Quantum Non Linear Sigma Models

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Quantum Non Linear Sigma Models

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Author : Sergei V. Ketov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Quantum Non Linear Sigma Models written by Sergei V. Ketov 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 2013-03-09 with Science categories.

This is the first comprehensive presentation of the quantum non-linear sigma-models. The original papers consider in detail geometrical properties and renormalization of a generic non-linear sigma-model, illustrated by explicit multi-loop calculations in perturbation theory.

Quantum Non Linear Sigma Models

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Author : Sergei V. Ketov
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-09-14

Quantum Non Linear Sigma Models written by Sergei V. Ketov 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 2000-09-14 with Mathematics categories.

Offers a systematic presentation of the modern quantum field theory of non-linear sigma-models. These models are very popular in theoretical high energy physics, string theory, and statistical physics. The geometric and quantum renormalization properties of the most general non-linear sigma-models are considered in detail within the framework of quantum perturbation theory. The main applications to be considered in the book can be found in string theory, conformal field theory, and general relativity.

Interacting Electrons And Quantum Magnetism

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Author : Assa Auerbach
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Interacting Electrons And Quantum Magnetism written by Assa Auerbach 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.

In the excitement and rapid pace of developments, writing pedagogical texts has low priority for most researchers. However, in transforming my lecture l notes into this book, I found a personal benefit: the organization of what I understand in a (hopefully simple) logical sequence. Very little in this text is my original contribution. Most of the knowledge was collected from the research literature. Some was acquired by conversations with colleagues; a kind of physics oral tradition passed between disciples of a similar faith. For many years, diagramatic perturbation theory has been the major theoretical tool for treating interactions in metals, semiconductors, itiner ant magnets, and superconductors. It is in essence a weak coupling expan sion about free quasiparticles. Many experimental discoveries during the last decade, including heavy fermions, fractional quantum Hall effect, high temperature superconductivity, and quantum spin chains, are not readily accessible from the weak coupling point of view. Therefore, recent years have seen vigorous development of alternative, nonperturbative tools for handling strong electron-electron interactions. I concentrate on two basic paradigms of strongly interacting (or con strained) quantum systems: the Hubbard model and the Heisenberg model. These models are vehicles for fundamental concepts, such as effective Ha miltonians, variational ground states, spontaneous symmetry breaking, and quantum disorder. In addition, they are used as test grounds for various nonperturbative approximation schemes that have found applications in diverse areas of theoretical physics.

An Introduction To Two Dimensional Quantum Field Theory With 0 2 Supersymmetry

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Author : Ilarion V. Melnikov
language : en
Publisher: Springer
Release Date : 2019-02-11

An Introduction To Two Dimensional Quantum Field Theory With 0 2 Supersymmetry written by Ilarion V. Melnikov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-11 with Science categories.

This book introduces two-dimensional supersymmetric field theories with emphasis on both linear and non-linear sigma models. Complex differential geometry, in connection with supersymmetry, has played a key role in most developments of the last thirty years in quantum field theory and string theory. Both structures introduce a great deal of rigidity compared to the more general categories of non-supersymmetric theories and real differential geometry, allowing for many general conceptual results and detailed quantitative predictions. Two-dimensional (0,2) supersymmetric quantum field theories provide a natural arena for the fruitful interplay between geometry and quantum field theory. These theories play an important role in string theory and provide generalizations, still to be explored fully, of rich structures such as mirror symmetry. They also have applications to non-perturbative four-dimensional physics, for instance as descriptions of surface defects or low energy dynamics of solitonic strings in four-dimensional supersymmetric theories. The purpose of these lecture notes is to acquaint the reader with these fascinating theories, assuming a background in conformal theory, quantum field theory and differential geometry at the beginning graduate level. In order to investigate the profound relations between structures from complex geometry and field theory the text begins with a thorough examination of the basic structures of (0,2) quantum field theory and conformal field theory. Next, a simple class of Lagrangian theories, the (0,2) Landau-Ginzburg models, are discussed, together with the resulting renormalization group flows, dynamics, and symmetries. After a thorough introduction and examination of (0,2) non-linear sigma models, the text introduces linear sigma models that, in particular, provide a unified treatment of non-linear sigma models and Landau-Ginzburg theories. Many exercises, along with discussions of relevant mathematical notions and important open problems in the field, are included in the text.

Quantum Field Theory Of Many Body Systems

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Author : Xiao-Gang Wen
language : en
Publisher: OUP Oxford
Release Date : 2004-06-04

Quantum Field Theory Of Many Body Systems written by Xiao-Gang Wen and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-04 with Science categories.

For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been the emergence of a new paradigm associated with fractionalisation, topological order, emergent gauge bosons and fermions, and string condensation. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and fermions in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods (which have fuelled the rapid developments) in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature. Topics covered are dissipative quantum systems, boson condensation, symmetry breaking and gapless excitations, phase transitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological and quantum order, spin liquids, and string condensation. Methods covered are the path integral, Green's functions, mean-field theory, effective theory, renormalization group, bosonization in one- and higher dimensions, non-linear sigma-model, quantum gauge theory, dualities, slave-boson theory, and exactly soluble models beyond one-dimension. This book is aimed at teaching graduate students and bringing them to the frontiers of research in condensed matter physics.

Solitons In Field Theory And Nonlinear Analysis

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Author : Yisong Yang
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-15

Solitons In Field Theory And Nonlinear Analysis written by Yisong Yang 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 2001-06-15 with Mathematics categories.

There are two approaches in the study of differential equations of field theory. The first, finding closed-form solutions, works only for a narrow category of problems. Written by a well-known active researcher, this book focuses on the second, which is to investigate solutions using tools from modern nonlinear analysis.

Quantum Scaling In Many Body Systems

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Author : Mucio Continentino
language : en
Publisher: Cambridge University Press
Release Date : 2017-04-17

Quantum Scaling In Many Body Systems written by Mucio Continentino and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-17 with Science categories.

Focusing on experimental results, this updated edition approaches the problem of quantum phase transitions from a new and unifying perspective.

Yang Baxter Deformation Of 2d Non Linear Sigma Models

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Author : Kentaroh Yoshida
language : en
Publisher: Springer Nature
Release Date : 2021-06-03

Yang Baxter Deformation Of 2d Non Linear Sigma Models written by Kentaroh Yoshida and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-03 with Science categories.

In mathematical physics, one of the fascinating issues is the study of integrable systems. In particular, non-perturbative techniques that have been developed have triggered significant insight for real physics. There are basically two notions of integrability: classical integrability and quantum integrability. In this book, the focus is on the former, classical integrability. When the system has a finite number of degrees of freedom, it has been well captured by the Arnold–Liouville theorem. However, when the number of degrees of freedom is infinite, as in classical field theories, the integrable structure is enriched profoundly. In fact, the study of classically integrable field theories has a long history and various kinds of techniques, including the classical inverse scattering method, which have been developed so far. In previously published books, these techniques have been collected and well described and are easy to find in traditional, standard textbooks. One of the intriguing subjects in classically integrable systems is the investigation of deformations preserving integrability. Usually, it is not considered systematic to perform such a deformation, and one must study systems case by case and show the integrability of the deformed systems by constructing the associated Lax pair or action-angle variables. Recently, a new, systematic method to perform integrable deformations of 2D non-linear sigma models was developed. It was invented by C. Klimcik in 2002, and the integrability of the deformed sigma models was shown in 2008. The original work was done for 2D principal chiral models, but it has been generalized in various directions nowadays. In this book, the recent progress on this Yang–Baxter deformation is described in a pedagogical manner, including some simple examples. Applications of Yang–Baxter deformation to string theory are also described briefly.

Quantum Field Theory And Critical Phenomena

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Author : Jean Zinn-Justin
language : en
Publisher: Oxford University Press, USA
Release Date : 1993

Quantum Field Theory And Critical Phenomena written by Jean Zinn-Justin and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Language Arts & Disciplines categories.

Describes particle physics and critical phenomena in statistical mechanics in a unified framework, incorporating graduate lecture notes from the 1970s and 1980s at several universities in Europe and the US. Deals with general field theory, functional integrals, and functional methods; renormalization properties of theories with symmetries and specific applications to particle physics; lattice gauge theories and asymptotic freedom in four dimensions; and the role of instantons and the application of instanton calculus to the large-order behavior of perturbation theory and the problem of summation of the perturbative expansion. Several chapters close with exercise, solutions or hints for which are provided. No dates are noted for the previous editions. Annotation copyright by Book News, Inc., Portland, OR

Field Theories Of Condensed Matter Physics

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Author : Eduardo Fradkin
language : en
Publisher: Cambridge University Press
Release Date : 2013-02-28

Field Theories Of Condensed Matter Physics written by Eduardo Fradkin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-28 with Science categories.

Presenting the physics of the most challenging problems in condensed matter using the conceptual framework of quantum field theory, this book is of great interest to physicists in condensed matter and high energy and string theorists, as well as mathematicians. Revised and updated, this second edition features new chapters on the renormalization group, the Luttinger liquid, gauge theory, topological fluids, topological insulators and quantum entanglement. The book begins with the basic concepts and tools, developing them gradually to bring readers to the issues currently faced at the frontiers of research, such as topological phases of matter, quantum and classical critical phenomena, quantum Hall effects and superconductors. Other topics covered include one-dimensional strongly correlated systems, quantum ordered and disordered phases, topological structures in condensed matter and in field theory and fractional statistics.