Finite Volume Form Factors in Integrable Field Theory
Finite Volume Form Factors in Integrable Field Theory

Author: Balázs Pozsgay

Publisher: LAP Lambert Academic Publishing

Published: 2010-08

Total Pages: 152

ISBN-13: 9783838383514

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The study of integrable models is one of the most exciting areas of modern theoretical physics. It has inspired physicists and mathematicians over the last 40 years, with a continuing progress in theoretical ideas. On the other hand, there are direct connections to experimental physics: in the last ten years it has become possible to realize integrable models with the help of optical and magnetic traps. This presents a novel opportunity to study strongly interacting quantum systems. The present work is a PhD thesis which concerns a certain sub-class of integrable models, namely integrable Quantum Field Theories. The main goal of the thesis is to obtain correlation functions of local observables at finite temperatures. A new finite volume regularization scheme is introduced, which is built upon the knowledge of form factors in the finite volume. The thesis also includes an introductory chapter, where the basic concepts of integrable QFT and Conformal Field Theory are explained.

Form Factors in Completely Integrable Models of Quantum Field Theory
Form Factors in Completely Integrable Models of Quantum Field Theory

Author: F. A. Smirnov

Publisher: World Scientific

Published: 1992

Total Pages: 234

ISBN-13: 9789810202446

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The monograph summarizes recent achievements in the calculation of matrix elements of local operators (form factors) for completely integrable models. Particularly, it deals with sine-Gordon, chiral Gross-Neven and O(3) nonlinear s models. General requirements on form factors are formulated and explicit formulas for form factors of most fundamental local operators are presented for the above mentioned models.

Integrable Quantum Field Theories and Their Application
Integrable Quantum Field Theories and Their Application

Author: Changrim Ahn

Publisher: World Scientific

Published: 2001

Total Pages: 360

ISBN-13: 9789812799739

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Applications of reflection amplitudes in Toda-type theories / C. Ahn, C. Kim and C. Rim -- Lax pairs and involutive Hamiltonians for CN and BCN Ruijsenaars-Schneider models / Kai Chen, B.-Y. Hou and W.-L. Yang -- Fateev's models and their applications / D. Controzzi and A.M. Tsvelik -- The ODE/IM correspondence / P. Dorey, C. Dunning and R. Tateo -- Integrable sigma models / P. Fendley -- Lorentz lattice gases and spin chains / M.J. Martins -- Quantum Calogero-Moser models for any root system / R. Sasaki -- Quasi-particles in conformal field theories for fractional quantum Hall systems / K. Schoutens and R.A.J. van Elburg -- Towards form factors in finite volume / F.A. Smirnov -- Static and dynamic properties of trapped Bose-Einstein condensates / T. Tsurumi, H. Morise and M. Wadati -- Integrability of the Calogero Model: Conserved quantities, the classical general solution and the quantum orthogonal basis / H. Ujino, A. Nishino and M. Wadati -- Conformal boundary conditions / J.-B. Zuber

Integrable Quantum Field Theories And Their Applications - Procs Of The Apctp Winter School
Integrable Quantum Field Theories And Their Applications - Procs Of The Apctp Winter School

Author: Changrim Ahn

Publisher: World Scientific

Published: 2001-09-25

Total Pages: 354

ISBN-13: 9814490180

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This volume includes several lecture notes on the fundamentals and elementary techniques of integrable field theories and on their applications to low-dimensional physics systems contributed by leading scientists in the respective fields. The main topics covered are various aspects of the thermodynamic Bethe ansatz, form factors, Calogero (and related) models, sigma models, conformal boundary conditions, etc. The volume presents both pedagogical material and a current research trend in the field.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)

From Integrable Models To Gauge Theories: A Volume In Honor Of Sergei Matinyan
From Integrable Models To Gauge Theories: A Volume In Honor Of Sergei Matinyan

Author: Vahe G Gurzadyan

Publisher: World Scientific

Published: 2002-04-22

Total Pages: 327

ISBN-13: 9814488755

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This collection of twenty articles in honor of the noted physicist and mentor Sergei Matinyan focuses on topics that are of fundamental importance to high-energy physics, field theory and cosmology. The topics range from integrable quantum field theories, three-dimensional Ising models, parton models and tests of the Standard Model, to black holes in loop quantum gravity, the cosmological constant and magnetic fields in cosmology. A pedagogical essay by Lev Okun concentrates on the problem of fundamental units. The articles have been written by well-known experts and are addressed to graduate students and researchers.

