Integrable Structures Of Exactly Solvable Two Dimensional Models Of Quantum Field Theory

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Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory

S. Pakuliak,G. von Gehlen
Integrable Structures of Exactly Solvable Two Dimensional Models of Quantum Field Theory Book PDF

Author : S. Pakuliak,G. von Gehlen
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401006705

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Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory by S. Pakuliak,G. von Gehlen Pdf

Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.

Non-perturbative Methods in 2 Dimensional Quantum Field Theory

Elcio Abdalla,M. Cristina B. Abdalla
Non perturbative Methods in 2 Dimensional Quantum Field Theory Book PDF

Author : Elcio Abdalla,M. Cristina B. Abdalla
Publisher : World Scientific
Page : 834 pages
File Size : 43,8 Mb
Release : 2001
Category : Science
ISBN : 9789812810151

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Non-perturbative Methods in 2 Dimensional Quantum Field Theory by Elcio Abdalla,M. Cristina B. Abdalla Pdf

The second edition of Non-Perturbative Methods in Two-Dimensional Quantum Field Theory is an extensively revised version, involving major changes and additions. Although much of the material is special to two dimensions, the techniques used should prove helpful also in the development of techniques applicable in higher dimensions. In particular, the last three chapters of the book will be of direct interest to researchers wanting to work in the field of conformal field theory and strings. This book is intended for students working for their PhD degree and post-doctoral researchers wishing to acquaint themselves with the non-perturbative aspects of quantum field theory. Contents: Free Fields; The Thirring Model; Determinants and Heat Kernels; Self-Interacting Fermionic Models; Nonlinear a Models: Classical Aspects; Nonlinear a Models OCo Quantum Aspects; Exact S-Matrices of 2D Models; The Wess-Zumino-Witten Theory; QED 2: Operator Approach; Quantum Chromodynamics; QED 2: Functional Approach; The Finite Temperature Schwinger Model; Non-Abelian Chiral Gauge Theories; Chiral Quantum Electrodynamics; Conformally Invariant Field Theory; Conformal Field Theory with Internal Symmetry; 2D Gravity and String-Related Topics. Readership: Graduate students and researchers in high energy and quantum physics."

Quasi-Exactly Solvable Models in Quantum Mechanics

A.G Ushveridze
Quasi Exactly Solvable Models in Quantum Mechanics Book PDF

Author : A.G Ushveridze
Publisher : CRC Press
Page : 480 pages
File Size : 47,6 Mb
Release : 2017-07-12
Category : Science
ISBN : 9781351420327

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Quasi-Exactly Solvable Models in Quantum Mechanics by A.G Ushveridze Pdf

Exactly solvable models, that is, models with explicitly and completely diagonalizable Hamiltonians are too few in number and insufficiently diverse to meet the requirements of modern quantum physics. Quasi-exactly solvable (QES) models (whose Hamiltonians admit an explicit diagonalization only for some limited segments of the spectrum) provide a practical way forward. Although QES models are a recent discovery, the results are already numerous. Collecting the results of QES models in a unified and accessible form, Quasi-Exactly Solvable Models in Quantum Mechanics provides an invaluable resource for physicists using quantum mechanics and applied mathematicians dealing with linear differential equations. By generalizing from one-dimensional QES models, the expert author constructs the general theory of QES problems in quantum mechanics. He describes the connections between QES models and completely integrable theories of magnetic chains, determines the spectra of QES Schrödinger equations using the Bethe-Iansatz solution of the Gaudin model, discusses hidden symmetry properties of QES Hamiltonians, and explains various Lie algebraic and analytic approaches to the problem of quasi-exact solubility in quantum mechanics. Because the applications of QES models are very wide, such as, for investigating non-perturbative phenomena or as a good approximation to exactly non-solvable problems, researchers in quantum mechanics-related fields cannot afford to be unaware of the possibilities of QES models.

Elements of Classical and Quantum Integrable Systems

Gleb Arutyunov
Elements of Classical and Quantum Integrable Systems Book PDF

Author : Gleb Arutyunov
Publisher : Springer
Page : 414 pages
File Size : 54,7 Mb
Release : 2019-07-23
Category : Science
ISBN : 9783030241988

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Elements of Classical and Quantum Integrable Systems by Gleb Arutyunov Pdf

Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland and Ruijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.

