Non Perturbative Quantum Field Theory Mathematical Aspects And Applications

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Non-perturbative Quantum Field Theory: Mathematical Aspects And Applications

Jurg Frohlich
Non perturbative Quantum Field Theory Mathematical Aspects And Applications Book PDF

Author : Jurg Frohlich
Publisher : World Scientific
Page : 854 pages
File Size : 43,7 Mb
Release : 1992-04-29
Category : Electronic
ISBN : 9789814506564

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Non-perturbative Quantum Field Theory: Mathematical Aspects And Applications by Jurg Frohlich Pdf

Compiled to illustrate the recent history of Quantum Field Theory and its trends, this collection of selected reprints by Jürg Fröhlich, a leading theoretician in the field, is a comprehensive guide of the more mathematical aspects of the subject. Results and methods of the past fifteen years are reviewed. The analytical methods employed are non-perturbative and, for the larger part, mathematically rigorous. Most articles are review articles surveying certain important developments in quantum field theory and guiding the reader towards the original literature.The volume begins with a comprehensive introduction by Jürg Fröhlich.The theory of phase transitions and continuous symmetry breaking is reviewed in the first section. The second section discusses the non-perturbative quantization of topological solitons. The third section is devoted to the study of gauge fields. A paper on the triviality of λϖ4 — theory in four and more dimensions is found in the fourth section, while the fifth contains two articles on “random geometry”. The sixth and final part addresses topics in low-dimensional quantum field theory, including braid statistics, two-dimensional conformal field theory and an application to condensed matter theory.

Non-perturbative Quantum Field Theory

Jürg Fröhlich
Non perturbative Quantum Field Theory Book PDF

Author : Jürg Fröhlich
Publisher : World Scientific Publishing Company Incorporated
Page : 841 pages
File Size : 47,9 Mb
Release : 1992
Category : Science
ISBN : 9810204329

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Non-perturbative Quantum Field Theory by Jürg Fröhlich Pdf

Compiled to illustrate the recent history of Quantum Field Theory and its trends, this collection of selected reprints by Jürg Fröhlich, a leading theoretician in the field, is a comprehensive guide of the more mathematical aspects of the subject. Results and methods of the past fifteen years are reviewed. The analytical methods employed are non-perturbative and, for the larger part, mathematically rigorous. Most articles are review articles surveying certain important developments in quantum field theory and guiding the reader towards the original literature.The volume begins with a comprehensive introduction by Jürg Fröhlich.The theory of phase transitions and continuous symmetry breaking is reviewed in the first section. The second section discusses the non-perturbative quantization of topological solitons. The third section is devoted to the study of gauge fields. A paper on the triviality of λϖ4 — theory in four and more dimensions is found in the fourth section, while the fifth contains two articles on “random geometry”. The sixth and final part addresses topics in low-dimensional quantum field theory, including braid statistics, two-dimensional conformal field theory and an application to condensed matter theory.

Mathematical Aspects of Quantum Field Theories

Damien Calaque,Thomas Strobl
Mathematical Aspects of Quantum Field Theories Book PDF

Author : Damien Calaque,Thomas Strobl
Publisher : Springer
Page : 572 pages
File Size : 51,9 Mb
Release : 2015-01-06
Category : Science
ISBN : 9783319099491

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Mathematical Aspects of Quantum Field Theories by Damien Calaque,Thomas Strobl Pdf

Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.

Perturbative Algebraic Quantum Field Theory

Kasia Rejzner
Perturbative Algebraic Quantum Field Theory Book PDF

Author : Kasia Rejzner
Publisher : Springer
Page : 180 pages
File Size : 45,9 Mb
Release : 2016-03-16
Category : Science
ISBN : 9783319259017

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Perturbative Algebraic Quantum Field Theory by Kasia Rejzner Pdf

Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn’t require the use of divergent quantities and works on a large class of Lorenzian manifolds. We discuss in detail the examples of scalar fields, gauge theories and the effective quantum gravity. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all, of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses effective quantum gravity. The book aims to be accessible to researchers and graduate students, who are interested in the mathematical foundations of pQFT.

Nonperturbative Quantum Field Theory

G. Hooft,A. Jaffe,G. Mack,P.K. Mitter,R. Stora
Nonperturbative Quantum Field Theory Book PDF

Author : G. Hooft,A. Jaffe,G. Mack,P.K. Mitter,R. Stora
Publisher : Springer Science & Business Media
Page : 603 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461307297

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Nonperturbative Quantum Field Theory by G. Hooft,A. Jaffe,G. Mack,P.K. Mitter,R. Stora Pdf

