Nonperturbative Quantum Field Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 1461307295
Total Pages : 603 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Nonperturbative Quantum Field Theory by : G. Hooft

Download or read book Nonperturbative Quantum Field Theory written by G. Hooft and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Non-perturbative Quantum Field Theory: Mathematical Aspects And Applications

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Author :
Publisher : World Scientific
ISBN 13 : 9814506567
Total Pages : 854 pages
Book Rating : 4.8/5 (145 download)

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

Download or read book Non-perturbative Quantum Field Theory: Mathematical Aspects And Applications written by Jurg Frohlich and published by World Scientific. This book was released on 1992-04-29 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Non-Perturbative Foundations of Quantum Field Theory

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Author :
Publisher : OUP Oxford
ISBN 13 : 0191651346
Total Pages : 272 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis An Introduction to Non-Perturbative Foundations of Quantum Field Theory by : Franco Strocchi

Download or read book An Introduction to Non-Perturbative Foundations of Quantum Field Theory written by Franco Strocchi and published by OUP Oxford. This book was released on 2013-02-14 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Field Theory (QFT) has proved to be the most useful strategy for the description of elementary particle interactions and as such is regarded as a fundamental part of modern theoretical physics. In most presentations, the emphasis is on the effectiveness of the theory in producing experimentally testable predictions, which at present essentially means Perturbative QFT. However, after more than fifty years of QFT, we still are in the embarrassing situation of not knowing a single non-trivial (even non-realistic) model of QFT in 3+1 dimensions, allowing a non-perturbative control. As a reaction to these consistency problems one may take the position that they are related to our ignorance of the physics of small distances and that QFT is only an effective theory, so that radically new ideas are needed for a consistent quantum theory of relativistic interactions (in 3+1 dimensions). The book starts by discussing the conflict between locality or hyperbolicity and positivity of the energy for relativistic wave equations, which marks the origin of quantum field theory, and the mathematical problems of the perturbative expansion (canonical quantization, interaction picture, non-Fock representation, asymptotic convergence of the series etc.). The general physical principles of positivity of the energy, Poincare' covariance and locality provide a substitute for canonical quantization, qualify the non-perturbative foundation and lead to very relevant results, like the Spin-statistics theorem, TCP symmetry, a substitute for canonical quantization, non-canonical behaviour, the euclidean formulation at the basis of the functional integral approach, the non-perturbative definition of the S-matrix (LSZ, Haag-Ruelle-Buchholz theory). A characteristic feature of gauge field theories is Gauss' law constraint. It is responsible for the conflict between locality of the charged fields and positivity, it yields the superselection of the (unbroken) gauge charges, provides a non-perturbative explanation of the Higgs mechanism in the local gauges, implies the infraparticle structure of the charged particles in QED and the breaking of the Lorentz group in the charged sectors. A non-perturbative proof of the Higgs mechanism is discussed in the Coulomb gauge: the vector bosons corresponding to the broken generators are massive and their two point function dominates the Goldstone spectrum, thus excluding the occurrence of massless Goldstone bosons. The solution of the U(1) problem in QCD, the theta vacuum structure and the inevitable breaking of the chiral symmetry in each theta sector are derived solely from the topology of the gauge group, without relying on the semiclassical instanton approximation.

Non-Perturbative Field Theory

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Author :
Publisher : Cambridge University Press
ISBN 13 : 1139486489
Total Pages : 455 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Non-Perturbative Field Theory by : Yitzhak Frishman

Download or read book Non-Perturbative Field Theory written by Yitzhak Frishman and published by Cambridge University Press. This book was released on 2010-04-08 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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Publisher : Springer Science & Business Media
ISBN 13 : 0306471310
Total Pages : 327 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Nonperturbative Quantum Field Theory and the Structure of Matter by : T. Borne

Download or read book Nonperturbative Quantum Field Theory and the Structure of Matter written by T. Borne and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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 Description of Quantum Systems

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Publisher : Springer
ISBN 13 : 3319130064
Total Pages : 362 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Non-perturbative Description of Quantum Systems by : Ilya Feranchuk

Download or read book Non-perturbative Description of Quantum Systems written by Ilya Feranchuk and published by Springer. This book was released on 2014-12-18 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Instantons and Large N

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Publisher : Cambridge University Press
ISBN 13 : 1316368548
Total Pages : 381 pages
Book Rating : 4.3/5 (163 download)

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Book Synopsis Instantons and Large N by : Marcos Mariño

Download or read book Instantons and Large N written by Marcos Mariño and published by Cambridge University Press. This book was released on 2015-09-03 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This highly pedagogical textbook for graduate students in particle, theoretical and mathematical physics, explores advanced topics of quantum field theory. Clearly divided into two parts; the first focuses on instantons with a detailed exposition of instantons in quantum mechanics, supersymmetric quantum mechanics, the large order behavior of perturbation theory, and Yang–Mills theories, before moving on to examine the large N expansion in quantum field theory. The organised presentation style, in addition to detailed mathematical derivations, worked examples and applications throughout, enables students to gain practical experience with the tools necessary to start research. The author includes recent developments on the large order behavior of perturbation theory and on large N instantons, and updates existing treatments of classic topics, to ensure that this is a practical and contemporary guide for students developing their understanding of the intricacies of quantum field theory.

