Large Order Behaviour Of Perturbation Theory

Author : J.C. Le Guillou,J. Zinn-Justin
Publisher : Elsevier
Page : 595 pages
File Size : 45,5 Mb
Release : 2012-12-02
Category : Mathematics
ISBN : 9780444596208

Get Book

Large-Order Behaviour of Perturbation Theory by J.C. Le Guillou,J. Zinn-Justin Pdf

This volume is concerned with the determination of the behaviour of perturbation theory at large orders in quantum mechanics and quantum field theory, and its application to the problem of summation of perturbation series. Perturbation series in quantum field theory and in many quantum mechanics models are only asymptotic and thus diverge for all values of the expansion parameter. Their behaviour at large orders provides information about whether they define the theory uniquely (the problem of Borel summability). It suggests methods to extract numerical information from the series when the expansion parameter is not small. The articles reprinted here deal with the explicit evaluation of large-order behaviour in many quantum mechanics and field theory models. The large-order behaviour is related to barrier penetration effects for unphysical values of the expansion parameter, which can be calculated by WKB or instanton methods. The calculation of critical exponents of &fgr;4 field theory is presented as a practical application.

Author : Jean-Claude Le Guillou,Jean Zinn-Justin
Publisher : North Holland
Page : 580 pages
File Size : 41,6 Mb
Release : 1990-01-01
Category : Science
ISBN : 0444885978

Get Book

Large-order Behaviour of Perturbation Theory by Jean-Claude Le Guillou,Jean Zinn-Justin Pdf

Volume 7.

Author : Gustavo A. Arteca,Francisco M. Fernandez,Eduardo A. Castro
Publisher : Springer Science & Business Media
Page : 655 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642934698

Get Book

Large Order Perturbation Theory and Summation Methods in Quantum Mechanics by Gustavo A. Arteca,Francisco M. Fernandez,Eduardo A. Castro Pdf

The book provides a general, broad approach to aspects of perturbation theory. The aim has been to cover all topics of interest, from construction, analysis, and summation of perturbation series to applications. Emphasis is placed on simple methods, as well as clear, intuitive ideas stemming from the physics of systems of interest.

Author : Gustavo Alberto Arteca,Francisco M. Fernández,Eduardo Alberto Castro
Publisher : Springer Verlag
Page : 644 pages
File Size : 41,5 Mb
Release : 1990
Category : Science
ISBN : 0387528474

Get Book

Large Order Perturbation Theory and Summation Methods in Quantum Mechanics by Gustavo Alberto Arteca,Francisco M. Fernández,Eduardo Alberto Castro Pdf

Author : Jean Zinn-Justin
Publisher : Oxford University Press
Page : 1100 pages
File Size : 55,6 Mb
Release : 2021-04-15
Category : Science
ISBN : 9780192571618

Get Book

Quantum Field Theory and Critical Phenomena by Jean Zinn-Justin Pdf

Introduced as a quantum extension of Maxwell's classical theory, quantum electrodynamics has been the first example of a Quantum Field Theory (QFT). Eventually, QFT has become the framework for the discussion of all fundamental interactions at the microscopic scale except, possibly, gravity. More surprisingly, it has also provided a framework for the understanding of second order phase transitions in statistical mechanics. As this work illustrates, QFT is the natural framework for the discussion of most systems involving an infinite number of degrees of freedom with local couplings. These systems range from cold Bose gases at the condensation temperature (about ten nanokelvin) to conventional phase transitions (from a few degrees to several hundred) and high energy particle physics up to a TeV, altogether more than twenty orders of magnitude in the energy scale. Therefore, this text sets out to present a work in which the strong formal relations between particle physics and the theory of critical phenomena are systematically emphasized. This option explains some of the choices made in the presentation. A formulation in terms of field integrals has been adopted to study the properties of QFT. The language of partition and correlation functions has been used throughout, even in applications of QFT to particle physics. Renormalization and renormalization group properties are systematically discussed. The notion of effective field theory and the emergence of renormalisable theories are described. The consequences for fine tuning and triviality issue are emphasized. This fifth edition has been updated and fully revised, e.g. in particle physics with progress in neutrino physics and the discovery of the Higgs boson. The presentation has been made more homogeneous througout the volume, and emphasis has been put on the notion of effective field theory and discussion of the emergence of renormalisable theories.

