariant information on an observable level is warranted, using the Brout-Englert-Higgs theory as an example of particular current importance. Finally, the authors determine a set of yet to be answered questions to clarify the status of gauge symmetries.
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