Integrable Quantum Field Theories

L. Bonora,Giuseppe Mussardo,A. Schwimmer,L. Girardello,M. Martellini
Integrable Quantum Field Theories Book PDF

Author : L. Bonora,Giuseppe Mussardo,A. Schwimmer,L. Girardello,M. Martellini
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 49,6 Mb
Release : 2013-11-11
Category : Science
ISBN : 9781489915160

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Integrable Quantum Field Theories by L. Bonora,Giuseppe Mussardo,A. Schwimmer,L. Girardello,M. Martellini Pdf

Proceedings of a NATO ARW held in Como, Italy, September 14-19, 1992

Non-perturbative Methods in 2 Dimensional Quantum Field Theory

Elcio Abdalla,M. Cristina B. Abdalla,Klaus Dieter Rothe
Non perturbative Methods in 2 Dimensional Quantum Field Theory Book PDF

Author : Elcio Abdalla,M. Cristina B. Abdalla,Klaus Dieter Rothe
Publisher : World Scientific
Page : 834 pages
File Size : 41,9 Mb
Release : 2001
Category : Science
ISBN : 9789810245962

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Non-perturbative Methods in 2 Dimensional Quantum Field Theory by Elcio Abdalla,M. Cristina B. Abdalla,Klaus Dieter Rothe Pdf

The second edition of Non-Perturbative Methods in Two-Dimensional Quantum Field Theory is an extensively revised version, involving major changes and additions. Although much of the material is special to two dimensions, the techniques used should prove helpful also in the development of techniques applicable in higher dimensions. In particular, the last three chapters of the book will be of direct interest to researchers wanting to work in the field of conformal field theory and strings.This book is intended for students working for their PhD degree and post-doctoral researchers wishing to acquaint themselves with the non-perturbative aspects of quantum field theory.

Integrable Systems, Quantum Groups, and Quantum Field Theories

Alberto Ibort,M.A. Rodríguez
Integrable Systems Quantum Groups and Quantum Field Theories Book PDF

Author : Alberto Ibort,M.A. Rodríguez
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401119801

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Integrable Systems, Quantum Groups, and Quantum Field Theories by Alberto Ibort,M.A. Rodríguez Pdf

In many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics. This book contains the lectures delivered at the NATO-ASI Summer School on `Recent Problems in Mathematical Physics' held at Salamanca, Spain (1992), offering a pedagogical and updated approach to some of the problems that have been at the heart of these events. Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the book. Apart from these, traditional and new problems in quantum gravity are reviewed. Other contributions to the School included in the book range from symmetries in partial differential equations to geometrical phases in quantum physics. The book is addressed to researchers in the fields covered, PhD students and any scientist interested in obtaining an updated view of the subjects.

Planar Ising Correlations

John Palmer
Planar Ising Correlations Book PDF

Author : John Palmer
Publisher : Springer Science & Business Media
Page : 377 pages
File Size : 42,9 Mb
Release : 2007-07-27
Category : Mathematics
ISBN : 9780817642488

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Planar Ising Correlations by John Palmer Pdf

Steady progress in recent years has been made in understanding the special mathematical features of certain exactly solvable models in statistical mechanics and quantum field theory, including the scaling limits of the 2-D Ising (lattice) model, and more generally, a class of 2-D quantum fields known as holonomic fields. New results have made it possible to obtain a detailed nonperturbative analysis of the multi-spin correlations. In particular, the book focuses on deformation analysis of the scaling functions of the Ising model, and will appeal to graduate students, mathematicians, and physicists interested in the mathematics of statistical mechanics and quantum field theory.

Recent Developments in Integrable Systems and Related Topics of Mathematical Physics

Victor M. Buchstaber,Sotiris Konstantinou-Rizos,Alexander V. Mikhailov
Recent Developments in Integrable Systems and Related Topics of Mathematical Physics Book PDF

Author : Victor M. Buchstaber,Sotiris Konstantinou-Rizos,Alexander V. Mikhailov
Publisher : Springer
Page : 216 pages
File Size : 40,7 Mb
Release : 2018-12-30
Category : Science
ISBN : 9783030048075

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Recent Developments in Integrable Systems and Related Topics of Mathematical Physics by Victor M. Buchstaber,Sotiris Konstantinou-Rizos,Alexander V. Mikhailov Pdf

This volume, whose contributors include leading researchers in their field, covers a wide range of topics surrounding Integrable Systems, from theoretical developments to applications. Comprising a unique collection of research articles and surveys, the book aims to serve as a bridge between the various areas of Mathematics related to Integrable Systems and Mathematical Physics. Recommended for postgraduate students and early career researchers who aim to acquire knowledge in this area in preparation for further research, this book is also suitable for established researchers aiming to get up to speed with recent developments in the area, and may very well be used as a guide for further study.

Quantum Groups

Benjamin Enriquez
Quantum Groups Book PDF

Author : Benjamin Enriquez
Publisher : European Mathematical Society
Page : 148 pages
File Size : 52,8 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190477

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Quantum Groups by Benjamin Enriquez Pdf

The volume starts with a lecture course by P. Etingof on tensor categories (notes by D. Calaque). This course is an introduction to tensor categories, leading to topics of recent research such as realizability of fusion rings, Ocneanu rigidity, module categories, weak Hopf algebras, Morita theory for tensor categories, lifting theory, categorical dimensions, Frobenius-Perron dimensions, and the classification of tensor categories. The remainder of the book consists of three detailed expositions on associators and the Vassiliev invariants of knots, classical and quantum integrable systems and elliptic algebras, and the groups of algebra automorphisms of quantum groups. The preface puts the results presented in perspective. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of the ongoing research in the domain of quantum groups, an important subject of current mathematical physics.

