Noncompact Lie Groups And Some Of Their Applications

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Noncompact Lie Groups and Some of Their Applications

Author : Elizabeth A. Tanner
Publisher : Springer Science & Business Media
ISBN 13 : 9401110786
Total Pages : 493 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Noncompact Lie Groups and Some of Their Applications by : Elizabeth A. Tanner

Download or read book Noncompact Lie Groups and Some of Their Applications written by Elizabeth A. Tanner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past two decades representations of noncompact Lie groups and Lie algebras have been studied extensively, and their application to other branches of mathematics and to physical sciences has increased enormously. Several theorems which were proved in the abstract now carry definite mathematical and physical sig nificance. Several physical observations which were not understood before are now explained in terms of models based on new group-theoretical structures such as dy namical groups and Lie supergroups. The workshop was designed to bring together those mathematicians and mathematical physicists who are actively working in this broad spectrum of research and to provide them with the opportunity to present their recent results and to discuss the challenges facing them in the many problems that remain. The objective of the workshop was indeed well achieved. This book contains 31 lectures presented by invited participants attending the NATO Advanced Research Workshop held in San Antonio, Texas, during the week of January 3-8, 1993. The introductory article by the editors provides a brief review of the concepts underlying these lectures (cited by author [*]) and mentions some of their applications. The articles in the book are grouped under the following general headings: Lie groups and Lie algebras, Lie superalgebras and Lie supergroups, and Quantum groups, and are arranged in the order in which they are cited in the introductory article. We are very thankful to Dr.

Lie Groups, Lie Algebras, and Some of Their Applications

Author : Robert Gilmore
Publisher : Courier Corporation
ISBN 13 : 0486131564
Total Pages : 610 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Lie Groups, Lie Algebras, and Some of Their Applications by : Robert Gilmore

Download or read book Lie Groups, Lie Algebras, and Some of Their Applications written by Robert Gilmore and published by Courier Corporation. This book was released on 2012-05-23 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.

Lie Groups

Author : Daniel Bump
Publisher : Springer Science & Business Media
ISBN 13 : 1461480248
Total Pages : 532 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Lie Groups by : Daniel Bump

Download or read book Lie Groups written by Daniel Bump and published by Springer Science & Business Media. This book was released on 2013-10-01 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range of material to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests. This second edition has substantial new material, including improved discussions of underlying principles, streamlining of some proofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the Peter–Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl group, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics that are treated are symmetric function theory, the representation theory of the symmetric group, Frobenius–Schur duality and GL(n) × GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the "philosophy of cusp forms" and the cohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations.

An Introduction to Lie Groups and Lie Algebras

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
ISBN 13 : 0521889693
Total Pages : 237 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis An Introduction to Lie Groups and Lie Algebras by : Alexander A. Kirillov

Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples

p-Adic Lie Groups

Author : Peter Schneider
Publisher : Springer Science & Business Media
ISBN 13 : 364221147X
Total Pages : 259 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis p-Adic Lie Groups by : Peter Schneider

Download or read book p-Adic Lie Groups written by Peter Schneider and published by Springer Science & Business Media. This book was released on 2011-06-11 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with a self-contained and detailed introduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets up the analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition of Lazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the structure of completed group rings.

Naive Lie Theory

Author : John Stillwell
Publisher : Springer Science & Business Media
ISBN 13 : 038778215X
Total Pages : 230 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Naive Lie Theory by : John Stillwell

Download or read book Naive Lie Theory written by John Stillwell and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra. This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history. John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).

Lie Groups, Physics, and Geometry

Author : Robert Gilmore
Publisher : Cambridge University Press
ISBN 13 : 113946907X
Total Pages : 5 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Lie Groups, Physics, and Geometry by : Robert Gilmore

Download or read book Lie Groups, Physics, and Geometry written by Robert Gilmore and published by Cambridge University Press. This book was released on 2008-01-17 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.

