Random Walks Critical Phenomena And Triviality In Quantum Field Theory
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Random Walks Critical Phenomena And Triviality In Quantum Field Theory
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Author : Roberto Fernandez
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Random Walks Critical Phenomena And Triviality In Quantum Field Theory written by Roberto Fernandez 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 2013-03-14 with Science categories.
Simple random walks - or equivalently, sums of independent random vari ables - have long been a standard topic of probability theory and mathemat ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk,were introduced into theoretical polymer physics, and gradu ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the results obtained by random-walk methods are the proof of triviality of the cp4 quantum field theo ryin space-time dimension d (::::) 4, and the proof of mean-field critical behavior for cp4 and Ising models in space dimension d (::::) 4. The principal goal of the present monograph is to present a detailed review of these developments. It is supplemented by a brief excursion to the theory of random surfaces and various applications thereof. This book has grown out of research carried out by the authors mainly from 1982 until the middle of 1985. Our original intention was to write a research paper. However, the writing of such a paper turned out to be a very slow process, partly because of our geographical separation, partly because each of us was involved in other projects that may have appeared more urgent.
Non Perturbative Quantum Field Theory Mathematical Aspects And Applications
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Author : Jurg Frohlich
language : en
Publisher: World Scientific
Release Date : 1992-04-29
Non Perturbative Quantum Field Theory Mathematical Aspects And Applications written by Jurg Frohlich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-04-29 with categories.
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 : Franco Strocchi
language : en
Publisher: OUP Oxford
Release Date : 2013-02-14
An Introduction To Non Perturbative Foundations Of Quantum Field Theory written by Franco Strocchi and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-14 with Science categories.
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.
Introduction To A Renormalisation Group Method
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Author : Roland Bauerschmidt
language : en
Publisher: Springer Nature
Release Date : 2019-10-16
Introduction To A Renormalisation Group Method written by Roland Bauerschmidt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-16 with Science categories.
This is a primer on a mathematically rigorous renormalisation group theory, presenting mathematical techniques fundamental to renormalisation group analysis such as Gaussian integration, perturbative renormalisation and the stable manifold theorem. It also provides an overview of fundamental models in statistical mechanics with critical behaviour, including the Ising and φ4 models and the self-avoiding walk. The book begins with critical behaviour and its basic discussion in statistical mechanics models, and subsequently explores perturbative and non-perturbative analysis in the renormalisation group. Lastly it discusses the relation of these topics to the self-avoiding walk and supersymmetry. Including exercises in each chapter to help readers deepen their understanding, it is a valuable resource for mathematicians and mathematical physicists wanting to learn renormalisation group theory.
Progress In High Dimensional Percolation And Random Graphs
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Author : Markus Heydenreich
language : en
Publisher: Springer
Release Date : 2017-11-22
Progress In High Dimensional Percolation And Random Graphs written by Markus Heydenreich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
This text presents an engaging exposition of the active field of high-dimensional percolation that will likely provide an impetus for future work. With over 90 exercises designed to enhance the reader’s understanding of the material, as well as many open problems, the book is aimed at graduate students and researchers who wish to enter the world of this rich topic. The text may also be useful in advanced courses and seminars, as well as for reference and individual study. Part I, consisting of 3 chapters, presents a general introduction to percolation, stating the main results, defining the central objects, and proving its main properties. No prior knowledge of percolation is assumed. Part II, consisting of Chapters 4–9, discusses mean-field critical behavior by describing the two main techniques used, namely, differential inequalities and the lace expansion. In Parts I and II, all results are proved, making this the first self-contained text discussing high-dime nsional percolation. Part III, consisting of Chapters 10–13, describes recent progress in high-dimensional percolation. Partial proofs and substantial overviews of how the proofs are obtained are given. In many of these results, the lace expansion and differential inequalities or their discrete analogues are central. Part IV, consisting of Chapters 14–16, features related models and further open problems, with a focus on the big picture.
Spectral Theory And Mathematical Physics A Festschrift In Honor Of Barry Simon S 60th Birthday
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Author : Fritz Gesztesy
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Spectral Theory And Mathematical Physics A Festschrift In Honor Of Barry Simon S 60th Birthday written by Fritz Gesztesy and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This Festschrift had its origins in a conference called SimonFest held at Caltech, March 27-31, 2006, to honor Barry Simon's 60th birthday. It is not a proceedings volume in the usual sense since the emphasis of the majority of the contributions is on reviews of the state of the art of certain fields, with particular focus on recent developments and open problems. The bulk of the articles in this Festschrift are of this survey form, and a few review Simon's contributions to aparticular area. Part 1 contains surveys in the areas of Quantum Field Theory, Statistical Mechanics, Nonrelativistic Two-Body and $N$-Body Quantum Systems, Resonances, Quantum Mechanics with Electric and Magnetic Fields, and the Semiclassical Limit. Part 2 contains surveys in the areas of Random andErgodic Schrodinger Operators, Singular Continuous Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory. In several cases, this collection of surveys portrays both the history of a subject and its current state of the art. A substantial part of the contributions to this Festschrift are survey articles on the state of the art of certain areas with special emphasis on open problems. This will benefit graduate students as well as researchers who want to get a quick, yet comprehensiveintroduction into an area covered in this volume.
Statistical Mechanics Of Lattice Systems
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Author : Sacha Friedli
language : en
Publisher: Cambridge University Press
Release Date : 2017-11-23
Statistical Mechanics Of Lattice Systems written by Sacha Friedli 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 2017-11-23 with Mathematics categories.
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Sojourns In Probability Theory And Statistical Physics I
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Author : Vladas Sidoravicius
language : en
Publisher: Springer Nature
Release Date : 2019-10-17
Sojourns In Probability Theory And Statistical Physics I written by Vladas Sidoravicius and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-17 with Mathematics categories.
Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II. Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.
Random Magnetism High Temperature Superconductivity Proceedings Of T Raymond L Orbach Inauguration Symposium
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Author : Nai-li Haung Liu
language : en
Publisher: World Scientific
Release Date : 1994-10-25
Random Magnetism High Temperature Superconductivity Proceedings Of T Raymond L Orbach Inauguration Symposium written by Nai-li Haung Liu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-25 with categories.
On 19 March 1993, Raymond L. Orbach was inaugurated as the eighth Chancellor of the University of California, Riverside. In connection with this occasion, a two-day scientific symposium was held. Invited and contributed papers were presented on subjects related to 2 vital areas of condensed-matter physics in which Chancellor Orbach has made seminal contributions: the effects of disorder on magnetic behavior, and the theory of high-temperature superconductivity. The papers in this book, many of which are by outstanding contributors to these important fields, give an up-to-date overview of recent progress.
Poincar Seminar 2002
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Author : Vincent Rivasseau
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-04-24
Poincar Seminar 2002 written by Vincent Rivasseau 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 2003-04-24 with Science categories.
The Poincaré Seminar is held twice a year at the Institut Henri Poincaré in Paris. This volume contains the lectures of the 2002 seminars. The main topic of the first one was the vacuum energy, in particular the Casimir effect and the nature of the cosmological constant. The second one concentrated on renormalization, giving a comprehensive account of its mathematical structure and applications to high energy physics, statistical mechanics and classical mechanics. Students will find excellent introductions to the subjects with further lectures leading to the frontiers of experimental and theoretical research, scientists will profit from contributions by outstanding experts.