During the past 15 years, quantum field theory and classical statistical mechanics have merged into a single field, and the need for nonperturbative methods for the description of critical phenomena in statistical mechanics as well as for problems in elementary particle physics are generally acknowledged. Such methods formed the central theme of the 1987 Cargese Advanced Study Institut. e on "Nonpert. urbat. ive Quantum Field Theory." The use of conformal symmet. ry has been of central interest in recent years, and was a main subject at. t. he ASI. Conformal invariant quantum field theory describes statistical mechanical systems exactly at a critical point, and can be analysed to a remarkable ext. ent. by group t. heoretical methods. Very strong results have been obtained for 2-dimensional systems. Conformal field theory is also the basis of string theory, which offers some hope of providing a unified t. heory of all interactions between elementary particles. Accordingly, a number of lectures and seminars were presented on these two topics. After syst. ematic introductory lectures, conformal field theory on Riemann surfaces, orbifolds, sigma models, and application of loop group theory and Grassmannians were discussed, and some ideas on modular geometry were presented. Other lectures combined' traditional techniques of constructive quant. um field theory with new methods such as the use of index-t. heorems and infinite dimensional (Kac Moody) symmetry groups. The problems encountered in a quantum mechanical description of black holes were discussed in detail.

Mathematical Aspects of Quantum Field Theory

Edson de Faria,Welington de Melo
Mathematical Aspects of Quantum Field Theory Book PDF

Author : Edson de Faria,Welington de Melo
Publisher : Unknown
Page : 312 pages
File Size : 43,9 Mb
Release : 2010
Category : Field theory (Physics)
ISBN : 0511912900

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Mathematical Aspects of Quantum Field Theory by Edson de Faria,Welington de Melo Pdf

Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.

An Introduction to the Mathematical Structure of Quantum Mechanics

F. Strocchi
An Introduction to the Mathematical Structure of Quantum Mechanics Book PDF

Author : F. Strocchi
Publisher : World Scientific
Page : 193 pages
File Size : 50,8 Mb
Release : 2008
Category : Science
ISBN : 9789812835222

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An Introduction to the Mathematical Structure of Quantum Mechanics by F. Strocchi Pdf

Arising out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students, this book formulates the mathematical structure of QM in terms of the C*-algebra of observables, which is argued on the basis of the operational definition of measurements and the duality between states and observables.

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 : 55,5 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.

Nonperturbative Quantum Field Theory and the Structure of Matter

T. Borne,G. Lochak,H. Stumpf
Nonperturbative Quantum Field Theory and the Structure of Matter Book PDF

Author : T. Borne,G. Lochak,H. Stumpf
Publisher : Springer Science & Business Media
Page : 327 pages
File Size : 53,8 Mb
Release : 2006-04-11
Category : Science
ISBN : 9780306471315

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Nonperturbative Quantum Field Theory and the Structure of Matter by T. Borne,G. Lochak,H. Stumpf Pdf

"This book, which presents a new view of quantum field theory, may serve as a research monograph and an alternative textbook examining topics which are not usually treated in conventional works." "Audience: This volume will appeal to researchers concerned with the foundation of the theory of matter and forces including gravitation. It will also be interesting to those working with quantum field theoretic methods in various disciplines, such as particle physics, nuclear physics, condensed mater physics, and relativity."--Jacket.

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 : 41,6 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.

Non-Perturbative Methods in 2 Dimensional Quantum Field Theory

Elcio Abdalla,Maria Cristina Batoni Abdalla,Klaus Dieter Rothe
Non Perturbative Methods in 2 Dimensional Quantum Field Theory Book PDF

Author : Elcio Abdalla,Maria Cristina Batoni Abdalla,Klaus Dieter Rothe
Publisher : World Scientific
Page : 836 pages
File Size : 41,7 Mb
Release : 2001-07-31
Category : Science
ISBN : 9789814491228

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Non-Perturbative Methods in 2 Dimensional Quantum Field Theory by Elcio Abdalla,Maria Cristina Batoni 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. Contents:Free FieldsThe Thirring ModelDeterminants and Heat KernelsSelf-Interacting Fermionic ModelsNonlinear σ Models: Classical AspectsNonlinear σ Models — Quantum AspectsExact S-Matrices of 2D ModelsThe Wess-Zumino-Witten TheoryQED2: Operator ApproachQuantum ChromodynamicsQED2: Functional ApproachThe Finite Temperature Schwinger ModelNon-Abelian Chiral Gauge TheoriesChiral Quantum ElectrodynamicsConformally Invariant Field TheoryConformal Field Theory with Internal Symmetry2D Gravity and String-Related Topics Readership: Graduate students and researchers in high energy and quantum physics. Keywords:Reviews:“… there are carefully written chapters on the Thirring, Gross-Neveu, and nonlinear Sigma models, as well as the sine-Gordon and Wess-Zumino-Witten theory … In particular, the last three chapters might be of interest to those who work in string theory, in view of the recently discovered AdS/CFT correspondence.”Mathematics Abstracts

An Introduction to Non-Perturbative Foundations of Quantum Field Theory

Franco Strocchi
An Introduction to Non Perturbative Foundations of Quantum Field Theory Book PDF

Author : Franco Strocchi
Publisher : Oxford University Press
Page : 270 pages
File Size : 40,8 Mb
Release : 2013-02-14
Category : Science
ISBN : 9780199671571

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An Introduction to Non-Perturbative Foundations of Quantum Field Theory by Franco Strocchi Pdf

The book discusses fundamental aspects of Quantum Field Theory and of Gauge theories, with attention to mathematical consistency. Basic issues of the standard model of elementary particles (Higgs mechanism and chiral symmetry breaking in quantum Chromodynamics) are treated without relying on the perturbative expansion and on instanton calculus.

