From Integrable Models To Gauge Theories

Author : V G Gurzadyan,A G Sedrakian
Publisher : World Scientific
Page : 328 pages
File Size : 44,6 Mb
Release : 2002-04-22
Category : Science
ISBN : 9789814488754

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From Integrable Models to Gauge Theories by V G Gurzadyan,A G Sedrakian Pdf

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. Contents:3D Ising Model on Dual BCC Lattice: The Sign-Factor (J Ambjorn et al.)On Algebra of the Baxter Q-Operators (A A Belavin & R A Usmanov)Aspect of Locality in the Form Factor Program (O A Castro-Alvaredo & A Fring)On the Origin of Symmetries (J L Chkareuli)Generalization of Magnetic Fields in Cosmology (A D Dolgov)On the Cosmological Constant and Vacuum Energy (V G Gurzadyan & S S Xue)Topics in Parton Model (O V Kancheli)Bjorken Asymptotics of QCD and Integrable Systems (D Karakhanyan & R Kirschner)Entropy and Area of Black Holes in Loop Quantum Gravity (I B Khriplovich)Statistical Ensembles and Density of States (V Kostrykin & R Schrader)The Anthropic Principle Revisted (B Müller)Fundamental Units (L B Okun)Structure Constant of Boundary Operators in Liouville Field Theory (B Ponsot & J Teschner)Winding Number Versus Chern–Pontryagin Charge (T Tchrakian)Magnetically Induced Vacuum-Energy Releasing (S S Xue)and other papers Readership: High energy physicists and mathematical researchers. Keywords:Gauge;Standard Model;Baxter;Parton;Loop Quantum Gravity

Author : V. G. Gurzadyan,Ara G. Sedrakian
Publisher : World Scientific
Page : 330 pages
File Size : 44,5 Mb
Release : 2002
Category : Science
ISBN : 9812777474

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From Integrable Models to Gauge Theories by V. G. Gurzadyan,Ara G. Sedrakian Pdf

"This collection of 20 articles in honour 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 experts and are addressed to graduate students and researchers."--[Source inconnue].

Author : Patrick Dorey,Gregory Korchemsky,Nikita Nekrasov,Volker Schomerus,Didina Serban,Leticia Cugliandolo
Publisher : Oxford University Press
Page : 608 pages
File Size : 53,7 Mb
Release : 2019-07-24
Category : Science
ISBN : 9780192563316

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Integrability: From Statistical Systems to Gauge Theory by Patrick Dorey,Gregory Korchemsky,Nikita Nekrasov,Volker Schomerus,Didina Serban,Leticia Cugliandolo Pdf

This volume, 106 of the Les Houches Summer School series, brings together applications of integrability to supersymmetric gauge and string theory. The book focuses on the application of integrability and problems in quantum field theory. Particular emphasis is given to the exact solution of planar N=4 super-Yang-Mills theory and its relation with string theory on the one hand, and the exact determination of the low-energy physics of N=2 super-Yang-Mills theories on the other; links with other domains are also explored. The purpose of the Les Houches Summer School was to bring together young researchers and specialists from statistical physics, condensed matter physics, gauge and string theory, and mathematics, to stimulate discussion across these different research areas.

Author : Andreas Fring
Publisher : World Scientific Publishing Company
Page : 170 pages
File Size : 53,6 Mb
Release : 2019-04-28
Category : Science
ISBN : 9813237570

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Lectures of David Olive on Gauge Theories and Lie Algebras by Andreas Fring Pdf

Professor David Olive was a renowned British theoretical physicist who made seminal contributions to superstrings, quantum gauge theories and mathematical physics. He was awarded the Dirac Medal by the International Centre for Theoretical Physics in Trieste in 1997, with his long-standing collaborator Peter Goddard. David Olive was a Fellow of the Royal Society and a Founding Fellow of the Learned Society of Wales. David Olive was known for his visionary conjectures, including electromagnetic duality in spontaneously broken gauge theories, as well as his exceptionally clear and insightful style of exposition.These lectures, delivered by David Olive in 1982 at the University of Virginia, provide a pedagogical, self-contained introduction to gauge theory, Lie algebras, electromagnetic duality and integrable models. Despite enormous subsequent developments, they still provide a valuable entry point to some of the deepest topics in quantum gauge theory.

