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Infinite Dimensional Groups And Algebras In Quantum Physics
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Book Synopsis Infinite Dimensional Groups and Algebras in Quantum Physics by : Johnny T. Ottesen
Download or read book Infinite Dimensional Groups and Algebras in Quantum Physics written by Johnny T. Ottesen and published by Springer Science & Business Media. This book was released on 2008-09-11 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of writing this book appeared when I was working on some problems related to representations of physically relevant infinite - mensional groups of operators on physically relevant Hilbert spaces. The considerations were local, reducing the subject to dealing with representations of infinite-dimensional Lie algebras associated with the associated groups. There is a large number of specialized articles and books on parts of this subject, but to our suprise only a few represent the point of view given in this book. Moreover, none of the written material was self-contained. At present, the subject has not reached its final form and active research is still being undertaken. I present this subject of growing importance in a unified manner and by a fairly simple approach. I present a route by which students can absorb and understand the subject, only assuming that the reader is familliar with functional analysis, especially bounded and unbounded operators on Hilbert spaces. Moreover, I assume a little basic knowledge of algebras , Lie algebras, Lie groups, and manifolds- at least the definitions. The contents are presented in detail in the introduction in Chap. The manuscript of this book has been succesfully used by some advanced graduate students at Aarhus University, Denmark, in their "A-exame'. I thank them for comments.
Book Synopsis Infinite Dimensional Groups and Manifolds by : Tilmann Wurzbacher
Download or read book Infinite Dimensional Groups and Manifolds written by Tilmann Wurzbacher and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is a collection of refereed research papers on infinite dimensional groups and manifolds in mathematics and quantum physics. Topics covered are: new classes of Lie groups of mappings, the Burgers equation, the Chern--Weil construction in infinite dimensions, the hamiltonian approach to quantum field theory, and different aspects of large N limits ranging from approximation methods in quantum mechanics to modular forms and string/gauge theory duality. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of important themes of research at the forefront of mathematics and theoretical physics.
Book Synopsis Infinite-dimensional Representations of 2-groups by : John C. Baez
Download or read book Infinite-dimensional Representations of 2-groups written by John C. Baez and published by American Mathematical Soc.. This book was released on 2012 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: A “$2$-group'' is a category equipped with a multiplication satisfying laws like those of a group. Just as groups have representations on vector spaces, $2$-groups have representations on “$2$-vector spaces'', which are categories analogous to vector spaces. Unfortunately, Lie $2$-groups typically have few representations on the finite-dimensional $2$-vector spaces introduced by Kapranov and Voevodsky. For this reason, Crane, Sheppeard and Yetter introduced certain infinite-dimensional $2$-vector spaces called ``measurable categories'' (since they are closely related to measurable fields of Hilbert spaces), and used these to study infinite-dimensional representations of certain Lie $2$-groups. Here they continue this work.
They begin with a detailed study of measurable categories. Then they give a geometrical description of the measurable representations, intertwiners and $2$-intertwiners for any skeletal measurable $2$-group. They study tensor products and direct sums for representations, and various concepts of subrepresentation. They describe direct sums of intertwiners, and sub-intertwiners--features not seen in ordinary group representation theory and study irreducible and indecomposable representations and intertwiners. They also study “irretractable'' representations--another feature not seen in ordinary group representation theory. Finally, they argue that measurable categories equipped with some extra structure deserve to be considered “separable $2$-Hilbert spaces'', and compare this idea to a tentative definition of $2$-Hilbert spaces as representation categories of commutative von Neumann algebras.