Symmetries, Integrable Systems and Representations

Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy
Symmetries Integrable Systems and Representations Book PDF

Author : Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy
Publisher : Springer Science & Business Media
Page : 633 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447148630

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Symmetries, Integrable Systems and Representations by Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy Pdf

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.

Non-Perturbative Field Theory

Yitzhak Frishman,Jacob Sonnenschein
Non Perturbative Field Theory Book PDF

Author : Yitzhak Frishman,Jacob Sonnenschein
Publisher : Cambridge University Press
Page : 455 pages
File Size : 43,6 Mb
Release : 2010-04-08
Category : Science
ISBN : 9781139486484

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Non-Perturbative Field Theory by Yitzhak Frishman,Jacob Sonnenschein Pdf

Providing a new perspective on quantum field theory, this book is useful for graduate students and researchers within and outside the field. It describes non-perturbative methods, and explores two-dimensional and four-dimensional gauge dynamics using those methods. Applications are thoroughly described.

An Invitation to Noncommutative Geometry

Masoud Khalkhali,Matilde Marcolli
An Invitation to Noncommutative Geometry Book PDF

Author : Masoud Khalkhali,Matilde Marcolli
Publisher : World Scientific
Page : 515 pages
File Size : 45,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812706164

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An Invitation to Noncommutative Geometry by Masoud Khalkhali,Matilde Marcolli Pdf

This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory.

Handbook of Teichmüller Theory

Athanase Papadopoulos
Handbook of Teichm ller Theory Book PDF

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
Page : 812 pages
File Size : 40,7 Mb
Release : 2007
Category : Mathematics
ISBN : 3037190299

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Handbook of Teichmüller Theory by Athanase Papadopoulos Pdf

The Teichmuller space of a surface was introduced by O. Teichmuller in the 1930s. It is a basic tool in the study of Riemann's moduli spaces and the mapping class groups. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics. The original setting of Teichmuller theory is complex analysis. The work of Thurston in the 1970s brought techniques of hyperbolic geometry to the study of Teichmuller space and its asymptotic geometry. Teichmuller spaces are also studied from the point of view of the representation theory of the fundamental group of the surface in a Lie group $G$, most notably $G=\mathrm{PSL}(2,\mathbb{R})$ and $G=\mathrm{PSL}(2,\mathbb{C})$. In the 1980s, there evolved an essentially combinatorial treatment of the Teichmuller and moduli spaces involving techniques and ideas from high-energy physics, namely from string theory. The current research interests include the quantization of Teichmuller space, the Weil-Petersson symplectic and Poisson geometry of this space as well as gauge-theoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3-manifolds. The purpose of this handbook is to give a panorama of some of the most important aspects of Teichmuller theory. The handbook should be useful to specialists in the field, to graduate students, and more generally to mathematicians who want to learn about the subject. All the chapters are self-contained and have a pedagogical character. They are written by leading experts in the subject.

Models in Statistical Physics and Quantum Field Theory

Harald Grosse
Models in Statistical Physics and Quantum Field Theory Book PDF

Author : Harald Grosse
Publisher : Springer Science & Business Media
Page : 159 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642835049

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Models in Statistical Physics and Quantum Field Theory by Harald Grosse Pdf

In these lectures we summarize certain results on models in statistical physics and quantum field theory and especially emphasize the deep relation ship between these subjects. From a physical point of view, we study phase transitions of realistic systems; from a more mathematical point of view, we describe field theoretical models defined on a euclidean space-time lattice, for which the lattice constant serves as a cutoff. The connection between these two approaches is obtained by identifying partition functions for spin models with discretized functional integrals. After an introduction to critical phenomena, we present methods which prove the existence or nonexistence of phase transitions for the Ising and Heisenberg models in various dimensions. As an example of a solvable system we discuss the two-dimensional Ising model. Topological excitations determine sectors of field theoretical models. In order to illustrate this, we first discuss soliton solutions of completely integrable classical models. Afterwards we dis cuss sectors for the external field problem and for the Schwinger model. Then we put gauge models on a lattice, give a survey of some rigorous results and discuss the phase structure of some lattice gauge models. Since great interest has recently been shown in string models, we give a short introduction to both the classical mechanics of strings and the bosonic and fermionic models. The formulation of the continuum limit for lattice systems leads to a discussion of the renormalization group, which we apply to various models.