Author : Andrei Marshakov
Publisher : World Scientific
Page : 259 pages
File Size : 43,5 Mb
Release : 1999-03-26
Category : Science
ISBN : 9789814495578

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Seiberg-witten Theory And The Integrable Systems by Andrei Marshakov Pdf

In the past few decades many attempts have been made to search for a consistent formulation of quantum field theory beyond perturbation theory. One of the most interesting examples is the Seiberg-Witten ansatz for the N=2 SUSY supersymmetric Yang-Mills gauge theories in four dimensions. The aim of this book is to present in a clear form the main ideas of the relation between the exact solutions to the supersymmetric (SUSY) Yang-Mills theories and integrable systems. This relation is a beautiful example of reformulation of close-to-realistic physical theory in terms widely known in mathematical physics — systems of integrable nonlinear differential equations and their algebro-geometric solutions.First, the book reviews what is known about the physical problem: the construction of low-energy effective actions for the N=2 Yang-Mills theories from the traditional viewpoint of quantum field theory. Then the necessary background information from the theory of integrable systems is presented. In particular the author considers the definition of the algebro-geometric solutions to integrable systems in terms of complex curves or Riemann surfaces and the generating meromorphic 1-form. These definitions are illustrated in detail on the basic example of the periodic Toda chain.Several “toy-model” examples of string theory solutions where the structures of integrable systems appear are briefly discussed. Then the author proceeds to the Seiberg-Witten solutions and show that they are indeed defined by the same data as finite-gap solutions to integrable systems. The complete formulation requires the introduction of certain deformations of the finite-gap solutions described in terms of quasiclassical or Whitham hierarchies. The explicit differential equations and direct computations of the prepotential of the effective theory are presented and compared when possible with the well-known computations from supersymmetric quantum gauge theories.Finally, the book discusses the properties of the exact solutions to SUSY Yang-Mills theories and their relation to integrable systems in the general context of the modern approach to nonperturbative string or M-theory.

Author : Andrei Marshakov
Publisher : World Scientific
Page : 268 pages
File Size : 54,9 Mb
Release : 1999
Category : Science
ISBN : 9810236360

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Seiberg-Witten Theory and Integrable Systems by Andrei Marshakov Pdf

In the past few decades many attempts have been made to search for a consistent formulation of quantum field theory beyond perturbation theory. One of the most interesting examples is the Seiberg-Witten ansatz for the N=2 SUSY supersymmetric Yang-Mills gauge theories in four dimensions. The aim of this book is to present in a clear form the main ideas of the relation between the exact solutions to the supersymmetric (SUSY) Yang-Mills theories and integrable systems. This relation is a beautiful example of reformulation of close-to-realistic physical theory in terms widely known in mathematical physics ? systems of integrable nonlinear differential equations and their algebro-geometric solutions.First, the book reviews what is known about the physical problem: the construction of low-energy effective actions for the N=2 Yang-Mills theories from the traditional viewpoint of quantum field theory. Then the necessary background information from the theory of integrable systems is presented. In particular the author considers the definition of the algebro-geometric solutions to integrable systems in terms of complex curves or Riemann surfaces and the generating meromorphic 1-form. These definitions are illustrated in detail on the basic example of the periodic Toda chain.Several ?toy-model? examples of string theory solutions where the structures of integrable systems appear are briefly discussed. Then the author proceeds to the Seiberg-Witten solutions and show that they are indeed defined by the same data as finite-gap solutions to integrable systems. The complete formulation requires the introduction of certain deformations of the finite-gap solutions described in terms of quasiclassical or Whitham hierarchies. The explicit differential equations and direct computations of the prepotential of the effective theory are presented and compared when possible with the well-known computations from supersymmetric quantum gauge theories.Finally, the book discusses the properties of the exact solutions to SUSY Yang-Mills theories and their relation to integrable systems in the general context of the modern approach to nonperturbative string or M-theory.

