The Orbit Method In Geometry And Physics

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The Orbit Method in Geometry and Physics

Christian Duval,Laurent Guieu,Valentin Ovsienko
The Orbit Method in Geometry and Physics Book PDF

Author : Christian Duval,Laurent Guieu,Valentin Ovsienko
Publisher : Springer Science & Business Media
Page : 478 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200291

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The Orbit Method in Geometry and Physics by Christian Duval,Laurent Guieu,Valentin Ovsienko Pdf

The orbit method influenced the development of several areas of mathematics in the second half of the 20th century and remains a useful and powerful tool in such areas as Lie theory, representation theory, integrable systems, complex geometry, and mathematical physics. Among the distinguished names associated with the orbit method is that of A.A. Kirillov, whose pioneering paper on nilpotent orbits (1962), places him as the founder of orbit theory. The original research papers in this volume are written by prominent mathematicians and reflect recent achievements in orbit theory and other closely related areas such as harmonic analysis, classical representation theory, Lie superalgebras, Poisson geometry, and quantization. Contributors: A. Alekseev, J. Alev, V. Baranovksy, R. Brylinski, J. Dixmier, S. Evens, D.R. Farkas, V. Ginzburg, V. Gorbounov, P. Grozman, E. Gutkin, A. Joseph, D. Kazhdan, A.A. Kirillov, B. Kostant, D. Leites, F. Malikov, A. Melnikov, P.W. Michor, Y.A. Neretin, A. Okounkov, G. Olshanski, F. Petrov, A. Polishchuk, W. Rossmann, A. Sergeev, V. Schechtman, I. Shchepochkina. The work will be an invaluable reference for researchers in the above mentioned fields, as well as a useful text for graduate seminars and courses.

Lectures on the Orbit Method

Aleksandr Aleksandrovich Kirillov
Lectures on the Orbit Method Book PDF

Author : Aleksandr Aleksandrovich Kirillov
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 54,9 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821835302

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Lectures on the Orbit Method by Aleksandr Aleksandrovich Kirillov Pdf

Describes the essence of the orbit method for non-experts and gives a detailed exposition of the method. This work can be used as a text for a graduate course, as well as a handbook for non-experts and a reference book for research mathematicians and mathematical physicists.

Lectures on the Orbit Method

Aleksandr Aleksandrovich Kirillov
Lectures on the Orbit Method Book PDF

Author : Aleksandr Aleksandrovich Kirillov
Publisher : Unknown
Page : 408 pages
File Size : 44,6 Mb
Release : 1900
Category : Lie groups
ISBN : 1470417995

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Lectures on the Orbit Method by Aleksandr Aleksandrovich Kirillov Pdf

Isaac Newton encrypted his discoveries in analysis in the form of an anagram, which deciphers to the sentence ``It is worthwhile to solve differential equations''. Accordingly, one can express the main idea behind the Orbit Method by saying "It is worthwhile to study coadjoint orbits". The orbit method was introduced by the author, A. A. Kirillov, in the 1960s and remains a useful and powerful tool in areas such as Lie theory, group representations, integrable systems, complex and symplectic geometry, and mathematical physics. This book describes the essence of the orbit method for non-experts and gives the first systematic, detailed, and self-contained exposition of the method. It starts with a convenient ``User's Guide'' and contains numerous examples. It can be used as a text for a graduate course, as well as a handbook for non-experts and a reference book for research mathematicians and mathematical physicists.

Lectures on Geometric Methods in Mathematical Physics

Jerrold E. Marsden
Lectures on Geometric Methods in Mathematical Physics Book PDF

Author : Jerrold E. Marsden
Publisher : SIAM
Page : 103 pages
File Size : 53,7 Mb
Release : 1981-01-01
Category : Science
ISBN : 9780898711707

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Lectures on Geometric Methods in Mathematical Physics by Jerrold E. Marsden Pdf

A monograph on some of the ways geometry and analysis can be used in mathematical problems of physical interest. The roles of symmetry, bifurcation and Hamiltonian systems in diverse applications are explored.

