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

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Publisher : Springer
ISBN 13 : 9811327157
Total Pages : 427 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 by : Vladimir Dobrev

Download or read book Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 written by Vladimir Dobrev and published by Springer. This book was released on 2018-11-28 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2

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Publisher : Springer
ISBN 13 : 9811321795
Total Pages : 440 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2 by : Vladimir Dobrev

Download or read book Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2 written by Vladimir Dobrev and published by Springer. This book was released on 2018-09-30 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantum Mechanics

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Publisher : Springer Science & Business Media
ISBN 13 : 3642579760
Total Pages : 538 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Quantum Mechanics by : Walter Greiner

Download or read book Quantum Mechanics written by Walter Greiner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: Greiner's lectures, which underlie these volumes, are internationally noted for their clarity, their completeness and for the effort that he has devoted to making physics an integral whole; his enthusiasm for his science is contagious and shines through almost every page. These volumes represent only a part of a unique and Herculean effort to make all of theoretical physics accessible to the interested student. Beyond that, they are of enormous value to the professional physicist and to all others working with quantum phenomena. Again and again the reader will find that, after dipping into a particular volume to review a specific topic, he will end up browsing, caught up by often fascinating new insights and developments with which he had not previously been familiar. Having used a number of Greiner's volumes in their original German in my teaching and research at Yale, I welcome these new and revised English translations and would recommend them enthusiastically to anyone searching for a coherent overview of physics.

Lie Theory and Its Applications in Physics

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Publisher : Springer Nature
ISBN 13 : 9811577757
Total Pages : 552 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Lie Theory and Its Applications in Physics by : Vladimir Dobrev

Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer Nature. This book was released on 2020-10-15 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lie Theory and Its Applications in Physics

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Publisher : Springer Science & Business Media
ISBN 13 : 4431542701
Total Pages : 535 pages
Book Rating : 4.4/5 (315 download)

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Book Synopsis Lie Theory and Its Applications in Physics by : Vladimir Dobrev

Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Group Theory and Quantum Mechanics

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Publisher : Courier Corporation
ISBN 13 : 0486131661
Total Pages : 354 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Group Theory and Quantum Mechanics by : Michael Tinkham

Download or read book Group Theory and Quantum Mechanics written by Michael Tinkham and published by Courier Corporation. This book was released on 2012-04-20 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text develops the aspects of group theory most relevant to physics and chemistry (such as the theory of representations) and illustrates their applications to quantum mechanics. The first five chapters focus chiefly on the introduction of methods, illustrated by physical examples, and the final three chapters offer a systematic treatment of the quantum theory of atoms, molecules, and solids. The formal theory of finite groups and their representation is developed in Chapters 1 through 4 and illustrated by examples from the crystallographic point groups basic to solid-state and molecular theory. Chapter 5 is devoted to the theory of systems with full rotational symmetry, Chapter 6 to the systematic presentation of atomic structure, and Chapter 7 to molecular quantum mechanics. Chapter 8, which deals with solid-state physics, treats electronic energy band theory and magnetic crystal symmetry. A compact and worthwhile compilation of the scattered material on standard methods, this volume presumes a basic understanding of quantum theory.

Quantum Mechanics

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Publisher : Springer Science & Business Media
ISBN 13 : 366200707X
Total Pages : 351 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Quantum Mechanics by : Walter Greiner

Download or read book Quantum Mechanics written by Walter Greiner and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Dynamics is a major survey of quantum theory based on Walter Greiner's long-running and highly successful course at the University of Frankfurt. The key to understanding in quantum theory is to reinforce lecture attendance and textual study by working through plenty of representative and detailed examples. Firm belief in this principle led Greiner to develop his unique course and to transform it into a remarkable and comprehensive text. The text features a large number of examples and exercises involving many of the most advanced topics in quantum theory. These examples give practical and precise demonstrations of how to use the often subtle mathematics behind quantum theory. The text is divided into five volumes: Quantum Mechanics I - An Introduction, Quantum Mechanics II - Symmetries, Relativistic Quantum Mechanics, Quantum Electrodynamics, Gauge Theory of Weak Interactions. These five volumes take the reader from the fundamental postulates of quantum mechanics up to the latest research in particle physics. Volume 1, Quantum Mechanics I - An Introduction, lays the foundation for the rest of the course. Starting from black-body radiation, the photo-electric effect and wave-particle duality, Greiner goes on to discuss the uncertainty relations, spin and many-body systems, then discusses applications to the hydrogen atom and the Stern-Gerlach and Einstein-de Haas experiments. The mathematics of representation theory, S-matrices, perturbation theory, eigenvalues and hypergeometric differential equations are presented in detail, with 84 fully and carefully worked examples and exercises to consolidate the material. Volume 2 presents a particularly appealing and successful theme in advanced quantum mechanics - symmetries. After a brief introduction to symmetries in classical mechanics, the text turns to their relevance in quantum mechanics, the consequences of rotation symmetry and the general theory of Lie groups. The Isospin group, hypercharge, SU (3) and their applications are all dealt with in depth before a chapter on charm and SU (3) leads to the frontiers of research in particle physics. Almost a hundred detailed, worked examples and problems make this a truly unique text on a fascinating side of modern physics.

