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Group And Representation Theory, Vergados John D


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Автор: Vergados John D
Название:  Group And Representation Theory
ISBN: 9789813202443
Издательство: World Scientific Publishing
Классификация:


ISBN-10: 9813202440
Обложка/Формат: Hardback
Страницы: 348
Вес: 0.63 кг.
Дата издания: 23.02.2017
Серия: Physics
Язык: English
Размер: 231 x 155 x 23
Читательская аудитория: College/higher education
Ключевые слова: Particle & high-energy physics, SCIENCE / Physics / Nuclear,SCIENCE / Physics / Quantum Theory
Основная тема: Physics / Particle Physics/High Energy Physics, Quantum Fields
Ссылка на Издательство: Link
Поставляется из: Англии
Описание:

This volume goes beyond the understanding of symmetries and exploits them in the study of the behavior of both classical and quantum physical systems. Thus it is important to study the symmetries described by continuous (Lie) groups of transformations. We then discuss how we get operators that form a Lie algebra. Of particular interest to physics is the representation of the elements of the algebra and the group in terms of matrices and, in particular, the irreducible representations. These representations can be identified with physical observables.

This leads to the study of the classical Lie algebras, associated with unitary, unimodular, orthogonal and symplectic transformations. We also discuss some special algebras in some detail. The discussion proceeds along the lines of the Cartan-Weyl theory via the root vectors and root diagrams and, in particular, the Dynkin representation of the roots. Thus the representations are expressed in terms of weights, which are generated by the application of the elements of the algebra on uniquely specified highest weight states. Alternatively these representations can be described in terms of tensors labeled by the Young tableaux associated with the discrete symmetry Sn. The connection between the Young tableaux and the Dynkin weights is also discussed. It is also shown that in many physical systems the quantum numbers needed to specify the physical states involve not only the highest symmetry but also a number of sub-symmetries contained in them. This leads to the study of the role of subalgebras and in particular the possible maximal subalgebras. In many applications the physical system can be considered as composed of subsystems obeying a given symmetry. In such cases the reduction of the Kronecker product of irreducible representations of classical and special algebras becomes relevant and is discussed in some detail. The method of obtaining the relevant Clebsch-Gordan (C-G) coefficients for such algebras is discussed and some relevant algorithms are provided. In some simple cases suitable numerical tables of C-G are also included.

The above exposition contains many examples, both as illustrations of the main ideas as well as well motivated applications. To this end two appendices of 51 pages -- 11 tables in Appendix A, summarizing the material discussed in the main text and 39 tables in Appendix B containing results of more sophisticated examples are supplied. Reference to the tables is given in the main text and a guide to the appropriate section of the main text is given in the tables.




Monetary Theory and Policy, Third Edition

Автор: Walsh Carl E.
Название: Monetary Theory and Policy, Third Edition
ISBN: 0262013770 ISBN-13(EAN): 9780262013772
Издательство: MIT Press
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Цена: 8287.00 р.
Наличие на складе: Нет в наличии.

Описание: A new edition of the leading text in monetary economics, a comprehensive treatment revised and enhanced with new material reflecting recent advances in the field.

Microeconomic theory

Автор: Mas-Colell, Andreu
Название: Microeconomic theory
ISBN: 0195102681 ISBN-13(EAN): 9780195102680
Издательство: Oxford Academ
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Цена: 19931.00 р.
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Описание: This is a comprehensive textbook covering all of the topics taught in the graduate-level, two-semester course in microeconomic theory required of all graduate students in economics. It combines the results of the authors` experience of teaching microeconomics at Harvard and has been fully classroom tested.

