Lie Algebras Geometry And Toda Type Systems

Author : Alexander Vitalievich Razumov
Publisher : Cambridge University Press
ISBN 13 : 0521479231
Total Pages : 271 pages
Book Rating : 4.33/5 ( download)

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Download or read book Lie Algebras, Geometry, and Toda-Type Systems written by Alexander Vitalievich Razumov and published by Cambridge University Press. This book was released on 1997-05-15 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book describes integrable Toda type systems and their Lie algebra and differential geometry background.

Author : Fritz Gesztesy
Publisher : Cambridge University Press
ISBN 13 : 1139473778
Total Pages : 438 pages
Book Rating : 4.74/5 ( download)

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Download or read book Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models written by Fritz Gesztesy and published by Cambridge University Press. This book was released on 2008-09-04 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a partner to Volume 1: Dimensional Continuous Models, this monograph provides a self-contained introduction to algebro-geometric solutions of completely integrable, nonlinear, partial differential-difference equations, also known as soliton equations. The systems studied in this volume include the Toda lattice hierarchy, the Kac-van Moerbeke hierarchy, and the Ablowitz-Ladik hierarchy. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The theory presented includes trace formulas, algebro-geometric initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses basic techniques from the theory of difference equations and spectral analysis, some elements of algebraic geometry and especially, the theory of compact Riemann surfaces. The presentation is constructive and rigorous, with ample background material provided in various appendices. Detailed notes for each chapter, together with an exhaustive bibliography, enhance understanding of the main results.

Author : D. I. Kazakov
Publisher : World Scientific
ISBN 13 : 9789810248055
Total Pages : 488 pages
Book Rating : 4.59/5 ( download)

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Download or read book Proceedings of the IX International Conference on Supersymmetry and Unification of Fundamental Interactions written by D. I. Kazakov and published by World Scientific. This book was released on 2002 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the theoretical, phenomenological and experimental aspects of supersymmetry in particle physics as well as its implications in cosmology.

Author : R Costa
Publisher : CRC Press
ISBN 13 : 0429529996
Total Pages : 492 pages
Book Rating : 4.93/5 ( download)

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Download or read book NonasSociative Algebra and Its Applications written by R Costa and published by CRC Press. This book was released on 2019-05-20 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of lectures presented at the Fourth International Conference on Nonassociative Algebra and its Applications, held in Sao Paulo, Brazil. Topics in algebra theory include alternative, Bernstein, Jordan, lie, and Malcev algebras and superalgebras. The volume presents applications to population genetics theory, physics, and more.

Author : Jean-Philippe Anker
Publisher : Springer Science & Business Media
ISBN 13 : 0817681922
Total Pages : 341 pages
Book Rating : 4.20/5 ( download)

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Download or read book Lie Theory written by Jean-Philippe Anker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: * First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.

Author : Patrice Tauvel
Publisher : Springer Science & Business Media
ISBN 13 : 9783540241706
Total Pages : 676 pages
Book Rating : 4.01/5 ( download)

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Download or read book Lie Algebras and Algebraic Groups written by Patrice Tauvel and published by Springer Science & Business Media. This book was released on 2005-04-25 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devoted to the theory of Lie algebras and algebraic groups, this book includes a large amount of commutative algebra and algebraic geometry so as to make it as self-contained as possible. The aim of the book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero. Detailed proofs are included, and some recent results are discussed in the final chapters.

Author : Giampiero Esposito
Publisher : Cambridge University Press
ISBN 13 : 0521648629
Total Pages : 227 pages
Book Rating : 4.22/5 ( download)

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Download or read book Dirac Operators and Spectral Geometry written by Giampiero Esposito and published by Cambridge University Press. This book was released on 1998-08-20 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear, concise and up-to-date introduction to the theory of the Dirac operator and its wide range of applications in theoretical physics for graduate students and researchers.

Author : V.I. Arnol'd
Publisher : Springer Science & Business Media
ISBN 13 : 3662067919
Total Pages : 342 pages
Book Rating : 4.18/5 ( download)

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Download or read book Dynamical Systems IV written by V.I. Arnol'd and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews of the first edition:"... Here ... a wealth of material is displayed for us, too much to even indicate in a review. ... Your reviewer was very impressed by the contents of both volumes (EMS 2 and 4), recommending them without any restriction." Mededelingen van het Wiskundig genootshap 1992

Author : A.L. Onishchik
Publisher : Springer Science & Business Media
ISBN 13 : 9783540546832
Total Pages : 264 pages
Book Rating : 4.39/5 ( download)

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Download or read book Lie Groups and Lie Algebras III written by A.L. Onishchik and published by Springer Science & Business Media. This book was released on 1994-07-12 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and modern account of the structure and classification of Lie groups and finite-dimensional Lie algebras, by internationally known specialists in the field. This Encyclopaedia volume will be immensely useful to graduate students in differential geometry, algebra and theoretical physics.

Author : Masahito Hayashi
Publisher : Springer
ISBN 13 : 3319449060
Total Pages : 338 pages
Book Rating : 4.67/5 ( download)

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Download or read book Group Representation for Quantum Theory written by Masahito Hayashi and published by Springer. This book was released on 2016-11-18 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.