Quantum Mechanics

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Publisher :
ISBN 13 : 9783540187554
Total Pages : 347 pages
Book Rating : 4.1/5 (875 download)

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Book Synopsis Quantum Mechanics by : Walter Greiner

Download or read book Quantum Mechanics written by Walter Greiner and published by . This book was released on 1989 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Dynamics is a major survey of quantum theory based on Walter Greiner's long-running and highly successful course at the University of Frankfurt. The key to understanding in quantum theory is to reinforce lecture attendance and textual study by working through plenty of representative and detailed examples. Firm belief in this principle led Greiner to develop his unique course and to transform it into a remarkable and comprehensive text. The text features a large number of examples and exercises involving many of the most advanced topics in quantum theory. These examples give practical and precise demonstrations of how to use the often subtle mathematics behind quantum theory. The text is divided into five volumes: Quantum Mechanics I - An Introduction, Quantum Mechanics II - Symmetries, Relativistic Quantum Mechanics, Quantum Electrodynamics, Gauge Theory of Weak Interactions. These five volumes take the reader from the fundamental postulates of quantum mechanics up to the latest research in particle physics. Volume 1, Quantum Mechanics I - An Introduction, lays the foundation for the rest of the course. Starting from black-body radiation, the photo-electric effect and wave-particle duality, Greiner goes on to discuss the uncertainty relations, spin and many-body systems, then discusses applications to the hydrogen atom and the Stern-Gerlach and Einstein-de Haas experiments. The mathematics of representation theory, S-matrices, perturbation theory, eigenvalues and hypergeometric differential equations are presented in detail, with 84 fully and carefully worked examples and exercises to consolidate the material. Volume 2 presents a particularly appealing and successful theme in advanced quantum mechanics - symmetries. After a brief introduction to symmetries in classical mechanics, the text turns to their relevance in quantum mechanics, the consequences of rotation symmetry and the general theory of Lie groups. The Isospin group, hypercharge, SU (3) and their applications are all dealt with in depth before a chapter on charm and SU (3) leads to the frontiers of research in particle physics. Almost a hundred detailed, worked examples and problems make this a truly unique text on a fascinating side of modern physics.

Fundamental Mathematical Structures of Quantum Theory

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Publisher : Springer
ISBN 13 : 3030183467
Total Pages : 345 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Fundamental Mathematical Structures of Quantum Theory by : Valter Moretti

Download or read book Fundamental Mathematical Structures of Quantum Theory written by Valter Moretti and published by Springer. This book was released on 2019-06-20 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents in a concise and self-contained way the advanced fundamental mathematical structures in quantum theory. It is based on lectures prepared for a 6 months course for MSc students. The reader is introduced to the beautiful interconnection between logic, lattice theory, general probability theory, and general spectral theory including the basic theory of von Neumann algebras and of the algebraic formulation, naturally arising in the study of the mathematical machinery of quantum theories. Some general results concerning hidden-variable interpretations of QM such as Gleason's and the Kochen-Specker theorems and the related notions of realism and non-contextuality are carefully discussed. This is done also in relation with the famous Bell (BCHSH) inequality concerning local causality. Written in a didactic style, this book includes many examples and solved exercises. The work is organized as follows. Chapter 1 reviews some elementary facts and properties of quantum systems. Chapter 2 and 3 present the main results of spectral analysis in complex Hilbert spaces. Chapter 4 introduces the point of view of the orthomodular lattices' theory. Quantum theory form this perspective turns out to the probability measure theory on the non-Boolean lattice of elementary observables and Gleason's theorem characterizes all these measures. Chapter 5 deals with some philosophical and interpretative aspects of quantum theory like hidden-variable formulations of QM. The Kochen-Specker theorem and its implications are analyzed also in relation BCHSH inequality, entanglement, realism, locality, and non-contextuality. Chapter 6 focuses on the algebra of observables also in the presence of superselection rules introducing the notion of von Neumann algebra. Chapter 7 offers the idea of (groups of) quantum symmetry, in particular, illustrated in terms of Wigner and Kadison theorems. Chapter 8 deals with the elementary ideas and results of the so called algebraic formulation of quantum theories in terms of both *-algebras and C*-algebras. This book should appeal to a dual readership: on one hand mathematicians that wish to acquire the tools that unlock the physical aspects of quantum theories; on the other physicists eager to solidify their understanding of the mathematical scaffolding of quantum theories.

Relativity, Symmetry and the Structure of the Quantum Theory

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Publisher : Morgan & Claypool Publishers
ISBN 13 : 1627056246
Total Pages : 95 pages
Book Rating : 4.6/5 (27 download)

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Book Synopsis Relativity, Symmetry and the Structure of the Quantum Theory by : William H. Klink

Download or read book Relativity, Symmetry and the Structure of the Quantum Theory written by William H. Klink and published by Morgan & Claypool Publishers. This book was released on 2014-04-01 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum theory is one of the most successful of all physical theories. Our everyday world is dominated by devices that function because of knowledge of the quantum world. Yet many, physicists and non-physicists alike, find the theory which explains the beh

Lie Theory and Its Applications in Physics

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Publisher : World Scientific
ISBN 13 : 9814547085
Total Pages : 284 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Lie Theory and Its Applications in Physics by : H-D Doebner

Download or read book Lie Theory and Its Applications in Physics written by H-D Doebner and published by World Scientific. This book was released on 1996-10-16 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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:

Symmetries in Quantum Mechanics

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Publisher :
ISBN 13 : 9781003417187
Total Pages : 0 pages
Book Rating : 4.4/5 (171 download)

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Book Synopsis Symmetries in Quantum Mechanics by : Masud Chaichian

Download or read book Symmetries in Quantum Mechanics written by Masud Chaichian and published by . This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough, didactic exposition of the role of symmetry, particularly rotational symmetry, in quantum mechanics. The bulk of the book covers the description of rotations (geometrically and group-theoretically) and their representations, and the quantum theory of angular momentum. Later chapters introduce more advanced topics like relativistic theory, supersymmetry, anyons, fractional spin and statistics. Everything is explained clearly and in depth making the book ideal for use as a course text for postgraduate and advanced undergraduates students in physics, and those specializing in theoretical physics. The book will also be useful for researchers looking for an accessible introduction to this important area of quantum theory.

The Theory of Symmetry Actions in Quantum Mechanics

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Publisher : Springer Science & Business Media
ISBN 13 : 9783540228028
Total Pages : 132 pages
Book Rating : 4.2/5 (28 download)

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Book Synopsis The Theory of Symmetry Actions in Quantum Mechanics by : Gianni Cassinelli

Download or read book The Theory of Symmetry Actions in Quantum Mechanics written by Gianni Cassinelli and published by Springer Science & Business Media. This book was released on 2004-10-27 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about representing symmetry in quantum mechanics. The book is on a graduate and/or researcher level and it is written with an attempt to be concise, to respect conceptual clarity and mathematical rigor. The basic structures of quantum mechanics are used to identify the automorphism group of quantum mechanics. The main concept of a symmetry action is defined as a group homomorphism from a given group, the group of symmetries, to the automorphism group of quantum mechanics. The structure of symmetry actions is determined under the assumption that the symmetry group is a Lie group. The Galilei invariance is used to illustrate the general theory by giving a systematic presentation of a Galilei invariant elementary particle. A brief description of the Galilei invariant wave equations is also given.

Quantum Mechanics

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Publisher : Springer Science & Business Media
ISBN 13 : 9783540580805
Total Pages : 554 pages
Book Rating : 4.5/5 (88 download)

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Book Synopsis Quantum Mechanics by : Walter Greiner

Download or read book Quantum Mechanics written by Walter Greiner and published by Springer Science & Business Media. This book was released on 1994 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Quantum Mechanics - An Introduction" lays the foundations for the rest of the series on advanced quantum theory based on W. Greiner's highly successful course on advanced quantum mechanics and field theory. Starting from black-body radiation, the photoelectric effect and wave-particle duality, Greiner goes on to discuss the uncertainty relations, and spin and many-body systems; he includes applications to the hydrogen atom and the Stern-Gerlach and Einstein-de Haas experiments. The mathematics of representation theory, S matrices, perturbation theory, eigenvalue problems and hypergeometric differental equations are presented in detail, with 84 fully and carefully worked examples and exercises to consolidate the material. This second edition has been slightly corrected where necessary, but remains otherwise unchanged.

An Introduction to Covariant Quantum Mechanics

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Publisher : Springer Nature
ISBN 13 : 3030895890
Total Pages : 831 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis An Introduction to Covariant Quantum Mechanics by : Josef Janyška

Download or read book An Introduction to Covariant Quantum Mechanics written by Josef Janyška and published by Springer Nature. This book was released on 2022-04-06 with total page 831 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with an original contribution to the hypothetical missing link unifying the two fundamental branches of physics born in the twentieth century, General Relativity and Quantum Mechanics. Namely, the book is devoted to a review of a "covariant approach" to Quantum Mechanics, along with several improvements and new results with respect to the previous related literature. The first part of the book deals with a covariant formulation of Galilean Classical Mechanics, which stands as a suitable background for covariant Quantum Mechanics. The second part deals with an introduction to covariant Quantum Mechanics. Further, in order to show how the presented covariant approach works in the framework of standard Classical Mechanics and standard Quantum Mechanics, the third part provides a detailed analysis of the standard Galilean space-time, along with three dynamical classical and quantum examples. The appendix accounts for several non-standard mathematical methods widely used in the body of the book.

Integrability, Supersymmetry and Coherent States

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Publisher : Springer
ISBN 13 : 3030200876
Total Pages : 434 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Integrability, Supersymmetry and Coherent States by : Şengül Kuru

Download or read book Integrability, Supersymmetry and Coherent States written by Şengül Kuru and published by Springer. This book was released on 2019-07-12 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume shares and makes accessible new research lines and recent results in several branches of theoretical and mathematical physics, among them Quantum Optics, Coherent States, Integrable Systems, SUSY Quantum Mechanics, and Mathematical Methods in Physics. In addition to a selection of the contributions presented at the "6th International Workshop on New Challenges in Quantum Mechanics: Integrability and Supersymmetry", held in Valladolid, Spain, 27-30 June 2017, several high quality contributions from other authors are also included. The conference gathered 60 participants from many countries working in different fields of Theoretical Physics, and was dedicated to Prof. Véronique Hussin—an internationally recognized expert in many branches of Mathematical Physics who has been making remarkable contributions to this field since the 1980s. The reader will find interesting reviews on the main topics from internationally recognized experts in each field, as well as other original contributions, all of which deal with recent applications or discoveries in the aforementioned areas.

Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras

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Publisher : World Scientific
ISBN 13 : 9813236876
Total Pages : 476 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras by : Rubakov Valery A

Download or read book Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras written by Rubakov Valery A and published by World Scientific. This book was released on 2018-03-21 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the main approaches in study of algebraic structures of symmetries in models of theoretical and mathematical physics, namely groups and Lie algebras and their deformations. It covers the commonly encountered quantum groups (including Yangians). The second main goal of the book is to present a differential geometry of coset spaces that is actively used in investigations of models of quantum field theory, gravity and statistical physics. The third goal is to explain the main ideas about the theory of conformal symmetries, which is the basis of the AdS/CFT correspondence. The theory of groups and symmetries is an important part of theoretical physics. In elementary particle physics, cosmology and related fields, the key role is played by Lie groups and algebras corresponding to continuous symmetries. For example, relativistic physics is based on the Lorentz and Poincare groups, and the modern theory of elementary particles — the Standard Model — is based on gauge (local) symmetry with the gauge group SU(3) x SU(2) x U(1). This book presents constructions and results of a general nature, along with numerous concrete examples that have direct applications in modern theoretical and mathematical physics. Contents: Preface Groups and Transformations Lie Groups Lie Algebras Representations of Groups and Lie Algebras Compact Lie Algebras Root Systems and Classification of Simple Lie Algebras Homogeneous Spaces and their Geometry Solutions to Selected Problems Selected Bibliography References Index Readership: Graduate students and researchers in theoretical physics and mathematical physics. Keywords: Lie Groups;Lie Algebras;Representation Theory;Conformal Symmetries;Yangians;Coset Spaces;Differential Geometry;Casimir Operators;Root Systems;AdS Spaces;Lobachevskian GeometryReview:0