Book Synopsis Infinite Dimensional Lie Algebras and Groups by : V G Kac
Download or read book Infinite Dimensional Lie Algebras and Groups written by V G Kac and published by World Scientific. This book was released on 1989-07-01 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents:Integrable Representation of Kac-Moody Algebras: Results and Open Problems (V Chari & A Pressley)Existence of Certain Components in the Tensor Product of Two Integrable Highest Weight Modules for Kac-Moody Algebras (SKumar)Frobenius Action on the B-Cohomology (O Mathieu)Certain Rank Two Subsystems of Kac-Moody Root Systems (J Morita)Lie Groups Associated to Kac-Moody Lie Algebras: An Analytic Approach (E Rodriguez-Carrington)Almost Split-K-Forms of Kac-Moody Algebras (G Rousseau)Global Representations of the Diffeomorphism Groups of the Circle (F Bien)Path Space Realization of the Basic Representation of An(1) (E Date et al)Boson-Fermion Correspondence Over (C De Concini et al)Classification of Modular Invariant Representations of Affine Algebras (V G Kac & M Wakimoto)Standard Monomial Theory for SL2 (V Lakshmibai & C S Seshadri)Some Results on Modular Invariant Representations (S Lu)Current Algebras in 3+1 Space-Time Dimensions (J Mickelson)Standard Representations of An(1) (M Primc)Representations of the Algebra Uq(sI(2)), q-Orthogonal Polynomials and Invariants of Links (A N Kirillov & N Yu Reshetikhin)Infinite Super Grassmannians and Super Plücker Equations (M J Bergvelt)Drinfeld-Sokolov Hierarchies and t-Functions (H J Imbens)Super Boson-Fermion Correspondence of Type B (V G Kac & J W van de Leur)Prym Varieties and Soliton Equations (T Shiota)Polynomial Solutions of the BKP Hierarchy and Projective Representations of Symmetric Groups (Y You)Toward Generalized Macdonald's Identities (D Bernard)Conformal Theories with Non-Linearly Extended Virasoro Symmetries and Lie Algebra Classification (A Bilal & J-LGervais)Extended Conformal Algebras from Kac-Moody Algebras (P Bouwknegt)Meromorphic Conformal Field Theory (P Goddard)Local Extensions of the U(1) Current Algebra and Their Positive Energy Representations (R R Paunov & I T Todorov)Conformal Field Theory on Moduli Family of Stable Curves with Gauge Symmetries (A Tsuchiya & Y Yamada) Readership: Mathematicians and mathematical physicists
Book Synopsis Infinite Dimensional Lie Algebras and Quantum Field Theory by : Heinz Dietrich Doebner
Download or read book Infinite Dimensional Lie Algebras and Quantum Field Theory written by Heinz Dietrich Doebner and published by . This book was released on 1988 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Infinite Dimensional Lie Algebras by : Victor G. Kac
Download or read book Infinite Dimensional Lie Algebras written by Victor G. Kac and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fundamentals of Infinite Dimensional Representation Theory by : Raymond C. Fabec
Download or read book Fundamentals of Infinite Dimensional Representation Theory written by Raymond C. Fabec and published by CRC Press. This book was released on 2018-10-03 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation Theory provides an accessible account of the topics in analytic group representation theory and operator algebras from which much of the subject has evolved. It presents new and old results in a coherent and natural manner and studies a number of tools useful in various areas of this diversely applied subject. From Borel spaces and selection theorems to Mackey's theory of induction, measures on homogeneous spaces, and the theory of left Hilbert algebras, the author's self-contained treatment allows readers to choose from a wide variety of topics and pursue them independently according to their needs. Beyond serving as both a general reference and as a text for those requiring a background in group-operator algebra representation theory, for careful readers, this monograph helps reveal not only the subject's utility, but also its inherent beauty.
Book Synopsis Quantum Theory, Groups and Representations by : Peter Woit
Download or read book Quantum Theory, Groups and Representations written by Peter Woit and published by Springer. This book was released on 2017-11-01 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.
Book Synopsis Operational Quantum Theory I by : Heinrich Saller
Download or read book Operational Quantum Theory I written by Heinrich Saller and published by Springer Science & Business Media. This book was released on 2007-06-10 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operational Quantum Theory I is a distinguished work on quantum theory at an advanced algebraic level. The classically oriented hierarchy with objects such as particles as the primary focus, and interactions of these objects as the secondary focus is reversed with the operational interactions as basic quantum structures. Quantum theory, specifically nonrelativistic quantum mechanics, is developed from the theory of Lie group and Lie algebra operations acting on both finite and infinite dimensional vector spaces. In this book, time and space related finite dimensional representation structures and simple Lie operations, and as a non-relativistic application, the Kepler problem which has long fascinated quantum theorists, are dealt with in some detail. Operational Quantum Theory I features many structures which allow the reader to better understand the applications of operational quantum theory, and to provide conceptually appropriate descriptions of the subject. Operational Quantum Theory I aims to understand more deeply on an operational basis what one is working with in nonrelativistic quantum theory, but also suggests new approaches to the characteristic problems of quantum mechanics.
Book Synopsis Infinite Dimensional Algebras and Quantum Integrable Systems by : Petr P. Kulish
Download or read book Infinite Dimensional Algebras and Quantum Integrable Systems written by Petr P. Kulish and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems" held in July 2003 at the University of Algarve, Faro, Portugal, as a satellite workshop of the XIV International Congress on Mathematical Physics. In it, recent developments in the theory of infinite dimensional algebras, and their applications to quantum integrable systems, are reviewed by leading experts in the field.
Book Synopsis Fundamentals of Infinite Dimensional Representation Theory by : Raymond C. Fabec
Download or read book Fundamentals of Infinite Dimensional Representation Theory written by Raymond C. Fabec and published by CRC Press. This book was released on 2018-10-03 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation Theory provides an accessible account of the topics in analytic group representation theory and operator algebras from which much of the subject has evolved. It presents new and old results in a coherent and natural manner and studies a number of tools useful in various areas of this diversely applied subject. From Borel spaces and selection theorems to Mackey's theory of induction, measures on homogeneous spaces, and the theory of left Hilbert algebras, the author's self-contained treatment allows readers to choose from a wide variety of topics and pursue them independently according to their needs. Beyond serving as both a general reference and as a text for those requiring a background in group-operator algebra representation theory, for careful readers, this monograph helps reveal not only the subject's utility, but also its inherent beauty.
Book Synopsis Quantum Groups and Their Representations by : Anatoli Klimyk
Download or read book Quantum Groups and Their Representations written by Anatoli Klimyk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.
Book Synopsis Quantum and Non-Commutative Analysis by : Huzihiro Araki
Download or read book Quantum and Non-Commutative Analysis written by Huzihiro Araki and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments in mathematical physics and theory of operator algebras, the International Oji Seminar on Quantum Analysis was held at the Kansai Seminar House, Kyoto, JAPAN during June 25-29, 1992 by a generous sponsorship of the Japan Society for the Promotion of Science and the Fujihara Foundation of Science, as a workshop of relatively small number of (about 50) invited participants. This was followed by an open Symposium at RIMS, described below by its organizer, A. Kishimoto. The Oji Seminar began with two key-note addresses, one by V.F.R. Jones on Spin Models in Knot Theory and von Neumann Algebras and by A. Jaffe on Where Quantum Field Theory Has Led. Subsequently topics such as Subfactors and Sector Theory, Solvable Models of Statistical Mechanics, Quantum Field Theory, Quantum Groups, and Renormalization Group Ap proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held.
Book Synopsis Introduction to Finite and Infinite Dimensional Lie (Super)algebras by : Neelacanta Sthanumoorthy
Download or read book Introduction to Finite and Infinite Dimensional Lie (Super)algebras written by Neelacanta Sthanumoorthy and published by Academic Press. This book was released on 2016-04-26 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras Focuses on Kac-Moody algebras
Book Synopsis Representation of Lie Groups and Related Topics by : Anatoliĭ Moiseevich Vershik
Download or read book Representation of Lie Groups and Related Topics written by Anatoliĭ Moiseevich Vershik and published by CRC Press. This book was released on 1990 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eight papers provide mature readers with careful review of progress (through about 1983) toward the creation of a theory of the representations of infinite-dimensional Lie groups and algebras, and of some related topics. Recent developments in physics have provided major impetus for the development of such a theory, and the volume will be of special interest to mathematical physicists (quantum field theorists). Translated from the Russian edition of unstated date, and beautifully produced (which--at the price--it should be!). Book club price, $118. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Infinite-dimensional Lie Groups by : Hideki Omori
Download or read book Infinite-dimensional Lie Groups written by Hideki Omori and published by American Mathematical Soc.. This book was released on 1997 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops, from the viewpoint of abstract group theory, a general theory of infinite-dimensional Lie groups involving the implicit function theorem and the Frobenius theorem. Omori treats as infinite-dimensional Lie groups all the real, primitive, infinite transformation groups studied by E. Cartan. The book discusses several noncommutative algebras such as Weyl algebras and algebras of quantum groups and their automorphism groups. The notion of a noncommutative manifold is described, and the deformation quantization of certain algebras is discussed from the viewpoint of Lie algebras. This edition is a revised version of the book of the same title published in Japanese in 1979.
Book Synopsis Operational Quantum Theory II by : Heinrich Saller
Download or read book Operational Quantum Theory II written by Heinrich Saller and published by Springer Science & Business Media. This book was released on 2006-09-24 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operational Quantum Theory II is a distinguished work on quantum theory at an advanced algebraic level. The classically oriented hierarchy with objects such as particles as the primary focus, and interactions of the objects as the secondary focus is reversed with the operational interactions as basic quantum structures. Quantum theory, specifically relativistic quantum field theory is developed the theory of Lie group and Lie algebra operations acting on both finite and infinite dimensional vector spaces. This book deals with the operational concepts of relativistic space time, the Lorentz and Poincaré group operations and their unitary representations, particularly the elementary articles. Also discussed are eigenvalues and invariants for non-compact operations in general as well as the harmonic analysis of noncompact nonabelian Lie groups and their homogeneous spaces. In addition to the operational formulation of the standard model of particle interactions, an attempt is made to understand the particle spectrum with the masses and coupling constants as the invariants and normalizations of a tangent representation structure of a an homogeneous space time model. Operational Quantum Theory II aims to understand more deeply on an operational basis what one is working with in relativistic quantum field theory, but also suggests new solutions to previously unsolved problems.
