Lie Theory and Its Applications in Physics
Lie Theory and Its Applications in Physics

Author: Vladimir Dobrev

Publisher: Springer Science & Business Media

Published: 2013-04-09

Total Pages: 535

ISBN-13: 4431542701

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Traditionally, Lie Theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrisation of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrisation and symmetries are meant in their broadest sense, i.e., classical geometry, differential geometry, groups and quantum groups, infinite-dimensional (super-)algebras, and their representations. Furthermore, we include the necessary tools from functional analysis and number theory. This is a large interdisciplinary and interrelated field. Samples of these new trends are presented in this volume, based on contributions from the Workshop “Lie Theory and Its Applications in Physics” held near Varna, Bulgaria, in June 2011. This book is suitable for an extensive audience of mathematicians, mathematical physicists, theoretical physicists, and researchers in the field of Lie Theory.

Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics
Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics

Author: D.H. Sattinger

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 218

ISBN-13: 1475719108

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This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselves to the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.

Lie Theory And Its Applications In Physics - Proceedings Of An International Workshop
Lie Theory And Its Applications In Physics - Proceedings Of An International Workshop

Author: Vladimir K Dobrev

Publisher: World Scientific

Published: 1996-10-16

Total Pages: 286

ISBN-13: 9814547085

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There is an apparent trend towards geometrization of physical theories. During the last 20 years, the most successful mathematical models for the description and understanding of physical systems have been based on the Lie theory in its widest sense and various generalizations, for example, deformations of it.This proceedings volume reflects part of the development. On the mathematical side, they report on representations of Lie algebras, quantization procedures, non-commutative geometry, quantum groups, etc. Furthermore, possible physical applications of these techniques are discussed (e.g. quantization of classical systems, derivations of evolution equations, discrete and deformed physical systems).This volume complements the book Generalized Symmetries in Physics, published by World Scientific in 1994.

Lie Theory And Its Applications In Physics V, Proceedings Of The Fifth International Workshop
Lie Theory And Its Applications In Physics V, Proceedings Of The Fifth International Workshop

Author: Vladimir K Dobrev

Publisher: World Scientific

Published: 2004-07-21

Total Pages: 439

ISBN-13: 9814482188

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This volume is targeted at theoretical physicists, mathematical physicists and mathematicians working on mathematical models for physical systems based on symmetry methods and in the field of Lie theory understood in the widest sense. It includes contributions on Lie theory, with two papers by the famous mathematician Kac (one paper with Bakalov), further papers by Aoki, Moens. Some other important contributions are in: field theory - Todorov, Grosse, Kreimer, Sokatchev, Gomez; string theory — Minwalla, Staudacher, Kostov; integrable systems - Belavin, Helminck, Ragoucy; quantum-mechanical and probabilistic systems — Goldin, Van der Jeugt, Leandre; quantum groups and related objects — Jakobsen, Arnaudon, Andruskiewitsch; and others.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences

Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1
Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1

Author: Vladimir Dobrev

Publisher: Springer

Published: 2018-11-28

Total Pages: 419

ISBN-13: 9811327157

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This book is the first volume of proceedings from the joint conference X International Symposium “Quantum Theory and Symmetries” (QTS-X) and XII International Workshop “Lie Theory and Its Applications in Physics” (LT-XII), held on 19–25 June 2017 in Varna, Bulgaria. The QTS series was founded on the core principle that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium at the forefront of theoretical and mathematical physics. The LT series covers the whole field of Lie theory in its widest sense, together with its applications in many areas of physics. As an interface between mathematics and physics, the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In dividing the material between the two volumes, the Editor has sought to select papers that are more oriented toward mathematics for the first volume, and those focusing more on physics for the second. However, this division is relative, since many papers are equally suitable for either volume. The topics addressed in this volume represent the latest trends in the fields covered by the joint conferences: representation theory, integrability, entanglement, quantum groups, number theory, conformal geometry, quantum affine superalgebras, noncommutative geometry. Further, they present various mathematical results: on minuscule modules, symmetry breaking operators, Kashiwara crystals, meta-conformal invariance, the superintegrable Zernike system.

Lie Theory and Its Applications in Physics V
Lie Theory and Its Applications in Physics V

Author: H. D. Doebner

Publisher: World Scientific

Published: 2004

Total Pages: 439

ISBN-13: 9812702563

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This volume is targeted at theoretical physicists, mathematical physicists and mathematicians working on mathematical models for physical systems based on symmetry methods and in the field of Lie theory understood in the widest sense. It includes contributions on Lie theory, with two papers by the famous mathematician Kac (one paper with Bakalov), further papers by Aoki, Moens. Some other important contributions are in: field theory OCo Todorov, Grosse, Kreimer, Sokatchev, Gomez; string theory OCo Minwalla, Staudacher, Kostov; integrable systems OCo Belavin, Helminck, Ragoucy; quantum-mechanical and probabilistic systems OCo Goldin, Van der Jeugt, Leandre; quantum groups and related objects OCo Jakobsen, Arnaudon, Andruskiewitsch; and others. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences."

Lie Theory And Its Applications In Physics Ii - Proceedings Of The Ii International Workshop
Lie Theory And Its Applications In Physics Ii - Proceedings Of The Ii International Workshop

Author: Heinz-dietrich Doebner

Publisher: World Scientific

Published: 1998-12-07

Total Pages: 402

ISBN-13: 9814544655

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This book consists of about 20 lectures on theoretical and observational aspects of astrophysical black holes, by experts in the field. The basic principles and astrophysical applications of the black hole magnetosphere and the Blandford-Znajek process are reviewed in detail, as well as accretion by black holes, black hole X-Ray binaries, black holes with cosmic strings, and so on. Recent advances in X-Ray observations of galactic black holes and new understanding of supermassive black holes in AGNs and normal galaxies are also discussed.

An Introduction to Lie Groups and Lie Algebras
An Introduction to Lie Groups and Lie Algebras

Author: Alexander A. Kirillov

Publisher: Cambridge University Press

Published: 2008-07-31

Total Pages: 237

ISBN-13: 0521889693

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This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.

Automorphic Forms and Lie Superalgebras
Automorphic Forms and Lie Superalgebras

Author: Urmie Ray

Publisher: Springer Science & Business Media

Published: 2007-03-06

Total Pages: 293

ISBN-13: 1402050100

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This book provides the reader with the tools to understand the ongoing classification and construction project of Lie superalgebras. It presents the material in as simple terms as possible. Coverage specifically details Borcherds-Kac-Moody superalgebras. The book examines the link between the above class of Lie superalgebras and automorphic form and explains their construction from lattice vertex algebras. It also includes all necessary background information.

Supersymmetry
Supersymmetry

Author: Vladimir K. Dobrev

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2018-09-24

Total Pages: 228

ISBN-13: 3110527499

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With applications in quantum field theory, general relativity and elementary particle physics, this four-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This third volume covers supersymmetry, including detailed coverage of conformal supersymmetry in four and some higher dimensions, furthermore quantum superalgebras are also considered. Contents Lie superalgebras Conformal supersymmetry in 4D Examples of conformal supersymmetry for D > 4 Quantum superalgebras