Author : Harald J W Müller-Kirsten
Publisher : World Scientific Publishing Company
Page : 826 pages
File Size : 55,7 Mb
Release : 2006-03-03
Category : Science
ISBN : 9789813101876

Get Book

Introduction to Quantum Mechanics by Harald J W Müller-Kirsten Pdf

After a consideration of basic quantum mechanics, this introduction aims at a side by side treatment of fundamental applications of the Schrödinger equation on the one hand and the applications of the path integral on the other. Different from traditional texts and using a systematic perturbation method, the solution of Schrödinger equations includes also those with anharmonic oscillator potentials, periodic potentials, screened Coulomb potentials and a typical singular potential, as well as the investigation of the large order behavior of the perturbation series. On the path integral side, after introduction of the basic ideas, the expansion around classical configurations in Euclidean time, such as instantons, is considered, and the method is applied in particular to anharmonic oscillator and periodic potentials. Numerous other aspects are treated on the way, thus providing the reader an instructive overview over diverse quantum mechanical phenomena, e.g. many other potentials, Green's functions, comparison with WKB, calculation of lifetimes and sojourn times, derivation of generating functions, the Coulomb problem in various coordinates, etc. All calculations are given in detail, so that the reader can follow every step.

Author : Michael Borinsky
Publisher : Springer
Page : 173 pages
File Size : 55,5 Mb
Release : 2018-11-04
Category : Science
ISBN : 9783030035419

Get Book

Graphs in Perturbation Theory by Michael Borinsky Pdf

This book is the first systematic study of graphical enumeration and the asymptotic algebraic structures in perturbative quantum field theory. Starting with an exposition of the Hopf algebra structure of generic graphs, it reviews and summarizes the existing literature. It then applies this Hopf algebraic structure to the combinatorics of graphical enumeration for the first time, and introduces a novel method of asymptotic analysis to answer asymptotic questions. This major breakthrough has combinatorial applications far beyond the analysis of graphical enumeration. The book also provides detailed examples for the asymptotics of renormalizable quantum field theories, which underlie the Standard Model of particle physics. A deeper analysis of such renormalizable field theories reveals their algebraic lattice structure. The pedagogical presentation allows readers to apply these new methods to other problems, making this thesis a future classic for the study of asymptotic problems in quantum fields, network theory and far beyond.

Author : Jean Zinn-Justin
Publisher : Oxford University Press
Page : 544 pages
File Size : 55,7 Mb
Release : 2019-06-19
Category : Science
ISBN : 9780191091681

Get Book

From Random Walks to Random Matrices by Jean Zinn-Justin Pdf

Theoretical physics is a cornerstone of modern physics and provides a foundation for all modern quantitative science. It aims to describe all natural phenomena using mathematical theories and models, and in consequence develops our understanding of the fundamental nature of the universe. This books offers an overview of major areas covering the recent developments in modern theoretical physics. Each chapter introduces a new key topic and develops the discussion in a self-contained manner. At the same time the selected topics have common themes running throughout the book, which connect the independent discussions. The main themes are renormalization group, fixed points, universality, and continuum limit, which open and conclude the work. The development of modern theoretical physics has required important concepts and novel mathematical tools, examples discussed in the book include path and field integrals, the notion of effective quantum or statistical field theories, gauge theories, and the mathematical structure at the basis of the interactions in fundamental particle physics, including quantization problems and anomalies, stochastic dynamical equations, and summation of perturbative series.