Geometric Methods in Physics XXXVII

Piotr Kielanowski,Anatol Odzijewicz,Emma Previato
Geometric Methods in Physics XXXVII Book PDF

Author : Piotr Kielanowski,Anatol Odzijewicz,Emma Previato
Publisher : Springer Nature
Page : 260 pages
File Size : 54,8 Mb
Release : 2019-11-26
Category : Mathematics
ISBN : 9783030340728

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Geometric Methods in Physics XXXVII by Piotr Kielanowski,Anatol Odzijewicz,Emma Previato Pdf

The book consists of articles based on the XXXVII Białowieża Workshop on Geometric Methods in Physics, 2018. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. This edition of the workshop featured a special session dedicated to Professor Daniel Sternheimer on the occasion of his 80th birthday. The previously unpublished papers present cutting-edge current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past seven years, the Białowieża Workshops have been complemented by a School on Geometry and Physics comprising a series of advanced lectures for graduate students and early-career researchers. The book also includes abstracts of the five lecture series that were given at the seventh school.

Geometric Methods in Algebra and Number Theory

Fedor Bogomolov,Yuri Tschinkel
Geometric Methods in Algebra and Number Theory Book PDF

Author : Fedor Bogomolov,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 43,9 Mb
Release : 2004-11-12
Category : Mathematics
ISBN : 0817643494

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Geometric Methods in Algebra and Number Theory by Fedor Bogomolov,Yuri Tschinkel Pdf

* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry

Geometry and Physics

Fernando Etayo,Mario Fioravanti
Geometry and Physics Book PDF

Author : Fernando Etayo,Mario Fioravanti
Publisher : AIP Conference Proceedings (Nu
Page : 216 pages
File Size : 44,6 Mb
Release : 2009-06
Category : Mathematics
ISBN : UCSD:31822037777737

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Geometry and Physics by Fernando Etayo,Mario Fioravanti Pdf

These are the 2008 Proceedings of an international workshop that happens every fall since 1992, in Spain or Portugal. It brings together geometers and physicists, to discuss the ideas and developments, in the areas of Lie algebroids, mechanics, Poisson, symplectic, Riemannian and Semi-Riemannian geometries, quantum mechanics, theory of fields, supergravity and supersymmetry.

Quantum Theories and Geometry

M. Cahen,M. Flato
Quantum Theories and Geometry Book PDF

Author : M. Cahen,M. Flato
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400930551

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Quantum Theories and Geometry by M. Cahen,M. Flato Pdf

This book presents the text of most of the lectures which were de livered at the Meeting Quantum Theories and Geometry which was held at the Fondation Les Treilles from March 23 to March 27, 1987. The general aim of this meeting was to bring together mathemati cians and physicists who have worked in this growing field of contact between the two disciplines, namely this region where geometry and physics interact creatively in both directions. It 1S the strong belief of the organizers that these written con tributions will be a useful document for research people workin~ 1n geometry or physics. Three lectures were devoted to the deformation approach to quantum mechanics which involves a modification of both the associative and the Lie structure of the algebra of functions on classical phase space. A. Lichnerowicz shows how one can view classical and quantum statistical mechanics in terms of a deformation with a parameter inversely propor tional to temperature. S. Gutt reviews the physical background of star products and indicates their applications in Lie groups representa tion theory and in harmonic analysis. D. Arnal gives a rigorous theory Vll viii PREFACI of the star exponential in the case of the Heisenberg group and shows how this can be extended to arbitrary nilpotent groups.

Methods of Noncommutative Geometry for Group C*-Algebras

Do Ngoc Diep
Methods of Noncommutative Geometry for Group C Algebras Book PDF

Author : Do Ngoc Diep
Publisher : CRC Press
Page : 4 pages
File Size : 53,5 Mb
Release : 1999-12-06
Category : Mathematics
ISBN : 1584880198

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Methods of Noncommutative Geometry for Group C*-Algebras by Do Ngoc Diep Pdf

The description of the structure of group C*-algebras is a difficult problem, but relevant to important new developments in mathematics, such as non-commutative geometry and quantum groups. Although a significant number of new methods and results have been obtained, until now they have not been available in book form. This volume provides an introduction to and presents research on the study of group C*-algebras, suitable for all levels of readers - from graduate students to professional researchers. The introduction provides the essential features of the methods used. In Part I, the author offers an elementary overview - using concrete examples-of using K-homology, BFD functors, and KK-functors to describe group C*-algebras. In Part II, he uses advanced ideas and methods from representation theory, differential geometry, and KK-theory, to explain two primary tools used to study group C*-algebras: multidimensional quantization and construction of the index of group C*-algebras through orbit methods. The structure of group C*-algebras is an important issue both from a theoretical viewpoint and in its applications in physics and mathematics. Armed with the background, tools, and research provided in Methods of Noncommutative Geometry for Group C*-Algebras, readers can continue this work and make significant contributions to perfecting the theory and solving this problem.

Geometric Methods in Physics XXXIX

Piotr Kielanowski,Alina Dobrogowska,Gerald A. Goldin,Tomasz Goliński
Geometric Methods in Physics XXXIX Book PDF

Author : Piotr Kielanowski,Alina Dobrogowska,Gerald A. Goldin,Tomasz Goliński
Publisher : Springer Nature
Page : 345 pages
File Size : 55,7 Mb
Release : 2023-07-21
Category : Science
ISBN : 9783031302848

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Geometric Methods in Physics XXXIX by Piotr Kielanowski,Alina Dobrogowska,Gerald A. Goldin,Tomasz Goliński Pdf

This volume collects papers based on lectures given at the XXXIX Workshop on Geometric Methods in Physics, held in Białystok, Poland in June 2022. These chapters provide readers an overview of cutting-edge research in geometry, analysis, and a wide variety of other areas. Specific topics include: Classical and quantum field theories Infinite-dimensional groups Integrable systems Lie groupoids and Lie algebroids Representation theory Geometric Methods in Physics XXXIX will be a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas.

Higher Structures in Geometry and Physics

Alberto S. Cattaneo,Anthony Giaquinto,Ping Xu
Higher Structures in Geometry and Physics Book PDF

Author : Alberto S. Cattaneo,Anthony Giaquinto,Ping Xu
Publisher : Springer Science & Business Media
Page : 371 pages
File Size : 55,9 Mb
Release : 2010-11-25
Category : Mathematics
ISBN : 9780817647353

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Higher Structures in Geometry and Physics by Alberto S. Cattaneo,Anthony Giaquinto,Ping Xu Pdf

This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics— such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics— and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. The volume is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures.

Developments and Retrospectives in Lie Theory

Geoffrey Mason,Ivan Penkov,Joseph A. Wolf
Developments and Retrospectives in Lie Theory Book PDF

Author : Geoffrey Mason,Ivan Penkov,Joseph A. Wolf
Publisher : Springer
Page : 274 pages
File Size : 47,9 Mb
Release : 2014-11-12
Category : Mathematics
ISBN : 9783319099347

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Developments and Retrospectives in Lie Theory by Geoffrey Mason,Ivan Penkov,Joseph A. Wolf Pdf

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades. At the beginning, the top universities in California and Utah hosted the meetings, which continue to run on a quarterly basis. Experts in representation theory/Lie theory from various parts of the US, Europe, Asia (China, Japan, Singapore, Russia), Canada, and South and Central America were routinely invited to give talks at these meetings. Nowadays, the workshops are also hosted at universities in Louisiana, Virginia, and Oklahoma. These Lie theory workshops have been sponsored by the NSF, noting the talks have been seminal in describing new perspectives in the field covering broad areas of current research. The contributors have all participated in these Lie theory workshops and include in this volume expository articles which will cover representation theory from the algebraic, geometric, analytic, and topological perspectives with also important connections to math physics. These survey articles, review and update the prominent seminal series of workshops in representation/Lie theory mentioned above, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, number theory, and mathematical physics. Many of the contributors have had prominent roles in both the classical and modern developments of Lie theory and its applications.

Applications of Contact Geometry and Topology in Physics

Arkady Leonidovich Kholodenko
Applications of Contact Geometry and Topology in Physics Book PDF

Author : Arkady Leonidovich Kholodenko
Publisher : World Scientific
Page : 492 pages
File Size : 42,6 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814412094

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Applications of Contact Geometry and Topology in Physics by Arkady Leonidovich Kholodenko Pdf

Although contact geometry and topology is briefly discussed in V I Arnol''d''s book Mathematical Methods of Classical Mechanics (Springer-Verlag, 1989, 2nd edition), it still remains a domain of research in pure mathematics, e.g. see the recent monograph by H Geiges An Introduction to Contact Topology (Cambridge U Press, 2008). Some attempts to use contact geometry in physics were made in the monograph Contact Geometry and Nonlinear Differential Equations (Cambridge U Press, 2007). Unfortunately, even the excellent style of this monograph is not sufficient to attract the attention of the physics community to this type of problems. This book is the first serious attempt to change the existing status quo. In it we demonstrate that, in fact, all branches of theoretical physics can be rewritten in the language of contact geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum computers, etc. The book is written in the style of famous Landau-Lifshitz (L-L) multivolume course in theoretical physics. This means that its readers are expected to have solid background in theoretical physics (at least at the level of the L-L course). No prior knowledge of specialized mathematics is required. All needed new mathematics is given in the context of discussed physical problems. As in the L-L course some problems/exercises are formulated along the way and, again as in the L-L course, these are always supplemented by either solutions or by hints (with exact references). Unlike the L-L course, though, some definitions, theorems, and remarks are also presented. This is done with the purpose of stimulating the interest of our readers in deeper study of subject matters discussed in the text.

Quantum Physics and Geometry

Edoardo Ballico,Alessandra Bernardi,Iacopo Carusotto,Sonia Mazzucchi,Valter Moretti
Quantum Physics and Geometry Book PDF

Author : Edoardo Ballico,Alessandra Bernardi,Iacopo Carusotto,Sonia Mazzucchi,Valter Moretti
Publisher : Springer
Page : 173 pages
File Size : 49,8 Mb
Release : 2019-03-13
Category : Science
ISBN : 9783030061227

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Quantum Physics and Geometry by Edoardo Ballico,Alessandra Bernardi,Iacopo Carusotto,Sonia Mazzucchi,Valter Moretti Pdf

This book collects independent contributions on current developments in quantum information theory, a very interdisciplinary field at the intersection of physics, computer science and mathematics. Making intense use of the most advanced concepts from each discipline, the authors give in each contribution pedagogical introductions to the main concepts underlying their present research and present a personal perspective on some of the most exciting open problems. Keeping this diverse audience in mind, special efforts have been made to ensure that the basic concepts underlying quantum information are covered in an understandable way for mathematical readers, who can find there new open challenges for their research. At the same time, the volume can also be of use to physicists wishing to learn advanced mathematical tools, especially of differential and algebraic geometric nature.

Geometric Methods in Physics

Piotr Kielanowski,Pierre Bieliavsky,Anatol Odzijewicz,Martin Schlichenmaier,Theodore Voronov
Geometric Methods in Physics Book PDF

Author : Piotr Kielanowski,Pierre Bieliavsky,Anatol Odzijewicz,Martin Schlichenmaier,Theodore Voronov
Publisher : Birkhäuser
Page : 326 pages
File Size : 43,8 Mb
Release : 2015-09-21
Category : Mathematics
ISBN : 9783319182124

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Geometric Methods in Physics by Piotr Kielanowski,Pierre Bieliavsky,Anatol Odzijewicz,Martin Schlichenmaier,Theodore Voronov Pdf

​This book presents a selection of papers based on the XXXIII Białowieża Workshop on Geometric Methods in Physics, 2014. The Białowieża Workshops are among the most important meetings in the field and attract researchers from both mathematics and physics. The articles gathered here are mathematically rigorous and have important physical implications, addressing the application of geometry in classical and quantum physics. Despite their long tradition, the workshops remain at the cutting edge of ongoing research. For the last several years, each Białowieża Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented; some of the lectures are reproduced here. The unique atmosphere of the workshop and school is enhanced by its venue, framed by the natural beauty of the Białowieża forest in eastern Poland. The volume will be of interest to researchers and graduate students in mathematical physics, theoretical physics and mathematmtics.