Group Representation for Quantum Theory

Автор: Hayashi
Название: Group Representation for Quantum Theory
ISBN: 3319449044 ISBN-13(EAN): 9783319449043
Издательство: Springer
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Цена: 15372.00 р.
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Описание: This book explains the group representation theory for quantum theory in the language of quantum theory. As is well known, group representation theory is very strong tool for quantum theory, in particular, angular momentum, hydrogen-type Hamiltonian, spin-orbit interaction, quark model, quantum optics, and quantum information processing including quantum error correction. To describe a big picture of application of representation theory to quantum theory, the book needs to contain the following six topics, permutation group, SU(2) and SU(d), Heisenberg representation, squeezing operation, Discrete Heisenberg representation, and the relation with Fourier transform from a unified viewpoint by including projective representation. Unfortunately, although there are so many good mathematical books for a part of six topics, no book contains all of these topics because they are too segmentalized. Further, some of them are written in an abstract way in mathematical style and, often, the materials are too segmented. At least, the notation is not familiar to people working with quantum theory.Others are good elementary books, but do not deal with topics related to quantum theory. In particular, such elementary books do not cover projective representation, which is more important in quantum theory. On the other hand, there are several books for physicists. However, these books are too simple and lack the detailed discussion. Hence, they are not useful for advanced study even in physics. To resolve this issue, this book starts with the basic mathematics for quantum theory. Then, it introduces the basics of group representation and discusses the case of the finite groups, the symmetric group, e.g. Next, this book discusses Lie group and Lie algebra. This part starts with the basics knowledge, and proceeds to the special groups, e.g., SU(2), SU(1,1), and SU(d). After the special groups, it explains concrete applications to physical systems, e.g., angular momentum, hydrogen-type Hamiltonian, spin-orbit interaction, and quark model. Then, it proceeds to the general theory for Lie group and Lie algebra. Using this knowledge, this book explains the Bosonic system, which has the symmetries of Heisenberg group and the squeezing symmetry by SL(2,R) and Sp(2n,R). Finally, as the discrete version, this book treats the discrete Heisenberg representation which is related to quantum error correction. To enhance readers' undersnding, this book contains 54 figures, 23 tables, and 111 exercises with solutions.

A Course in Finite Group Representation Theory

Автор: Webb
Название: A Course in Finite Group Representation Theory
ISBN: 1107162394 ISBN-13(EAN): 9781107162396
Издательство: Cambridge Academ
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Цена: 9979.00 р.
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Описание: This classroom-tested graduate text provides a thorough grounding in the representation theory of finite groups over fields and rings. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, and block theory.

Introduction To Classical And Modern Analysis And Their Application To Group Representation Theory

Автор: Basu Debabrata
Название: Introduction To Classical And Modern Analysis And Their Application To Group Representation Theory
ISBN: 9814273295 ISBN-13(EAN): 9789814273299
Издательство: World Scientific Publishing
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Цена: 11246.00 р.
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Описание: Suitable for graduate course on analytical methods and their application to representation theory, this book develops each concept with special emphasis on lucidity and clarity. It also shows the direct link of Cauchy-Pochhammer theory with the Hadmard-Reisz-Schwartz-Gel`fand regularization.

Laser Machining: Theory and Practice

Автор: E.L.K.E
Название: Laser Machining: Theory and Practice
ISBN: 1475740867 ISBN-13(EAN): 9781475740868
Издательство: Springer
Рейтинг:
Цена: 9141.00 р.
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Описание: Laser Machining: Theory and Practice addresses state-of-the-art laser machining in a way useful for research- ers, academicians and practitioners, particularly manufacturing engineers, who are considering lasers as a solution to the machining requirements of their factories and plants.

Cryptography: Theory and Practice, Third Edition

Автор: Stinson, Douglas R.
Название: Cryptography: Theory and Practice, Third Edition
ISBN: 1584885084 ISBN-13(EAN): 9781584885085
Издательство: Taylor&Francis
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Цена: 7501.00 р.
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Описание: This third edition of a standard text provides complete coverage of the use of cryptographic protocols which establish a series of steps that must be taken before any type of secret transmission can be completed. The book shows the reader how the various parties to the transaction establish their cryptographic identities or keys. It covers many of the cryptographic tools used in network security along with topic such as copyright protection techniques and public key infrastructure. The book is a text for senior graduate courses introducing cryptography and is also a useful reference for professionals interested in network security and cryptographic protocols.


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