Author : F A Smirnov
Publisher : World Scientific
Page : 224 pages
File Size : 55,9 Mb
Release : 1992-08-07
Category : Science
ISBN : 9789814506908

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Form Factors in Completely Integrable Models of Quantum Field Theory by F A Smirnov Pdf

' 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. Contents:Completely Integrable Models of Quantum Field TheoryThe Space of Physical StatesThe Necessary Properties of Form FactorsThe Local Commutativity TheoremSoliton Form Factors in SG ModelThe Main Properties of the Soliton Form FactorsBreathers Form Factors in SG ModelProperties of the Operators jμ, Tμν, exp(± iβu/2) in SG ModelForm Factors in SU(2)-Invariant Thirring ModelForm Factors in O(3)-Nonlinear σ-modelAsymptotics of Form FactorsCurrent AlgebrasForm Factors in SU(N) — Invariant Thirring Model (SU(N) Chiral Gross-Neveu Model)Phenomenological Reasonings Readership: Mathematical physicists. Keywords:Integrable;Quantum Field Theory in Two Dimensions;S-Matrix;Existence of Completely Integrable Models;Scattering Operator;Many-Particle Scattering;Yang-Baxter Triangle Equation;Soluable Lattice Models of Classical Statistical Mechanics;Form Factors;Zamolodchikov-Faddeev Approach;SU(2)-Invariant Thirring Model;Kinks;O(3)-Invariant σ-Model “It will be of great help to those who look for a reliable source of the numerous detailed calculations that have been performed over the years by many experts.” Mathematics Abstracts '

Author : Jörg Teschner
Publisher : Springer
Page : 467 pages
File Size : 40,5 Mb
Release : 2015-11-17
Category : Science
ISBN : 9783319187693

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New Dualities of Supersymmetric Gauge Theories by Jörg Teschner Pdf

This book reviews a number of spectacular advances that have been made in the study of supersymmetric quantum field theories in the last few years. Highlights include exact calculations of Wilson loop expectation values, and highly nontrivial quantitative checks of the long-standing electric-magnetic duality conjectures The book starts with an introductory article presenting a survey of recent advances, aimed at a wide audience with a background and interest in theoretical physics. The following articles are written for advanced students and researchers in quantum field theory, string theory and mathematical physics, our goal being to familiarize these readers with the forefront of current research. The topics covered include recent advances in the classification and vacuum structure of large families of N=2 supersymmetric field theories, followed by an extensive discussion of the localisation method, one of the most powerful tools for exact studies of supersymmetric field theories. The quantities that have been studied in this way are partition functions, expectation values of line operators, and supersymmetric indices. The book also reviews recently discovered connections between SUSY field theories in four dimensions and two-dimensional conformal field theory. These connections have a counterpart in relations between three-dimensional gauge theories and Chern-Simons theory; the book’s closing chapters explore connections with string theory.

Author : Pavel Exner
Publisher : World Scientific
Page : 709 pages
File Size : 54,6 Mb
Release : 2010
Category : Science
ISBN : 9789814304627

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Sixteenth International Congress on Mathematical Physics by Pavel Exner Pdf

The International Congress on Mathematical Physics is the flagship conference in this exciting field. Convening every three years, it gives a survey on the progress achieved in all branches of mathematical physics. It also provides a superb platform to discuss challenges and new ideas. The present volume collects material from the XVIth ICMP which was held in Prague, August 2009, and features most of the plenary lectures and invited lectures in topical sessions as well as information on other parts of the congress program. This volume provides a broad coverage of the field of mathematical physics, from dominantly mathematical subjects to particle physics, condensed matter, and application of mathematical physics methods in various areas such as astrophysics and ecology, amongst others.

Author : Olivier Babelon,Denis Bernard,Michel Talon
Publisher : Cambridge University Press
Page : 622 pages
File Size : 55,9 Mb
Release : 2003-04-17
Category : Mathematics
ISBN : 052182267X

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Introduction to Classical Integrable Systems by Olivier Babelon,Denis Bernard,Michel Talon Pdf

This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field.