Quantum Chromodynamics

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Publisher : Cambridge University Press
ISBN 13 : 0521631483
Total Pages : 597 pages
Book Rating : 4.5/5 (216 download)

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Book Synopsis Quantum Chromodynamics by : B. L. Ioffe

Download or read book Quantum Chromodynamics written by B. L. Ioffe and published by Cambridge University Press. This book was released on 2010-01-21 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students and researchers in theoretical physics, this book presents the modern theory of strong interaction: quantum chromodynamics (QCD). The book exposes various perturbative and nonperturbative approaches to the theory, including chiral effective theory, the problems of anomalies, vacuum tunnel transitions, and the problem of divergence of the perturbative series. The QCD sum rules approach is exposed in detail. A great variety of hadronic properties (masses of mesons and baryons, magnetic moments, form factors, quark distributions in hadrons, etc.) have been found using this method. The evolution of hadronic structure functions is presented in detail, together with polarization phenomena. The problem of jets in QCD is treated through theoretical description and experimental observation. The connection with Regge theory is emphasized. The book covers many aspects of theory which are not discussed in other books, such as CET, QCD sum rules, and BFKL. • Provides a deep understanding of various aspects of the modern theory of strong interaction • Presents the general properties of QCD, before exploring perturbative and nonperturbative approaches • Discusses aspects of the theory such as CET, QCD sum rules, and BFKL, which are not covered in other books

Quantum Field Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 0387250980
Total Pages : 560 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Quantum Field Theory by : V. P. Nair

Download or read book Quantum Field Theory written by V. P. Nair and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum field theory, which started with Paul Dirac’s work shortly after the discovery of quantum mechanics, has produced an impressive and important array of results. Quantum electrodynamics, with its extremely accurate and well-tested predictions, and the standard model of electroweak and chromodynamic (nuclear) forces are examples of successful theories. Field theory has also been applied to a variety of phenomena in condensed matter physics, including superconductivity, superfluidity and the quantum Hall effect. The concept of the renormalization group has given us a new perspective on field theory in general and on critical phenomena in particular. At this stage, a strong case can be made that quantum field theory is the mathematical and intellectual framework for describing and understanding all physical phenomena, except possibly for a quantum theory of gravity. Quantum Field Theory: A Modern Perspective presents Professor Nair’s view of certain topics in field theory loosely knit together as it grew out of courses on field theory and particle physics taught at Columbia University and the City College of CUNY. The first few chapters, up to Chapter 12, contain material that generally goes into any course on quantum field theory, although there are a few nuances of presentation which readers may find to be different from other books. This first part of the book can be used for a general course on field theory, omitting, perhaps, the last three sections in Chapter 3, the last two in Chapter 8 and sections 6 and 7 in Chapter 10. The remaining chapters cover some of the more modern developments over the last three decades, involving topological and geometrical features. The introduction given to the mathematical basis of this part of the discussion is necessarily brief and should be accompanied by books on the relevant mathematical topics as indicated in the bibliography. Professor Nair also concentrates on developments pertinent to a better understanding of the standard model. There is no discussion of supersymmetry, supergravity, developments in field theory inspired by string theory, etc. There is also no detailed discussion of the renormalization group. Each of these topics would require a book in its own right to do justice to the topic. Quantum Field Theory: A Modern Perspective serves as a portal to so many more topics of detailed and ongoing research, referring readers to more detailed treatments for many specific topics. The book also contains extensive references, providing readers a more comprehensive perspective on the literature and the historical development of the subject. V. Parameswaran Nair is Professor of Physics at City College of The City University of New York (CUNY). Professor Nair has held Visiting Professorships at The Abdus Salam International Center for Theoretical Physics, Rockefeller University, Institute for Advanced Study at Princeton, and Massachusetts Institute of Technology.

Quantum Non-linear Sigma-Models

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Publisher : Springer Science & Business Media
ISBN 13 : 3662041928
Total Pages : 429 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Quantum Non-linear Sigma-Models by : Sergei V. Ketov

Download or read book Quantum Non-linear Sigma-Models written by Sergei V. Ketov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Non-perturbative Methods in 2 Dimensional Quantum Field Theory

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Publisher : World Scientific
ISBN 13 : 9812810153
Total Pages : 834 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Non-perturbative Methods in 2 Dimensional Quantum Field Theory by : Elcio Abdalla

Download or read book Non-perturbative Methods in 2 Dimensional Quantum Field Theory written by Elcio Abdalla and published by World Scientific. This book was released on 2001 with total page 834 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Fields; The Thirring Model; Determinants and Heat Kernels; Self-Interacting Fermionic Models; Nonlinear a Models: Classical Aspects; Nonlinear a Models OCo Quantum Aspects; Exact S-Matrices of 2D Models; The Wess-Zumino-Witten Theory; QED 2: Operator Approach; Quantum Chromodynamics; QED 2: Functional Approach; The Finite Temperature Schwinger Model; Non-Abelian Chiral Gauge Theories; Chiral Quantum Electrodynamics; Conformally Invariant Field Theory; Conformal Field Theory with Internal Symmetry; 2D Gravity and String-Related Topics. Readership: Graduate students and researchers in high energy and quantum physics."