Author : Joel S. Feldman,Lon M. Rosen,Université de Montréal. Centre de recherches mathématiques,Natural Sciences and Engineering Research Council Canada
Publisher : American Mathematical Soc.
Page : 280 pages
File Size : 53,5 Mb
Release : 1988
Category : Science
ISBN : 0821860143

Get Book

Mathematical Quantum Field Theory and Related Topics by Joel S. Feldman,Lon M. Rosen,Université de Montréal. Centre de recherches mathématiques,Natural Sciences and Engineering Research Council Canada Pdf

Suitable for researchers and advanced graduate students in mathematical physics, this book constitutes the proceedings of a conference on mathematical quantum field theory and related topics. The conference was held at the Centre de Recherches Matheematiques of the Universite de Montreal in September 1987.

Author : Giorgio Parisi
Publisher : World Scientific
Page : 518 pages
File Size : 51,7 Mb
Release : 1992
Category : Science
ISBN : 9810213565

Get Book

Field Theory, Disorder and Simulations by Giorgio Parisi Pdf

This volume is a collection of lectures and selected papers by Giorgio Parisi on the subjects of Field Theory (perturbative expansions, nonperturbative phenomena and phase transitions), Disordered Systems (mainly spin glasses) and Computer Simulations (lattice gauge theories).The basic problems discussed in the Field Theory section concern the interplay between perturbation theory and nonperturbative phenomena which are present when one deals with infrared or ultraviolet divergences or with nonconvergent perturbative expansions. The section on Disordered Systems contains a complete discussion about the replica method and its probabilistic interpretation, and also includes a short paper on multifractals. In the Simulations section, there is a series of lectures devoted to the study of quantum chromodynamics and a review paper on simulations in complex systems.The works of Giorgio Parisi have repeatedly displayed a remarkable depth of originality and innovation, and have paved the way for new research in many areas. This personal selection of his lectures and papers, complete with an original introduction by him, undoubtedly serves as a vital reference book for physicists and mathematicians working in these fields.

Author : Anonim
Publisher : Elsevier
Page : 517 pages
File Size : 45,7 Mb
Release : 2000-09-21
Category : Science
ISBN : 9780080538761

Get Book

Phase Transitions and Critical Phenomena by Anonim Pdf

The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results. It has moved into a central place in condensed matter studies.Statistical physics, and more specifically, the theory of transitions between states of matter, more or less defines what we know about 'everyday' matter and its transformations.The major aim of this serial is to provide review articles that can serve as standard references for research workers in the field, and for graduate students and others wishing to obtain reliable information on important recent developments.

Author : Keith A. Olive,Arkady Vainshtein,Mikhail A. Shifman
Publisher : World Scientific
Page : 660 pages
File Size : 55,8 Mb
Release : 2002
Category : Science
ISBN : 9789812776310

