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
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Author : S. Pakuliak
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integrable Structures Of Exactly Solvable Two Dimensional Models Of Quantum Field Theory written by S. Pakuliak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Handbook Of Teichm Ller Theory
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Author : Athanase Papadopoulos
language : en
Publisher: European Mathematical Society
Release Date : 2007
Handbook Of Teichm Ller Theory written by Athanase Papadopoulos and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
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.
An Invitation To Noncommutative Geometry
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Author : Masoud Khalkhali
language : en
Publisher: World Scientific
Release Date : 2008
An Invitation To Noncommutative Geometry written by Masoud Khalkhali and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
A walk in the noncommutative garden / A. Connes and M. Marcolli -- Renormalization of noncommutative quantum field theory / H. Grosse and R. Wulkenhaar -- Lectures on noncommutative geometry / M. Khalkhali -- Noncommutative bundles and instantons in Tehran / G. Landi and W. D. van Suijlekom -- Lecture notes on noncommutative algebraic geometry and noncommutative tori / S. Mahanta -- Lectures on derived and triangulated categories / B. Noohi -- Examples of noncommutative manifolds: complex tori and spherical manifolds / J. Plazas -- D-branes in noncommutative field theory / R. J. Szabo.
From Representation Theory To Mathematical Physics And Back
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Author : Mikhail Khovanov
language : en
Publisher: American Mathematical Society
Release Date : 2025-05-14
From Representation Theory To Mathematical Physics And Back written by Mikhail Khovanov and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-14 with Mathematics categories.
This volume is a proceedings of a workshop at the Simons Center for Geometry and Physics from May 31– June 4, 2022. The workshop highlighted progress in the areas of vertex operator algebras, conformal field theory, categorification, low dimensional topology and representation theory of affine Lie algebras, loop groups, and quantum groups. In the past 40 years, string theory gave rise to the mathematical theory of vertex operator algebras, which led to the construction of representations of affine Lie algebras and the Moonshine module of the Monster group. These mathematical constructions have in turn led to ideas about 3-dimensional quantum gravity. In another direction, the discovery of the Jones polynomial led to a physical construction of 3-dimensional topological quantum field theories (TQFTs), which in turn advanced many mathematical developments in quantum groups and low dimensional topology. Louis Crane and Igor Frenkel introduced the categorification program with the goal of upgrading 3-dimensional TQFTs coming from representation theory of quantum groups to 4-dimensional TQFTs. This idea gave rise to the development of link homologies constructed from representation-theoretic, algebraic-geometric, combinatorial, and physical structures. Articles in this volume present both classical and new results related to these topics. They will be interesting to researchers and graduate students working in mathematical aspects of modern quantum field theory.
Geometric Representation Theory And Gauge Theory
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Author : Alexander Braverman
language : en
Publisher: Springer Nature
Release Date : 2019-11-22
Geometric Representation Theory And Gauge Theory written by Alexander Braverman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-22 with Mathematics categories.
This book offers a review of the vibrant areas of geometric representation theory and gauge theory, which are characterized by a merging of traditional techniques in representation theory with the use of powerful tools from algebraic geometry, and with strong inputs from physics. The notes are based on lectures delivered at the CIME school "Geometric Representation Theory and Gauge Theory" held in Cetraro, Italy, in June 2018. They comprise three contributions, due to Alexander Braverman and Michael Finkelberg, Andrei Negut, and Alexei Oblomkov, respectively. Braverman and Finkelberg’s notes review the mathematical theory of the Coulomb branch of 3D N=4 quantum gauge theories. The purpose of Negut’s notes is to study moduli spaces of sheaves on a surface, as well as Hecke correspondences between them. Oblomkov's notes concern matrix factorizations and knot homology. This book will appeal to both mathematicians and theoretical physicists and will be a source of inspiration for PhD students and researchers.
Encyclopedia Of Nonlinear Science
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Author : Alwyn Scott
language : en
Publisher: Routledge
Release Date : 2006-05-17
Encyclopedia Of Nonlinear Science written by Alwyn Scott and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-17 with Reference categories.
In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.
Partitions Q Series And Modular Forms
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Author : Krishnaswami Alladi
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-01
Partitions Q Series And Modular Forms written by Krishnaswami Alladi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-01 with Mathematics categories.
Partitions, q-Series, and Modular Forms contains a collection of research and survey papers that grew out of a Conference on Partitions, q-Series and Modular Forms at the University of Florida, Gainesville in March 2008. It will be of interest to researchers and graduate students that would like to learn of recent developments in the theory of q-series and modular and how it relates to number theory, combinatorics and special functions.
Asymptotic Combinatorics With Application To Mathematical Physics
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Author : V.A. Malyshev
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Combinatorics With Application To Mathematical Physics written by V.A. Malyshev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
New and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.
Energy Research Abstracts
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Author :
language : en
Publisher:
Release Date : 1995
Energy Research Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Power resources categories.
New Dualities Of Supersymmetric Gauge Theories
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Author : Jörg Teschner
language : en
Publisher: Springer
Release Date : 2015-11-17
New Dualities Of Supersymmetric Gauge Theories written by Jörg Teschner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-17 with Science categories.
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.