Perturbative Algebraic Quantum Field Theory

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Publisher : Springer
ISBN 13 : 3319259016
Total Pages : 180 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Perturbative Algebraic Quantum Field Theory by : Kasia Rejzner

Download or read book Perturbative Algebraic Quantum Field Theory written by Kasia Rejzner and published by Springer. This book was released on 2016-03-16 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

What Is a Quantum Field Theory?

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Publisher : Cambridge University Press
ISBN 13 : 1108247113
Total Pages : 760 pages
Book Rating : 4.1/5 (82 download)

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Book Synopsis What Is a Quantum Field Theory? by : Michel Talagrand

Download or read book What Is a Quantum Field Theory? written by Michel Talagrand and published by Cambridge University Press. This book was released on 2022-03-17 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum field theory (QFT) is one of the great achievements of physics, of profound interest to mathematicians. Most pedagogical texts on QFT are geared toward budding professional physicists, however, whereas mathematical accounts are abstract and difficult to relate to the physics. This book bridges the gap. While the treatment is rigorous whenever possible, the accent is not on formality but on explaining what the physicists do and why, using precise mathematical language. In particular, it covers in detail the mysterious procedure of renormalization. Written for readers with a mathematical background but no previous knowledge of physics and largely self-contained, it presents both basic physical ideas from special relativity and quantum mechanics and advanced mathematical concepts in complete detail. It will be of interest to mathematicians wanting to learn about QFT and, with nearly 300 exercises, also to physics students seeking greater rigor than they typically find in their courses. Erratum for the book can be found at michel.talagrand.net/erratum.pdf.

Advanced Topics in Quantum Field Theory

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Publisher : Cambridge University Press
ISBN 13 : 0521190843
Total Pages : 641 pages
Book Rating : 4.5/5 (211 download)

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Book Synopsis Advanced Topics in Quantum Field Theory by : M. Shifman

Download or read book Advanced Topics in Quantum Field Theory written by M. Shifman and published by Cambridge University Press. This book was released on 2012-01-19 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devoted specifically to modern field theory, this is an indispensable book for graduate students and researchers in theoretical physics. It emphasizes nonperturbative phenomena and supersymmetry, and discusses various phases of gauge theories, extended objects and their quantization, and global supersymmetry from a modern perspective.

Nonequilibrium Quantum Field Theory

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Publisher : Cambridge University Press
ISBN 13 : 1009289985
Total Pages : 553 pages
Book Rating : 4.0/5 (92 download)

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Book Synopsis Nonequilibrium Quantum Field Theory by : Esteban A. Calzetta

Download or read book Nonequilibrium Quantum Field Theory written by Esteban A. Calzetta and published by Cambridge University Press. This book was released on 2023-01-31 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2008 book, reissued as OA, captures the essence of nonequilibrium quantum field theory, graduate students and researchers.

Modern Quantum Field Theory

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Publisher : Cambridge University Press
ISBN 13 : 1139473891
Total Pages : 323 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Modern Quantum Field Theory by : Tom Banks

Download or read book Modern Quantum Field Theory written by Tom Banks and published by Cambridge University Press. This book was released on 2008-09-18 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a variety of topics that are only briefly touched on in other texts, this book provides a thorough introduction to the techniques of field theory. Covering Feynman diagrams and path integrals, the author emphasizes the path integral approach, the Wilsonian approach to renormalization, and the physics of non-abelian gauge theory. It provides a thorough treatment of quark confinement and chiral symmetry breaking, topics not usually covered in other texts at this level. The Standard Model of particle physics is discussed in detail. Connections with condensed matter physics are explored, and there is a brief, but detailed, treatment of non-perturbative semi-classical methods. Ideal for graduate students in high energy physics and condensed matter physics, the book contains many problems,which help students practise the key techniques of quantum field theory.

Introduction to Quantum Fields on a Lattice

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Publisher : Cambridge University Press
ISBN 13 : 1009402749
Total Pages : 285 pages
Book Rating : 4.0/5 (94 download)

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Book Synopsis Introduction to Quantum Fields on a Lattice by : Jan Smit

Download or read book Introduction to Quantum Fields on a Lattice written by Jan Smit and published by Cambridge University Press. This book was released on 2023-07-31 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: