Non Perturbative Field Theory
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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.
Nonperturbative Quantum Field Theory
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Author : G. Hooft
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonperturbative Quantum Field Theory written by G. Hooft 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.
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 Field Theory
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Author : Yitzhak Frishman
language : en
Publisher: Cambridge University Press
Release Date : 2023-07-27
Non Perturbative Field Theory written by Yitzhak Frishman 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 2023-07-27 with Science categories.
Providing a new perspective on quantum field theory, this book gives a pedagogical exposition of non-perturbative methods in relativistic quantum field theory and introduces the reader to modern research in theoretical physics. After describing non-perturbative methods in detail, it uses these methods to explore two-dimensional and four-dimensional gauge dynamics. The book concludes with a summary emphasizing the interplay between two- and four-dimensional gauge theories. Aimed at graduate students and researchers, this book covers topics from two-dimensional conformal symmetry, affine Lie algebras, solitons, integrable models, bosonization, and 't Hooft model, to four-dimensional conformal invariance, integrability, large N expansion, Skyrme model, monopoles and instantons. Applications, first to simple field theories and gauge dynamics in two dimensions, and then to gauge theories in four dimensions and quantum chromodynamics in particular, are thoroughly described. Published originally in 2010, this title has been reissued as an Open Access publication on Cambridge Core.
Non Perturbative Methods In 2 Dimensional Quantum Field Theory
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Author : Elcio Abdalla
language : en
Publisher: World Scientific
Release Date : 1991
Non Perturbative Methods In 2 Dimensional Quantum Field Theory written by Elcio Abdalla and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Science categories.
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.
Nonperturbative Quantum Field Theory And The Structure Of Matter
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Author : T. Borne
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-19
Nonperturbative Quantum Field Theory And The Structure Of Matter written by T. Borne 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 2005-12-19 with Science categories.
"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 Field Theory
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Author : Yitzhak Frishman
language : en
Publisher: Cambridge University Press
Release Date : 2023-07-27
Non Perturbative Field Theory written by Yitzhak Frishman 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 2023-07-27 with Science categories.
Pedagogical exposition providing a new perspective on relativistic quantum field theory for graduate students and researchers.
Non Perturbative Renormalization
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Author : Vieri Mastropietro
language : en
Publisher: World Scientific
Release Date : 2008
Non Perturbative Renormalization written by Vieri Mastropietro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
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.
Basics Of Thermal Field Theory
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Author : Mikko Laine
language : en
Publisher: Springer
Release Date : 2016-06-09
Basics Of Thermal Field Theory written by Mikko Laine and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-09 with Science categories.
This book presents thermal field theory techniques, which can be applied in both cosmology and the theoretical description of the QCD plasma generated in heavy-ion collision experiments. It focuses on gauge interactions (whether weak or strong), which are essential in both contexts. As well as the many differences in the physics questions posed and in the microscopic forces playing a central role, the authors also explain the similarities and the techniques, such as the resummations, that are needed for developing a formally consistent perturbative expansion. The formalism is developed step by step, starting from quantum mechanics; introducing scalar, fermionic and gauge fields; describing the issues of infrared divergences; resummations and effective field theories; and incorporating systems with finite chemical potentials. With this machinery in place, the important class of real-time (dynamic) observables is treated in some detail. This is followed by an overview of a number of applications, ranging from the study of phase transitions and particle production rate computations, to the concept of transport and damping coefficients that play a ubiquitous role in current developments. The book serves as a self-contained textbook on relativistic thermal field theory for undergraduate and graduate students of theoretical high-energy physics.
Instantons And Large N
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Author : Marcos Mariño
language : en
Publisher: Cambridge University Press
Release Date : 2015-09-03
Instantons And Large N written by Marcos Mariño 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 2015-09-03 with Science categories.
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.
Ground States Of Quantum Field Models
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Author : Fumio Hiroshima
language : en
Publisher: Springer
Release Date : 2019-08-16
Ground States Of Quantum Field Models written by Fumio Hiroshima and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-16 with Science categories.
This book provides self-contained proofs of the existence of ground states of several interaction models in quantum field theory. Interaction models discussed here include the spin-boson model, the Nelson model with and without an ultraviolet cutoff, and the Pauli–Fierz model with and without dipole approximation in non-relativistic quantum electrodynamics. These models describe interactions between bose fields and quantum mechanical matters.A ground state is defined as the eigenvector associated with the bottom of the spectrum of a self-adjoint operator describing the Hamiltonian of a model. The bottom of the spectrum is however embedded in the continuum and then it is non-trivial to show the existence of ground states in non-perturbative ways. We show the existence of the ground state of the Pauli–Fierz mode, the Nelson model, and the spin-boson model, and several kinds of proofs of the existence of ground states are explicitly provided. Key ingredients are compact sets and compact operators in Hilbert spaces. For the Nelson model with an ultraviolet cutoff and the Pauli–Fierz model with dipole approximation we show not only the existence of ground states but also enhanced binding. The enhanced binding means that a system for zero-coupling has no ground state but it has a ground state after turning on an interaction.The book will be of interest to graduate students of mathematics as well as to students of the natural sciences who want to learn quantum field theory from a mathematical point of view. It begins with abstract compactness arguments in Hilbert spaces and definitions of fundamental facts of quantum field theory: boson Fock spaces, creation operators, annihilation operators, and second quantization. This book quickly takes the reader to a level where a wider-than-usual range of quantum field theory can be appreciated, and self-contained proofs of the existence of ground states and enhanced binding are presented.