Non-perturbative QFT Methods and Their Applications

Author : Z. Horv th
Publisher : World Scientific
ISBN 13 : 9810246498
Total Pages : 471 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Non-perturbative QFT Methods and Their Applications by : Z. Horv th

Download or read book Non-perturbative QFT Methods and Their Applications written by Z. Horv th and published by World Scientific. This book was released on 2001 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: http://www.worldscientific.com/worldscibooks/10.1142/4727

Non-perturbative Qft Methods And Their Applications, Procs Of The Johns Hopkins Workshop On Current Problems In Particle Theory 24

Author : Zalan Horvath
Publisher : World Scientific
ISBN 13 : 9814490830
Total Pages : 471 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Non-perturbative Qft Methods And Their Applications, Procs Of The Johns Hopkins Workshop On Current Problems In Particle Theory 24 by : Zalan Horvath

Download or read book Non-perturbative Qft Methods And Their Applications, Procs Of The Johns Hopkins Workshop On Current Problems In Particle Theory 24 written by Zalan Horvath and published by World Scientific. This book was released on 2001-05-18 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents:Conformal Boundary Conditions — and What They Teach Us (V B Petkova & J-B Zuber)A Physical Basis for the Entropy of the AdS3 Black Hole (S Fernando & F Mansouri)Spinon Formulation of the Kondo Problem (A Klümper & J R Reyes-Martinez)Boundary Integrable Quantum Field Theories (P Dorey)Finite Size Effects in Integrable Quantum Field Theories (F Ravanini)Nonperturbative Analysis of the Two-Frequency Sine-Gordon Model (Z Bajnok et al.)Screening in Hot SU(2) Gauge Theory and Propagators in 3D Adjoint Higgs Model (A Cucchieri et al.)Effective Average Action in Statistical Physics and Quantum Field Theory (Ch Wetterich)Phase Transitions in Non-Hermitean Matrix Models and the “Single Ring” Theorem (J Feinberg et al.)Unraveling the Mystery of Flavor (A Falk)The Nahm Transformation on R2 X T2 (C Ford)A 2D Integrable Axion Model and Target Space Duality (P Forgács)Supersymmetric Ward Identities and Chiral Symmetry Breaking in SUSY QED (M L Walker)and other papers Readership: Theoretical, mathematical and high energy physicists. Keywords:

The Mathematical Legacy of Harish-Chandra

Author : Harish-Chandra
Publisher : American Mathematical Soc.
ISBN 13 : 0821811975
Total Pages : 551 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Mathematical Legacy of Harish-Chandra by : Harish-Chandra

Download or read book The Mathematical Legacy of Harish-Chandra written by Harish-Chandra and published by American Mathematical Soc.. This book was released on 2000 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harish-Chandra was a mathematician of great power, vision, and remarkable ingenuity. His profound contributions to the representation theory of Lie groups, harmonic analysis, and related areas left researchers a rich legacy that continues today. This book presents the proceedings of an AMS Special Session entitled, ""Representation Theory and Noncommutative Harmonic Analysis: A Special Session Honoring the Memory of Harish-Chandra"", which marked 75 years since his birth and 15 years since his untimely death at age 60. Contributions to the volume were written by an outstanding group of internationally known mathematicians. Included are expository and historical surveys and original research papers.The book also includes talks given at the IAS Memorial Service in 1983 by colleagues who knew Harish-Chandra well. Also reprinted are two articles entitled, ""Some Recollections of Harish-Chandra"", by A. Borel, and ""Harish-Chandra's c-Function: A Mathematical Jewel"", by S. Helgason. In addition, an expository paper, ""An Elementary Introduction to Harish-Chandra's Work"", gives an overview of some of his most basic mathematical ideas with references for further study. This volume offers a comprehensive retrospective of Harish-Chandra's professional life and work. Personal recollections give the book particular significance. Readers should have an advanced-level background in the representation theory of Lie groups and harmonic analysis. For other wonderful titles written by this author see: ""Euler through Time: A New Look at Old Themes"", ""Supersymmetry for Mathematicians: An Introduction"", ""The Selected Works of V.S. Varadarajan"", and ""Algebra in Ancient and Modern Times"".

