Gauge symmetries, symmetry breaking, and gauge-invariant approaches, Berghofer, Philipp (universitat Graz, Austria) Francois, Jordan (universite De Mons, Belgium) Friederich, Simon (rijksuniversiteit Groningen, The Neth
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.
The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.
Автор: Bruno Gruber; Michael Ramek Название: Symmetries in Science IX ISBN: 1461377153 ISBN-13(EAN): 9781461377153 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Proceedings of a symposium held in Bregenz, Austria, August 6-10, 1996
Автор: Heinrich Saller Название: Operational Symmetries ISBN: 3319586637 ISBN-13(EAN): 9783319586632 Издательство: Springer Рейтинг: Цена: 17468.00 р. 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: Longo Giuseppe Название: Biological Time, Symmetries and Singularities ISBN: 364235937X ISBN-13(EAN): 9783642359378 Издательство: Springer Рейтинг: Цена: 23508.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book provides a novel and genuinely theoretical approach to biology. Coverage includes a characterization of physical versus biological as well as introduces the concept of anti-entropy as a measure for the potential of variability.
Автор: Bailin, D. Название: Cosmology in Gauge Field Theory and String Theory ISBN: 0750304928 ISBN-13(EAN): 9780750304924 Издательство: Taylor&Francis Рейтинг: Цена: 13779.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The aim of this book is to develop a contraction method for classical orthogonal and unitary groups (algebras), and apply it to the investigation of physical structures, offering a new and unique interpretation to the high-energy limit of the Standard Model. Readers will find a comprehensive and rigorous study, summarized as follows: The space-time models (or kinematics) are described on the motion group level. The Jordan-Schwinger representations of the groups are shown to be closely connected to the properties of stationary quantum systems, whose Hamiltonians are quadratic in creation and annihilation operators. The high-temperature limit of the Standard Model is associated with the contraction of its gauge group, and the tending-to-zero contraction parameter is connected to the inverse average energy (temperature) of the Universe. This makes it possible to re-establish the evolution of particles and their interactions in the early Universe up to Planck energy, where readers shall discover that the properties of elementary particles change drastically in the infinite temperature limit: all particles lose mass, all quarks are monochromatic, electroweak interactions become long range and are mediated by neutral currents.Absent in all known literature, this book would be the first in describing the dynamics of particle properties and their interactions at different stages in the evolution of the Universe. Presenting both physical and mathematical approaches to various problems, and their applications to the physics of the early Universe, this book will be a valuable addition to the sparse literature on the subject matter.
Автор: Alexander Braverman; Michael Finkelberg; Andrei Ne Название: Geometric Representation Theory and Gauge Theory ISBN: 3030268551 ISBN-13(EAN): 9783030268558 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book offers a review of the vibrant areas of geometric representation theory and gauge theory, which are characterized by a merging of traditional techniques in representation theory with the use of powerful tools from algebraic geometry, and with strong inputs from physics.
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: 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.
Автор: Bruno Gruber Название: Symmetries in Science III ISBN: 1461280826 ISBN-13(EAN): 9781461280828 Издательство: Springer Рейтинг: Цена: 12157.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The Symposium "Symmetries in Science III" was held at Schloss Hofen, Vorarl- berg, Austria, during the period July 25-28, 1988. Some 70 invited scientists from 24 countries attended the Symposium and presented reviews, research papers and re- ports, as well as participated in workshops. The format of the Symposium was delib- erately kept international and interdisciplinary, and also provided an opportunity for presentations of symmetry applications in fields other than in the conventional disci- plines. The Symposium was co-sponsored by Southern Illinois University at Carbondale Land Vorarlberg, U.S. Office of Naval Research (Special Session), and IBM Austria. Support by these institutions is gratefully acknowledged. Several individuals have contributed significantly to the success of Sym- sium III. They are Dr. John C. Guyon, President, Southern Illinois University, at Carbondale, Dr. Martin Purtscher, Landeshauptman des Landes Vorarlberg, Dr. Guntram Lins, Landesrat des Landes Vorarlberg, and Dr. Hubert Regner, Direktor, Landesbildungszentrum Schloss Hofen. I wish to thank these individuals for their support of Symposium III, also in the name of the participating scientists. The Symposium provided these scientists with an opportunity to get together and exchange scientific information in an efficient manner, and in a very pleasant environment.
Автор: J?rg Teschner Название: New Dualities of Supersymmetric Gauge Theories ISBN: 3319344722 ISBN-13(EAN): 9783319344720 Издательство: Springer Рейтинг: Цена: 13059.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Exact results on N = 2 supersymmetric gauge theories.- Families of N = 2 field theories.- Hitchin systems in N = 2 field theory.- A review on instanton counting and W-algebras.- b-deformed Matrix Models and 2d/4d correspondence.- Localization For N = 2 Supersymmetric GaugeTheories in Four Dimensions.- Line operators in supersymmetric gauge theories and the 2d-4d relation.- Surface Operators.- A review on SUSY gauge theories on S3.- 3d Superconformal Theories from Three-Manifolds.- Supersymmetric gauge theories, quantization of Mflat, and conformal field theory.- Gauge/Vortex Duality and AGT.- B-Model Approach to Instanton Counting.
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