Author : Jacques Hurtubise,François Lalonde
Publisher : Springer Science & Business Media
Page : 242 pages
File Size : 45,7 Mb
Release : 1997-03-31
Category : Mathematics
ISBN : 0792345002

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Gauge Theory and Symplectic Geometry by Jacques Hurtubise,François Lalonde Pdf

Gauge theory, symplectic geometry and symplectic topology are important areas at the crossroads of several mathematical disciplines. The present book, with expertly written surveys of recent developments in these areas, includes some of the first expository material of Seiberg-Witten theory, which has revolutionised the subjects since its introduction in late 1994. Topics covered include: introductions to Seiberg-Witten theory, to applications of the S-W theory to four-dimensional manifold topology, and to the classification of symplectic manifolds; an introduction to the theory of pseudo-holomorphic curves and to quantum cohomology; algebraically integrable Hamiltonian systems and moduli spaces; the stable topology of gauge theory, Morse-Floer theory; pseudo-convexity and its relations to symplectic geometry; generating functions; Frobenius manifolds and topological quantum field theory.

Author : Jan F. van Diejen,Luc Vinet
Publisher : Springer Science & Business Media
Page : 572 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461212065

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Calogero—Moser— Sutherland Models by Jan F. van Diejen,Luc Vinet Pdf

In the 1970s F. Calogero and D. Sutherland discovered that for certain potentials in one-dimensional systems, but for any number of particles, the Schrödinger eigenvalue problem is exactly solvable. Until then, there was only one known nontrivial example of an exactly solvable quantum multi-particle problem. J. Moser subsequently showed that the classical counterparts to these models is also amenable to an exact analytical approach. The last decade has witnessed a true explosion of activities involving Calogero-Moser-Sutherland models, and these now play a role in research areas ranging from theoretical physics (such as soliton theory, quantum field theory, string theory, solvable models of statistical mechanics, condensed matter physics, and quantum chaos) to pure mathematics (such as representation theory, harmonic analysis, theory of special functions, combinatorics of symmetric functions, dynamical systems, random matrix theory, and complex geometry). The aim of this volume is to provide an overview of the many branches into which research on CMS systems has diversified in recent years. The contributions are by leading researchers from various disciplines in whose work CMS systems appear, either as the topic of investigation itself or as a tool for further applications.

Author : S. Pakuliak,G. von Gehlen
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 46,5 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.

Author : Yitzhak Frishman,Jacob Sonnenschein
Publisher : Cambridge University Press
Page : 457 pages
File Size : 45,5 Mb
Release : 2023-07-31
Category : Science
ISBN : 9781009401647

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

Author : Anton Rebhan
Publisher : World Scientific
Page : 566 pages
File Size : 51,8 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814412544

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Strings, Gauge Fields, and the Geometry Behind by Anton Rebhan Pdf

This book contains exclusively invited contributions from collaborators of Maximilian Kreuzer, giving accounts of his scientific legacy and original articles from renowned theoretical physicists and mathematicians, including Victor Batyrev, Philip Candelas, Michael Douglas, Alexei Morozov, Joseph Polchinski, Peter van Nieuwenhuizen, and Peter West. Besides a collection of review and research articles from high-profile researchers in string theory and related fields of mathematics (in particular, algebraic geometry) which discuss recent progress in the exploration of string theory vacua and corresponding mathematical developments, this book contains a pedagogical account of the important work of Brandt, Dragon, and Kreuzer on classification of anomalies in gauge theories. This highly cited work, which is also quoted in the textbook of Steven Weinberg on quantum field theory, has not yet been presented in full detail except in private lecture notes by Norbert Dragon. Similarly, the software package PALP (Package for Analyzing Lattice Polytopes with applications to toric geometry), which has been incorporated in the SAGE (Software for Algebra and Geometry Experimentation) project, has not yet been documented in full detail. This book contains a user manual for a new thoroughly revised version of PALP. By including these two very useful original contributions, researchers in quantum field theory, string theory, and mathematics will find added value in a pedagogical presentation of the classification of quantum gauge field anomalies, and the accompanying comprehensive manual and tutorial for the powerful software package PALP.