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.

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 855 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.

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."

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.

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.

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 608 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.

Download or read book Spectral Methods in Quantum Field Theory written by Noah Graham and published by Springer Science & Business Media. This book was released on 2009-05-08 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph we apply scattering theory methods to calculations in quantum ?eld theory, with a particular focus on properties of the quantum vacuum. These methods will provide e?cient and reliable solutions to a - riety of problems in quantum ?eld theory. Our approach will also elucidate in a concrete context many of the subtleties of quantum ?eld theory, such as divergences, regularization, and renormalization, by connecting them to more familiar results in quantum mechanics. We will use tools of scattering theory to characterize the spectrum of energyeigenstatesinapotentialbackground,hencethetermspectralmethods. This mode spectrum comprises both discrete bound states and a continuum of scattering states. We develop a powerful formalism that parameterizes the e?ects of the continuum by the density of states, which we compute from scattering data. Summing the zero-point energies of these modes gives the energy of the quantum vacuum, which is one of the central quantities we study.Althoughthemostcommonlystudiedbackgroundpotentialsarisefrom static soliton solutions to the classical equations of motion, these methods are not limited to such cases.

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 374 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.

Download or read book Markov Chain Monte Carlo Methods in Quantum Field Theories written by Anosh Joseph and published by Springer Nature. This book was released on 2020-04-16 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer is a comprehensive collection of analytical and numerical techniques that can be used to extract the non-perturbative physics of quantum field theories. The intriguing connection between Euclidean Quantum Field Theories (QFTs) and statistical mechanics can be used to apply Markov Chain Monte Carlo (MCMC) methods to investigate strongly coupled QFTs. The overwhelming amount of reliable results coming from the field of lattice quantum chromodynamics stands out as an excellent example of MCMC methods in QFTs in action. MCMC methods have revealed the non-perturbative phase structures, symmetry breaking, and bound states of particles in QFTs. The applications also resulted in new outcomes due to cross-fertilization with research areas such as AdS/CFT correspondence in string theory and condensed matter physics. The book is aimed at advanced undergraduate students and graduate students in physics and applied mathematics, and researchers in MCMC simulations and QFTs. At the end of this book the reader will be able to apply the techniques learned to produce more independent and novel research in the field.

Download or read book Instantons and Large N written by and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Non perturbative Methods In Two Dimensional Quantum Field Theory written by Elcio Abdalla and published by World Scientific. This book was released on 1991-08-12 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Non perturbative Renormalization written by Vieri Mastropietro and published by World Scientific. This book was released on 2008 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providing a mathematical construction of models at low dimensions and discussing the removal of the ultraviolet and infrared cut-off, the verification of the axioms and the validity of Ward Identities with the relative anomalies. The second part is devoted to lattice 2D Statistical Physics, analyzing in particular the theory of universality in perturbed Ising models and the computation of the non-universal critical indices in Vertex or Ashkin-Teller models. Finally the third part is devoted to the analysis of complex quantum fluids showing Luttinger of Fermi liquid behavior, like the 1D or 2D Hubbard model.

Download or read book Nonperturbative Methods In Quantum Field Theory Proceedings Of The Workshop written by Andreas W Schreiber and published by World Scientific. This book was released on 1999-01-15 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the Workshop on Nonperturbative Methods in Quantum Field Theory, held in Adelaide, Australia, in February 1998. Lattice gauge theory and calculations based on the use of Schwinger-Dyson equations feature prominently, with further contributions in the areas of variational and functional techniques, strong interaction phenomenology and chiral perturbation theory. QCD in the infrared regime as well as QCD at finite temperatures and densities is the subject matter of a number of papers, while other authors explore chiral symmetry breaking in QCD as well as in other field theories.

Download or read book Conformal Field Theory written by Yavuz Nutku and published by CRC Press. This book was released on 2018-03-14 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an understanding of conformal field theory and its importance to both statistical mechanics and string theory. It introduces the Wess-Zumino-Novokov-Witten (WZNW) models and their current algebras, the affine Kac-Moody algebras.

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 186 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.

Download or read book No Nonsense Quantum Field Theory written by Jakob Schwichtenberg and published by No-Nonsense Books. This book was released on 2020-03-22 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learning quantum field theory doesn’t have to be hard What if there were a book that allowed you to see the whole picture and not just tiny parts of it? Thoughts like this are the reason that No-Nonsense Quantum Field Theory now exists. What will you learn from this book? Get to know all fundamental concepts — Grasp what a quantum field is, why we use propagators to describe its behavior, and how Feynman diagrams help us to make sense of field interactions. Learn to describe quantum field theory mathematically — Understand the meaning and origin of the most important equations: the Klein-Gordon equation, the Dirac equation, the Proca equation, the Maxwell equations, and the canonical commutation/anticommutation relations. Master important quantum field theory interactions — Read fully annotated, step-by-step calculations and understand the general algorithm we use to particle interactions. Get an understanding you can be proud of —Learn about advanced topics like renormalization and regularization, spontaneous symmetry breaking, the renormalization group equations, non-perturbative phenomena, and effective field models. No-Nonsense Quantum Field Theory is one the most student-friendly book on quantum field theory ever written. Here’s why. First of all, it's nothing like a formal university lecture. Instead, it’s like a casual conservation with a more experienced student. This also means that nothing is assumed to be “obvious” or “easy to see”. Each chapter, each section, and each page focuses solely on the goal to help you understand. Nothing is introduced without a thorough motivation and it is always clear where each equation comes from. The book ruthlessly focuses on the fundamentals and makes sure you’ll understand them in detail. The primary focus on the readers’ needs is also visible in dozens of small features that you won’t find in any other textbook In total, the book contains more than 100 illustrations that help you understand the most important concepts visually. In each chapter, you’ll find fully annotated equations and calculations are done carefully step-by-step. This makes it much easier to understand what’s going on. Whenever a concept is used that was already introduced previously there is a short sidenote that reminds you where it was first introduced and often recites the main points. In addition, there are summaries at the beginning of each chapter that make sure you won’t get lost.

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.