Non-perturbative Description of Quantum Systems

Ilya Feranchuk,Alexey Ivanov,Van-Hoang Le,Alexander Ulyanenkov
Non perturbative Description of Quantum Systems Book PDF

Author : Ilya Feranchuk,Alexey Ivanov,Van-Hoang Le,Alexander Ulyanenkov
Publisher : Springer
Page : 362 pages
File Size : 53,6 Mb
Release : 2014-12-18
Category : Science
ISBN : 9783319130064

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Non-perturbative Description of Quantum Systems by Ilya Feranchuk,Alexey Ivanov,Van-Hoang Le,Alexander Ulyanenkov Pdf

This book introduces systematically the operator method for the solution of the Schrödinger equation. This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique compared with other non-perturbative methods due to its ability to deliver in zeroth approximation the uniformly suitable estimate for both ground and excited states of quantum system. The method has been generalized for the application to quantum statistics and quantum field theory. In this book, the numerous applications of operator method for various physical systems are demonstrated. Simple models are used to illustrate the basic principles of the method which are further used for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.

Nonperturbative Quantum-field-theoretic Methods and Their Applications

Z. Horv th,L. Palla
Nonperturbative Quantum field theoretic Methods and Their Applications Book PDF

Author : Z. Horv th,L. Palla
Publisher : World Scientific
Page : 474 pages
File Size : 50,7 Mb
Release : 2001
Category : Science
ISBN : 9812799966

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Nonperturbative Quantum-field-theoretic Methods and Their Applications by Z. Horv th,L. Palla Pdf

Contents: Conformal Boundary Conditions OCo and What They Teach Us (V B Petkova & J-B Zuber); A Physical Basis for the Entropy of the AdS 3 Black Hole (S Fernando & F Mansouri); Spinon Formulation of the Kondo Problem (A Klmper & J R Reyes-Martinez); Boundary Integrable Quantum Field Theories (P Dorey); Finite Size Effects in Integrable Quantum Field Theories (F Ravanini); Nonperturbative Analysis of the Two-Frequency Sine-Gordon Model (Z Bajnok et al.); Screening in Hot SU(2) Gauge Theory and Propagators in 3D Adjoint Higgs Model (A Cucchieri et al.); Effective Average Action in Statistical Physics and Quantum Field Theory (Ch Wetterich); Phase Transitions in Non-Hermitean Matrix Models and the OC Single RingOCO Theorem (J Feinberg et al.); Unraveling the Mystery of Flavor (A Falk); The Nahm Transformation on R 2 X T 2 (C Ford); A 2D Integrable Axion Model and Target Space Duality (P Forgics); Supersymmetric Ward Identities and Chiral Symmetry Breaking in SUSY QED (M L Walker); and other papers. Readership: Theoretical, mathematical and high energy physicists."

Non-Perturbative Methods in Two-Dimensional Quantum Field Theory

E Abdalla,M B Abdalla,D Rothe
Non Perturbative Methods in Two Dimensional Quantum Field Theory Book PDF

Author : E Abdalla,M B Abdalla,D Rothe
Publisher : World Scientific
Page : 748 pages
File Size : 41,6 Mb
Release : 1991-08-12
Category : Science
ISBN : 9789814506519

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Non-Perturbative Methods in Two-Dimensional Quantum Field Theory by E Abdalla,M B Abdalla,D Rothe Pdf

This book is a survey of methods used in the study of two-dimensional models in quantum field theory as well as applications of these theories in physics. It covers the subject since the first model, studied in the fifties, up to modern developments in string theories, and includes exact solutions, non-perturbative methods of study, and nonlinear sigma models. Contents:Free FieldsThe Thirring ModelFunctional DeterminantsFermionic Models with Self-InteractionNonlinear Sigma Models — Classical AspectsNonlinear Sigma Models — Quantum AspectsExact S-Matrices of Two-Dimensional ModelsThe Wess-Zumino-Witten TheoryElectrodynamics: Operator ApproachQuantum ChromodynamicsQuantum Electrodynamics: Functional ApproachNon-Abelian Chiral Gauge TheoriesChiral Quantum ElectrodynamicsConformally Invariant Field Theory in Two Dimensions Readership: High energy physicists. keywords:Bosonization;Solitons;Instantons;Functional Determinants;Cosets;Ising Model;Kac Moody Algebras;Finite Temperature;Spontaneous Symmetry Breaking;Conformal “The authors have made a great effort to present in a careful and systematic way such a complete treatise for the benefit of non-specialists. This book is thus of great value to students and research physicists interested in two-dimensional quantum field theory. Numerous (15) useful appendices help the reader to understand and rederive the results at will, making the book self-contained.” Jean-Pierre Ader Mathematical Reviews