Analysis On Infinite-dimensional Lie Groups And Algebras - Proceedings Of The International Colloquium

Author : Jean Marion
Publisher : World Scientific
ISBN 13 : 9814544841
Total Pages : 410 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Analysis On Infinite-dimensional Lie Groups And Algebras - Proceedings Of The International Colloquium by : Jean Marion

Download or read book Analysis On Infinite-dimensional Lie Groups And Algebras - Proceedings Of The International Colloquium written by Jean Marion and published by World Scientific. This book was released on 1998-10-30 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume can be considered as a monograph on the state-of-the-art in the wide range of analysis on infinite-dimensional algebraic-topological structures. Topics covered in this volume include integrability and regularity for Lie groups and Lie algebras, actions of infinite-dimensional Lie groups on manifolds of paths and related minimal orbits, quasi-invariant measures, white noise analysis, harmonic analysis on generalized convolution structures, and noncommutative geometry. A special feature of this volume is the interrelationship between problems of pure and applied mathematics and also between mathematics and physics.

Symmetry And Structural Properties Of Condensed Matter, Proceedings Of The 3rd International School On Theoretical Physics

Author : Tadeusz Lulek
Publisher : World Scientific
ISBN 13 : 9814550027
Total Pages : 526 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Symmetry And Structural Properties Of Condensed Matter, Proceedings Of The 3rd International School On Theoretical Physics by : Tadeusz Lulek

Download or read book Symmetry And Structural Properties Of Condensed Matter, Proceedings Of The 3rd International School On Theoretical Physics written by Tadeusz Lulek and published by World Scientific. This book was released on 1995-03-29 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reviews some selected problems in solid state physics with an emphasis on adequate mathematical tools. The three main subjects are magnetic structures and neutron scattering; Berry phases and energy bands in solids (symmetry, analicity, Hofstadter butterfly, van Hove singularities); and quasicrystals, finite systems, and group action on sets (unitary group approach, Schur functions). Software presentations are included as a separate part.

Lie Groups

Author : Luiz A. B. San Martin
Publisher : Springer Nature
ISBN 13 : 3030618242
Total Pages : 371 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Lie Groups by : Luiz A. B. San Martin

Download or read book Lie Groups written by Luiz A. B. San Martin and published by Springer Nature. This book was released on 2021-02-23 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an essential introduction to Lie groups, presenting the theory from its fundamental principles. Lie groups are a special class of groups that are studied using differential and integral calculus methods. As a mathematical structure, a Lie group combines the algebraic group structure and the differentiable variety structure. Studies of such groups began around 1870 as groups of symmetries of differential equations and the various geometries that had emerged. Since that time, there have been major advances in Lie theory, with ramifications for diverse areas of mathematics and its applications. Each chapter of the book begins with a general, straightforward introduction to the concepts covered; then the formal definitions are presented; and end-of-chapter exercises help to check and reinforce comprehension. Graduate and advanced undergraduate students alike will find in this book a solid yet approachable guide that will help them continue their studies with confidence.

Applications of Lie Groups to Differential Equations

Author : Peter J. Olver
Publisher : Springer Science & Business Media
ISBN 13 : 1468402749
Total Pages : 524 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Applications of Lie Groups to Differential Equations by : Peter J. Olver

Download or read book Applications of Lie Groups to Differential Equations written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.

Nonperturbative Quantum-field-theoretic Methods and Their Applications

Author : Z. Horv th
Publisher : World Scientific
ISBN 13 : 9789812799968
Total Pages : 474 pages
Book Rating : 4.7/5 (999 download)

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Book Synopsis Nonperturbative Quantum-field-theoretic Methods and Their Applications by : Z. Horv th

Download or read book Nonperturbative Quantum-field-theoretic Methods and Their Applications written by Z. Horv th and published by World Scientific. This book was released on 2001 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Conformal Boundary Conditions OCo and What They Teach Us (V B Petkova & J-B Zuber); A Physical Basis for the Entropy of the AdS 3 Black Hole (S Fernando & F Mansouri); Spinon Formulation of the Kondo Problem (A Klmper & J R Reyes-Martinez); Boundary Integrable Quantum Field Theories (P Dorey); Finite Size Effects in Integrable Quantum Field Theories (F Ravanini); Nonperturbative Analysis of the Two-Frequency Sine-Gordon Model (Z Bajnok et al.); Screening in Hot SU(2) Gauge Theory and Propagators in 3D Adjoint Higgs Model (A Cucchieri et al.); Effective Average Action in Statistical Physics and Quantum Field Theory (Ch Wetterich); Phase Transitions in Non-Hermitean Matrix Models and the OC Single RingOCO Theorem (J Feinberg et al.); Unraveling the Mystery of Flavor (A Falk); The Nahm Transformation on R 2 X T 2 (C Ford); A 2D Integrable Axion Model and Target Space Duality (P Forgics); Supersymmetric Ward Identities and Chiral Symmetry Breaking in SUSY QED (M L Walker); and other papers. Readership: Theoretical, mathematical and high energy physicists."