Get Book

Arkadyfest by Keith A. Olive,Arkady Vainshtein,Mikhail A. Shifman Pdf

The symposium and workshop OC Continuous Advances in QCD / ArkadyfestOCO was the fifth in the series of meetings organized by the William I Fine Theoretical Physics Institute at the University of Minnesota. This meeting brought together leading researchers in high-energy physics to exchange the latest ideas in QCD and gauge theories at strong coupling at large. It honored the 60th birthday of Professor Arkady Vainshtein, and the papers included in this proceedings volume also look back on the history of the subjects in which Arkady played such a central role: applications of PCAC, penguins, invisible axions, QCD sum rules, exact beta functions, condensates in supersymmetry, powerful heavy quark expansions, and new anomalies in 2D SUSY theories. The current status of these subjects was summarized in several excellent presentations that also outlined a historical perspective. A number of papers from leading researchers in the field present new developments and ideas in modern areas of study, such as the cosmological constant problem in extra-dimension theories, supersymmetric monopoles, solitons and confinement, AdS/CFT correspondence, and high density QCD. Contents: Perturbative and Nonperturbative QCD: Electromagnetic Form Factor of the Pion (H Leutwyler); Multiple Uses of the QCD Instantons (E V Shuryak); CP-Violation and Mixing in Charmed Mesons (A A Petrov); General Aspects of QCD and the Standard Model: Probing New Physics: From Charm to Superstrings (M K Gaillard); Dynamics of QCD in a Strong Magnetic Field (V A Miransky); On Mixed Phases in Gauge Theories (V L Chernyak); Gauge Dynamics at High Temperature and Density: What QCD Tells Us About Nature (F Wilczek); Domain Walls and Strings in Dense Quark Matter (A R Zhitnitsky); Topological Field Configurations, Dynamics in Supersymmetric Models, and Theoretical Issues: Non-Abelian Monopoles, Vortices and Confinement (K Konishi); Nonperturbative Solution of Supersymmetric Gauge Theories (J R Hiller); Testing ADS/CFT Correspondence with Wilson Loops (K Zarembo); Cosmology and Axions: Axions: Past, Present, and Future (M Srednicki); QCD Vacuum and Axions: What''s Happening? (G Gabadadze & M Shifman); Arkadyfest: Arkady in Siberia (E Shuryak); Of a Superior Breed (V Zelevinsky); Reminiscences in Pastels (M Shifman); and other papers. Readership: Graduate students and researchers in high-energy and theoretical physics."

Author : Karl Svozil
Publisher : World Scientific
Page : 331 pages
File Size : 41,9 Mb
Release : 2020-02-24
Category : Science
ISBN : 9789811208423

Get Book

Mathematical Methods Of Theoretical Physics by Karl Svozil Pdf

'This book could serve either as a good reference to remind students about what they have seen in their completed courses or as a starting point to show what needs more investigation. Svozil (Vienna Univ. of Technology) offers a very thorough text that leaves no mathematical area out, but it is best described as giving a synopsis of each application and how it relates to other areas … The text is organized well and provides a good reference list. Summing Up: Recommended. Upper-division undergraduates and graduate students.'CHOICEThis book contains very explicit proofs and demonstrations through examples for a comprehensive introduction to the mathematical methods of theoretical physics. It also combines and unifies many expositions of this subject, suitable for readers with interest in experimental and applied physics.

Author : P M Stevenson
Publisher : World Scientific
Page : 297 pages
File Size : 49,5 Mb
Release : 2022-03-21
Category : Science
ISBN : 9789811255700

Get Book

Renormalized Perturbation Theory And Its Optimization By The Principle Of Minimal Sensitivity by P M Stevenson Pdf

The results of renormalized perturbation theory, in QCD and other quantum field theories, are ambiguous at any finite order, due to renormalization-scheme dependence. The perturbative results depend upon extraneous scheme variables, including the renormalization scale, that the exact result cannot depend on. Such 'non-invariant approximations' occur in many other areas of physics, too. The sensible strategy is to find where the approximant is stationary under small variations of the extraneous variables. This general principle is explained and illustrated with various examples. Also dimensional transmutation, RG equations, the essence of renormalization and the origin of its ambiguities are explained in simple terms, assuming little or no background in quantum field theory. The minimal-sensitivity approach leads to 'optimized perturbation theory,' which is developed in detail. Applications to Re⁺e⁻, the infrared limit, and to the optimization of factorized quantities, are also discussed thoroughly.

Author : Zygmunt Ajduk,Andrzej Kajetan Wroblewski
Publisher : World Scientific
Page : 1878 pages
File Size : 55,8 Mb
Release : 1997-04-11
Category : Electronic
ISBN : 9789814547109

Get Book

Proceedings Of The 28th International Conference On High Energy Physics (In 2 Volumes) by Zygmunt Ajduk,Andrzej Kajetan Wroblewski Pdf

The 28th conference from the Rochester series was the major high energy physics conference in 1996. Volume one contains short reports on new theoretical and experimental results. Volume two consists of the review talks presented in the plenary sessions.