Lie Theory And Its Applications In Physics Ii

Author : Vladimir Dobrev
Publisher : Springer Science & Business Media
Page : 554 pages
File Size : 40,7 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9784431542704

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Lie Theory and Its Applications in Physics by Vladimir Dobrev Pdf

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.

Author : Heinz-dietrich Doebner,Joachim Hilgert,Vladimir K Dobrev
Publisher : World Scientific
Page : 402 pages
File Size : 51,5 Mb
Release : 1998-12-07
Category : Electronic
ISBN : 9789814544658

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Lie Theory And Its Applications In Physics Ii - Proceedings Of The Ii International Workshop by Heinz-dietrich Doebner,Joachim Hilgert,Vladimir K Dobrev Pdf

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.

Author : Heinz Dietrich Doebner,V. K. Dobrev,Joachim Hilgert
Publisher : World Scientific Publishing Company Incorporated
Page : 388 pages
File Size : 45,6 Mb
Release : 1998
Category : Science
ISBN : 9810235399

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Lie Theory and Its Applications in Physics II by Heinz Dietrich Doebner,V. K. Dobrev,Joachim Hilgert Pdf

Author : Vladimir Dobrev
Publisher : Springer Nature
Page : 552 pages
File Size : 50,7 Mb
Release : 2020-10-15
Category : Science
ISBN : 9789811577758

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Lie Theory and Its Applications in Physics by Vladimir Dobrev Pdf

This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2019. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization 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. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field. The topics covered in this volume from the workshop represent the most modern trends in the field : Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Author : H-D Doebner,J Hilgert,V K Dobrev
Publisher : World Scientific
Page : 284 pages
File Size : 40,8 Mb
Release : 1996-10-16
Category : Electronic
ISBN : 9789814547086

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Lie Theory and Its Applications in Physics by H-D Doebner,J Hilgert,V K Dobrev Pdf

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. Contents:Representation Theory and Quantization MethodsNoncommutative Geometry, Quantum Algebras and Applications to Relativistic and Nonrelativistic SystemsSpecial Applications to Physical Systems and Their Generalized ModelsRepresentation Theory and Quantization Methods Readership: Mathematicians and physicists. keywords:

Author : Vladimir Dobrev
Publisher : Springer
Page : 614 pages
File Size : 46,6 Mb
Release : 2016-12-10
Category : Science
ISBN : 9789811026362

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Lie Theory and Its Applications in Physics by Vladimir Dobrev Pdf

This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.Recently, the trend has been towards geometrization 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. Geometrization and symmetries are employed in their widest sense, embracing representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators (PDO), special functions, and others. Furthermore, the necessary tools from functional analysis are included.“div>This is a large interdisciplinary and interrelated field, and the present volume is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Author : H-D Doebner,V K Dobrev
Publisher : World Scientific
Page : 436 pages
File Size : 49,6 Mb
Release : 2004-07-21
Category : Mathematics
ISBN : 9789814482189

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Lie Theory and Its Applications in Physics V by H-D Doebner,V K Dobrev Pdf

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 Contents:Lie Theory:Twisted Modules over Lattice Vertex Algebras (B Bakalov & V G Kac)Structure Theory of Finite Lie Conformal Superalgebras (V G Kac et al.)On Characters and Dimension Formulas for Representations of the Lie Superalgebra gl(mn) (E M Moens & J Van der Jeugt)Matching Conditions for Invariant Eigendistributions on Some Semisimple Symmetric Spaces (S Aoki & S Kato)Field Theory:Rational Conformal Correlation Functions of Gauge Invariant Local Fields in Four Dimensions (I T Todorov et al.)Renormalisation of Noncommutative Scalar Field Theories (H Grosse & R Wulkenhaar)On the Insertion-Elimination Lie Algebra of Feynman Graphs (D Kreimer et al.)Superconformal Kinematics and Dynamics in the AdS/CFT Correspondence (E Sokatchev)Renormalons and Fractional Instantons (C Gomez)String Theory:The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories (S Minwalla et al.)Two-Loop Commuting Charges and the String/Gauge Duality (G Arutyunov & M Staudacher)Boundary Ground Ring and Disc Correlation Functions in Liouville Quantum Gravity (I Kostov)Integrable Systems:Quantum Group in Roots of Unity and the Restriction of XXZ Model (A Belavin)Spaces of Boundary Values Related to a Multipoint Version of the KP-Hierarchy (G F Helminck)Integrable Systems with Impurity (E Ragoucy)Quantum Mechanical and Probabilistic Systems:Measures on Spaces of Infinite-Dimensional Configurations, Group Representations, and Statistical Physics (G A Goldin et al.)On the n-Particle Wigner Quantum Oscillator: Noncommutative Coordinates and Particle Localisation (J Van der Jeugt et al.)Bundle Gerbes and Brownian Motion (R Léandre)Quantum Groups and Related Objects:Matrix Chain Models and Their q-Deformations (H P Jakobsen)Exotic Bialgebras: Non-Deformation Quantum Groups (D Arnaudon et al.)Irreducible Representations of Liftings of Quantum Planes (N Andruskiewitsch & M Beattie)and other papers Keywords:Lie Theory;Field Theory;String Theory;Integrable Systems;Quantum Mechanics;Probability;Quantum GroupsKey Features:Presents the latest developmentsCovers all the modern trendsIncludes contributions by the top scientists

Author : Vladimir Dobrev
Publisher : Springer
Page : 440 pages
File Size : 48,8 Mb
Release : 2018-09-30
Category : Science
ISBN : 9789811321795

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Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2 by Vladimir Dobrev Pdf

This book is the second volume of the proceedings of 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), 19–25 June 2017, Varna, Bulgaria. The QTS series started around the core concept that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium on the frontiers 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 facets of physics. As an interface between mathematics and physics the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In the division of the material between the two volumes, the Editor has tried to select for the first and second volumes papers that are more oriented toward mathematics and physics, respectively. However, this division is relative since many papers could have been placed in either volume. The topics covered in this volume represent the most modern trends in the fields of the joint conferences: symmetries in string theories, conformal field theory, holography, gravity theories and cosmology, gauge theories, foundations of quantum theory, nonrelativistic and classical theories.

Author : William A. Schwalm
Publisher : Morgan & Claypool Publishers
Page : 81 pages
File Size : 47,8 Mb
Release : 2017-05-02
Category : Science
ISBN : 9781681744506

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Lectures on Selected Topics in Mathematical Physics by William A. Schwalm Pdf

This book provides an introduction to Lie Theory for first year graduate students and professional physicists who may not have across the theory in their studies. In particular, it is a summary overview of the theory of finite groups, a brief description of a manifold, and then an informal development of the theory of one-parameter Lie groups, especially as they apply to ordinary differential equations. The treatment is informal, but systematic and reasonably self-contained, as it assumes a familiarity with basic physics and applied calculus, but it does not assume additional mathematical training. Interested readers should have a fair chance of finding symmetries of a second order differential equation and should be able to use it to reduce the order of the differential equation.

Author : Vladimir K Dobrev,Heinz-dietrich Doebner,Joachim Hilgert
Publisher : World Scientific
Page : 330 pages
File Size : 52,5 Mb
Release : 2000-09-29
Category : Electronic
ISBN : 9789814542760

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Lie Theory And Its Applications In Physics Iii - Proceedings Of The Third International Workshop by Vladimir K Dobrev,Heinz-dietrich Doebner,Joachim Hilgert Pdf

This book is a comprehensive treatise on the theory and applications of moment functions in image analysis. Moment functions are widely used in various realms of computer vision and image processing. Numerous algorithms and techniques have been developed using image moments, in the areas of pattern recognition, object identification, three-dimensional object pose estimation, robot sensing, image coding and reconstruction. This book provides a compilation of the theoretical aspects related to different types of moment functions, and their applications in the above areas.The book is organized into two parts. The first part discusses the fundamental concepts behind important moments such as geometric moments, complex moments, Legendre moments, Zernike moments, and moment tensors. Most of the commonly used properties of moment functions and the mathematical framework for the derivation of basic theorems and results are discussed in detail. This includes the derivation of moment invariants, implementation aspects of moments, transform properties, and fast methods for computing the moment functions for both binary and gray-level images. The second part presents the key application areas of moments such as pattern recognition, object identification, image-based pose estimation, edge detection, clustering, segmentation, coding and reconstruction. Important algorithms in each of these areas are discussed. A comprehensive list of bibliographical references on image moments is also included.

Author : Vladimir Dobrev
Publisher : Springer
Page : 427 pages
File Size : 46,5 Mb
Release : 2018-11-28
Category : Mathematics
ISBN : 9789811327155

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Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 by Vladimir Dobrev Pdf

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.

Author : Heinz Dietrich Doebner,V. K. Dobrev
Publisher : World Scientific Publishing Company Incorporated
Page : 426 pages
File Size : 53,8 Mb
Release : 2004-01-01
Category : Mathematics
ISBN : 9812389369

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Lie Theory and Its Applications in Physics V by Heinz Dietrich Doebner,V. K. Dobrev Pdf

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, Rostov; "integrable systems--Belavin, Helminck, Ragoucy, "quantum-mechanical and probabilistic systems--Goldin, Van der Jeugt, Leandre; "quantum groups and related objects--Jakobsen, Amaudon and Andruskiewitsch; and others.

Author : William A Schwalm
Publisher : Morgan & Claypool Publishers
Page : 114 pages
File Size : 41,8 Mb
Release : 2019-03-08
Category : Science
ISBN : 9781643273501

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Lectures on Selected Topics in Mathematical Physics by William A Schwalm Pdf

This book is a sequel to Lectures on Selected Topics in Mathematical Physics: Introduction to Lie theory with applications. This volume is devoted mostly to Lie groups. Lie algebras and generating functions, both for standard special functions and for solution of certain types of physical problems. It is an informal treatment of these topics intended for physics graduate students or others with a physics background wanting a brief and informal introduction to the subjects addressed in a style and vocabulary not completely unfamiliar.

Author : D.H. Sattinger,O.L. Weaver
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 49,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475719109

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Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics by D.H. Sattinger,O.L. Weaver Pdf

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.

Author : Karl-Hermann Neeb
Publisher : Walter de Gruyter
Page : 804 pages
File Size : 54,9 Mb
Release : 2011-04-20
Category : Mathematics
ISBN : 9783110808148

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Holomorphy and Convexity in Lie Theory by Karl-Hermann Neeb Pdf

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany