New Trends in Quantum Integrable Systems PDF Download

Author: Boris Feigin
Publisher: World Scientific
ISBN: 9814462926
Category :
Languages : en
Pages :

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Book Description
The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto Japan from 27 to 31 July 2009. As a continuation of the RIMS Research Project a Method of Algebraic Analysis in Integrable Systemsa in 2004 the workshop's aim was to cover exciting new developments that have emerged during the recent years.Collected here are research articles based on the talks presented at the workshop including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models integrable models in quantum field theory conformal field theory mathematical aspects of Bethe ansatz special functions and integrable differential/difference equations representation theory of infinite dimensional algebras integrable models and combinatorics.Through these topics the reader can learn about the most recent developments in the field of quantum integrable systems and related areas of mathematical physics."

Author: Boris Feigin
Publisher: World Scientific
ISBN: 9814324361
Category : Mathematics
Languages : en
Pages : 517

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Book Description
The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July 2009. As a continuation of the RIMS Research Project "Method of Algebraic Analysis in Integrable Systems" in 2004, the workshop's aim was to cover exciting new developments that have emerged during the recent years. Collected here are research articles based on the talks presented at the workshop, including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models, integrable models in quantum field theory, conformal field theory, mathematical aspects of Bethe ansatz, special functions and integrable differential/difference equations, representation theory of infinite dimensional algebras, integrable models and combinatorics. Through these topics, the reader is exposed to the most recent developments in the field of quantum integrable systems and related areas of mathematical physics.

Author: Boris Feigin
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description
Annotation. The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July 2009. As a continuation of the RIMS Research Project "Method of Algebraic Analysis in Integrable Systems" in 2004, the workshop's aim was to cover exciting new developments that have emerged during the recent years. Collected here are research articles based on the talks presented at the workshop, including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models, integrable models in quantum field theory, conformal field theory, mathematical aspects of Bethe ansatz, special functions and integrable differential/difference equations, representation theory of infinite dimensional algebras, integrable models and combinatorics. Through these topics, the reader can learn about the most recent developments in the field of quantum integrable systems and related areas of mathematical physics.

Author: Michio Jimbo
Publisher:
ISBN: 9789814324373
Category : Mathematics
Languages : en
Pages : 400

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Book Description
Properties of linear integral equations related to the six-vertex model with disorder parameter / Hermann Boos and Frank Gohmann -- Algebraic aspects of the correlation functions of the integrable higher-spin XXZ spin chains with arbitrary entries / Tetsuo Deguchi and Chihiro Matsui -- Characters of coinvariants in (1,p) logarithmic models / Boris L. Feigin and Ilya Yu. Tipunin -- XXZ scalar products, Miwa variables and discrete KP / Omar Foda and Gus Schrader -- Quantum spin chains at finite temperatures / Frank Gohmann and Junji Suzuki -- Tropical spectral curves, Fay's trisecant identity, and generalized ultradiscrete Toda lattice / Rei Inoue and Shinsuke Iwao -- On one-point functions of descendants in sine-Gordon model / Michio Jimbo, Tetsuji Miwa and Fedor Smirnov -- Perfect crystals for the quantum affine algebra U[symbol] / Seok-Jin Kang [und weitere] -- Boundary quantum Knizhnik-Zamolodchikov equation / Masahiro Kasatani -- A pentagon of identities, graded tensor products, and the Kirillov-Reshetikhin conjecture / Rinat Kedem -- TBA for the Toda chain / Karol Kajetan Kozlowski and Jorg Teschner -- Generalized energies and integrable D[symbol] cellular automaton / Atsuo Kuniba, Reiho Sakamoto and Yasuhiko Yamada -- Dyson's constant for the hypergeometric kernel / Oleg Lisovyy -- Representation theory of a small ramified partition algebra / Paul P. Martin -- The saga of the Ising susceptibility / Barry M. McCoy -- Bethe algebra of the [symbol] Gaudin model and algebra of functions on the critical set of the master function / Evgeny Mukhin, Vitaly Tarasov and Alexander Varchenko -- T-systems, Y-systems, and cluster algebras : Tamely laced case / Tomoki Nakanishi -- Periodic Benjamin-Ono equation with discrete Laplacian and 2D-Toda hierarchy / Jun'ichi Shiraishi and Yohei Tutiya -- KP and Toda tau functions in Bethe ansatz / Kanehisa Takasaki -- Introduction to middle convolution for differential equations with irregular singularities / Kouichi Takemura -- Differential equations compatible with boundary rational qKZ equation / Yoshihiro Takeyama -- Classification of solutions to the reflection equation for the critical Z[symbol]-symmetric vertex model I / Yuji Yamada

Author: A.B. Shabat
Publisher: Springer Science & Business Media
ISBN: 9400710232
Category : Science
Languages : en
Pages : 297

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Book Description
Proceedings of the NATO Advanced Research Workshop, held in Cadiz, Spain, from 12 to 16 June 2002

Author: Asesh Roy Chowdhury
Publisher: CRC Press
ISBN: 0203498011
Category : Science
Languages : en
Pages : 425

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Book Description
The study of integrable systems has opened new horizons in classical physics over the past few decades, particularly in the subatomic world. Yet despite the field now having reached a level of maturity, very few books provide an introduction to the field accessible to specialists and nonspecialists alike, and none offer a systematic survey of the m

Author: Kenji Iohara
Publisher: Springer Science & Business Media
ISBN: 1447148630
Category : Mathematics
Languages : en
Pages : 633

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Book Description
This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

Author: Petr P. Kulish
Publisher: Springer Science & Business Media
ISBN: 3764373415
Category : Mathematics
Languages : en
Pages : 266

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Book Description
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.

Author: Martin H Krieger
Publisher: World Scientific
ISBN: 9814571865
Category : Mathematics
Languages : en
Pages : 492

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Book Description
Doing Mathematics discusses some ways mathematicians and mathematical physicists do their work and the subject matters they uncover and fashion. The conventions they adopt, the subject areas they delimit, what they can prove and calculate about the physical world, and the analogies they discover and employ, all depend on the mathematics — what will work out and what won't. The cases studied include the central limit theorem of statistics, the sound of the shape of a drum, the connections between algebra and topology, and the series of rigorous proofs of the stability of matter. The many and varied solutions to the two-dimensional Ising model of ferromagnetism make sense as a whole when they are seen in an analogy developed by Richard Dedekind in the 1880s to algebraicize Riemann's function theory; by Robert Langlands' program in number theory and representation theory; and, by the analogy between one-dimensional quantum mechanics and two-dimensional classical statistical mechanics. In effect, we begin to see "an identity in a manifold presentation of profiles," as the phenomenologists would say. This second edition deepens the particular examples; it describe the practical role of mathematical rigor; it suggests what might be a mathematician's philosophy of mathematics; and, it shows how an "ugly" first proof or derivation embodies essential features, only to be appreciated after many subsequent proofs. Natural scientists and mathematicians trade physical models and abstract objects, remaking them to suit their needs, discovering new roles for them as in the recent case of the Painlevé transcendents, the Tracy-Widom distribution, and Toeplitz determinants. And mathematics has provided the models and analogies, the ordinary language, for describing the everyday world, the structure of cities, or God's infinitude. Contents:IntroductionConvention: How Means and Variances are Entrenched as StatisticsSubject: The Fields of TopologyAppendix: The Two-Dimensional Ising Model of a FerromagnetCalculation: Strategy, Structure, and Tactics in Applying Classical AnalysisAnalogy: A Syzygy Between a Research Program in Mathematics and a Research Program in PhysicsIn Concreto: The City of MathematicsAppendices:The Spontaneous Magnetization of a Two-Dimensional Ising Model (C N Yang)On the Dirac and Schwinger Corrections to the Ground-State Energy of an Atom (C Fefferman and L A Seco)Sur la Forme des Espaces Topologiques et sur les Points Fixes des Représentations (J Leray)Une Lettre à Simone Weil (A Weil) Readership: Mathematicians, physicists, philosophers and historians of science. Keywords:Means and Variances;Topology;SyzygyReviews: Reviews of the First Edition: "The book Doing Mathematics, by Martin Krieger is truly a masterpiece. He has not only explained ways of doing mathematical work to aspiring mathematicians and the intelligent laymen, but has also shown how various pieces of research work are related to each other. Even experts may not have realized such inter-relations. The cases studied include, especially, the stability of matter and the Ising model, two topics of great depth. Such clear explanations cannot be found anywhere else. Furthermore, his style of writing makes the book exceptionally enjoyable to read." T T Wu Gordon McKay Professor of Applied Physics Professor of Physics, Harvard University, USA "This is the first time I have seen a mathematician deal substantively with the issue of mathematics as culturally based, and he does it superbly and mathematically … Although this book is no easy read, it is well worth the effort, and I am sure it will stimulate and inform, perhaps even surprise, the most sophisticated of mathematical readers. It is refreshing to find such a book being published." Mathematical Reviews "Both challenging and provocative reading, Doing Mathematics sheds bright light on some of the main characteristics of the mathematical quest." Library of Science "Krieger has made some effort to accommodate different levels of readers; for example, structuring his text so that lay readers are alerted to sections that can be safely skipped and paragraphs that provide nontechnical summaries." Mathematical Association of America

Author: Ge Mo-lin
Publisher: World Scientific
ISBN: 9813233877
Category : Science
Languages : en
Pages : 636

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Book Description
Ludwig Faddeev is widely recognized as one of the titans of 20th century mathematical physics. His fundamental contributions to scattering theory, quantum gauge theories, and the theory of classical and quantum completely integrable systems played a key role in shaping modern mathematical physics. Ludwig Faddeev's major achievements include the solution of the three-body problem in quantum mechanics, the mathematical formulation of quantum gauge theories and corresponding Feynman rules, Hamiltonian and algebraic methods in mathematical physics, with applications to gauge theories with anomalies, quantum systems with constraints and solitons, the discovery of the algebraic structure of classical and quantum integrable systems and quantum groups, and solitons with the topology of knots. Faddeev's name is imprinted in many areas of mathematics and theoretical physics, including "Faddeev's equations" and "Faddeev's Green function" in scattering theory, "Faddeev-Popov ghosts" and "Faddeev-Popov determinant" in gauge theories, "Gardner-Faddeev-Zakharov bracket" for the KdV equation, "Faddeev-Zamolodchikov algebra" in quantum integrable systems, "Faddeev-Reshetikhin-Takhtajan construction" in the theory of quantum groups, knotted solitons in the "Skyrme-Faddeev model" and many others. Ludwig Faddeev founded the St. Petersburg school of modern mathematical physics and distinguished himself by serving the mathematics community for over three decades including his leadership of the International Mathematical Union in the period of 1986-1990. He was conferred numerous prizes and memberships of prestigious institutions in recognition of the importance of his work. These include the Dannie Heineman Prize for Mathematical Physics, the Dirac Medal, the Max Planck Medal, the Shaw Prize and the Lomonosov Gold Medal among others. A gathering of contributions from some of the biggest names in mathematics and physics, this volume serves as a tribute to this legendary figure. Volume contributors include: Fields medalist Sir Michael Atiyah, Jürg Fröhlich, Roman Jackiw, Vladimir Korepin, Nikita Nekrasov, André Neveu, Alexander M Polyakov, Samson Shatashvili, Fedor Smirnov as well as Nobel laureates Frank Wilczek and C N Yang. "Ludwig and I had been good friends since the early 1970s. We had overlapping interests in several areas of physics. He was very powerful mathematically. I had written in several places that he should have shared the 1999 Nobel Prize in Physics with 't Hooft and Veltman" C N Yang, Nobel Laureate in Physics 1997 in Seoul. Faddeev with Baxter and Yang. 2005 in Tsinghua University. Left to right: Faddeev, Yang, Niemi and Ge.