Complex Semisimple Quantum Groups and Representation Theory

Author : Christian Voigt
Publisher : Springer Nature
ISBN 13 : 3030524639
Total Pages : 382 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Complex Semisimple Quantum Groups and Representation Theory by : Christian Voigt

Download or read book Complex Semisimple Quantum Groups and Representation Theory written by Christian Voigt and published by Springer Nature. This book was released on 2020-09-24 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups. The presentation is comprehensive, beginning with background information on Hopf algebras, and ending with the classification of admissible representations of the q-deformation of a complex semisimple Lie group. The main components are: - a thorough introduction to quantized universal enveloping algebras over general base fields and generic deformation parameters, including finite dimensional representation theory, the Poincaré-Birkhoff-Witt Theorem, the locally finite part, and the Harish-Chandra homomorphism, - the analytic theory of quantized complex semisimple Lie groups in terms of quantized algebras of functions and their duals, - algebraic representation theory in terms of category O, and - analytic representation theory of quantized complex semisimple groups. Given its scope, the book will be a valuable resource for both graduate students and researchers in the area of quantum groups.

Path Integrals, Hyperbolic Spaces and Selberg Trace Formulae

Author : Christian Grosche
Publisher : World Scientific
ISBN 13 : 9814460095
Total Pages : 388 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Path Integrals, Hyperbolic Spaces and Selberg Trace Formulae by : Christian Grosche

Download or read book Path Integrals, Hyperbolic Spaces and Selberg Trace Formulae written by Christian Grosche and published by World Scientific. This book was released on 2013-07-26 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second edition, a comprehensive review is given for path integration in two- and three-dimensional (homogeneous) spaces of constant and non-constant curvature, including an enumeration of all the corresponding coordinate systems which allow separation of variables in the Hamiltonian and in the path integral. The corresponding path integral solutions are presented as a tabulation. Proposals concerning interbasis expansions for spheroidal coordinate systems are also given. In particular, the cases of non-constant curvature Darboux spaces are new in this edition. The volume also contains results on the numerical study of the properties of several integrable billiard systems in compact domains (i.e. rectangles, parallelepipeds, circles and spheres) in two- and three-dimensional flat and hyperbolic spaces. In particular, the discussions of integrable billiards in circles and spheres (flat and hyperbolic spaces) and in three dimensions are new in comparison to the first edition. In addition, an overview is presented on some recent achievements in the theory of the Selberg trace formula on Riemann surfaces, its super generalization, their use in mathematical physics and string theory, and some further results derived from the Selberg (super-) trace formula. Contents:IntroductionPath Integrals in Quantum MechanicsSeparable Coordinate Systems on Spaces of Constant CurvaturePath Integrals in Pseudo-Euclidean GeometryPath Integrals in Euclidean SpacesPath Integrals on SpheresPath Integrals on HyperboloidsPath Integral on the Complex SpherePath Integrals on Hermitian Hyperbolic SpacePath Integrals on Darboux SpacesPath Integrals on Single-Sheeted HyperboloidsMiscellaneous Results on Path IntegrationBilliard Systems and Periodic Orbit TheoryThe Selberg Trace FormulaThe Selberg Super-Trace FormulaSummary and Discussion Readership: Graduate and researchers in mathematical physics. Keywords:Path Integrals;Selberg Trace Formula;Quantum Chaos;Coordinate Systems;Homogeneous Spaces;Spaces of Non-Constant Curvature;Separation of VariablesKey Features:The 2nd edition brings the text up to date with new developments and results in the fieldContains enumeration of many explicit path integrals solutionsReviews: “This book is a good survey of results in a fascinating, highly geometrical, field in which much remains to be done.” Zentralblatt MATH