Quantum Correlations in Field Theory and Integrable Systems
Quantum Correlations in Field Theory and Integrable Systems

Author: Stefano Evangelisti

Publisher: Minkowski Institute Press

Published: 2013-05-31

Total Pages: 213

ISBN-13: 1927763096

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This doctoral thesis analytically and numerically examines some of the most important concepts in quantum correlations in low-dimensional physics: entanglement and out-of-equilibrium dynamics. As John Bell once said: "Entanglement expresses the spooky nonlocality inherent to quantum mechanics", and its study not only concerns the foundations of any quantum theory, but also has important applications in quantum information and condensed matter theory, amongst others. The first chapters are devoted to the study of "entanglement entropies", a popular measure of the "quantumness" of a physical system. The main focus of the analysis is the one-dimensional XYZ spin-1/2 chain in equilibrium, an interacting theory which in addition to being integrable also has interesting scaling limits, such as the sine-Gordon field theory. Moving away from equilibrium the subsequent chapters deal with the dynamics of quantum correlators after an instantaneous quantum quench. The emphasis is on two different models and techniques; the transverse field Ising chain is studied using the form-factor approach and the O(3) non-linear sigma model is studied by means of the semi-classical theory. In the final chapter the author highlights an important general result: in the absence of long-range interactions in the final Hamiltonian the dynamics of a quantum system are determined by the same statistical ensemble that describes static correlations.

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

Author: S. Pakuliak

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 334

ISBN-13: 9401006709

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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.

L. D. Faddeev's Seminar on Mathematical Physics
L. D. Faddeev's Seminar on Mathematical Physics

Author: Michael Semenov-Tian-Shansky

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 336

ISBN-13: 9780821821336

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Professor L. D. Faddeev's seminar at Steklov Mathematical Institute (St. Petersburg, Russia) has a long history of over 30 years of intensive work which shaped modern mathematical physics. This collection, honoring Professor Faddeev's 65th anniversary, has been prepared by his students and colleagues. Topics covered in the volume include classical and quantum integrable systems (both analytic and algebraic aspects), quantum groups and generalizations, quantum field theory, and deformation quantization. Included is a history of the seminar highlighting important developments, such as the invention of the quantum inverse scattering method and of quantum groups. The book will serve nicely as a comprehensive, up-to-date resource on the topic.

Statistical Field Theory
Statistical Field Theory

Author: Giuseppe Mussardo

Publisher: Oxford Graduate Texts

Published: 2020-03-06

Total Pages: 1017

ISBN-13: 019878810X

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Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetry breaking, scaling transformations, conformal symmetry and anomalous dimensions, have deeply changed the modern vision of many areas of physics, leading to remarkable developments in statistical mechanics, elementary particle theory, condensed matter physics and string theory. This self-contained book provides a thorough introduction to the fascinating world of phase transitions and frontier topics of exactly solved models in statistical mechanics and quantum field theory, such as renormalization groups, conformal models, quantum integrable systems, duality, elastic S-matrices, thermodynamic Bethe ansatz and form factor theory. The clear discussion of physical principles is accompanied by a detailed analysis of several branches of mathematics distinguished for their elegance and beauty, including infinite dimensional algebras, conformal mappings, integral equations and modular functions. Besides advanced research themes, the book also covers many basic topics in statistical mechanics, quantum field theory and theoretical physics. Each argument is discussed in great detail while providing overall coherent understanding of physical phenomena. Mathematical background is made available in supplements at the end of each chapter, when appropriate. The chapters include problems of different levels of difficulty. Advanced undergraduate and graduate students will find this book a rich and challenging source for improving their skills and for attaining a comprehensive understanding of the many facets of the subject.