Large Order Behaviour Of Perturbation Theory
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Large Order Behaviour Of Perturbation Theory
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Author : J.C. Le Guillou
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Large Order Behaviour Of Perturbation Theory written by J.C. Le Guillou and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.
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.
Large Order Behaviour Of Perturbation Theory
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Author : Jean-Claude Le Guillou
language : en
Publisher: North Holland
Release Date : 1990-01-01
Large Order Behaviour Of Perturbation Theory written by Jean-Claude Le Guillou and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Science categories.
Volume 7.
Graphs In Perturbation Theory
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Author : Michael Borinsky
language : en
Publisher: Springer
Release Date : 2018-11-04
Graphs In Perturbation Theory written by Michael Borinsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-04 with Science categories.
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.
Quantum Field Theory And Critical Phenomena
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Author : Jean Zinn-Justin
language : en
Publisher: Oxford University Press
Release Date : 2021-04-15
Quantum Field Theory And Critical Phenomena written by Jean Zinn-Justin and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-15 with Science categories.
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.
From Random Walks To Random Matrices
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Author : Jean Zinn-Justin
language : en
Publisher: Oxford University Press, USA
Release Date : 2019-06-27
From Random Walks To Random Matrices written by Jean Zinn-Justin and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-27 with Science categories.
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.
Mathematical Quantum Field Theory And Related Topics
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Author : Joel S. Feldman
language : en
Publisher: American Mathematical Soc.
Release Date : 1988
Mathematical Quantum Field Theory And Related Topics written by Joel S. Feldman 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 1988 with Science categories.
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.
Phase Transitions And Critical Phenomena
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Author :
language : en
Publisher: Elsevier
Release Date : 2000-09-21
Phase Transitions And Critical Phenomena written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-21 with Science categories.
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.
Field Theory Disorder And Simulations
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Author : Giorgio Parisi
language : en
Publisher: World Scientific
Release Date : 1992-10-09
Field Theory Disorder And Simulations written by Giorgio Parisi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-10-09 with Science categories.
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.
Continuous Advances In Qcd 2002 Arkadyfest Honoring The 60th Birthday Of Arkady Vainshtein Proceedings Of The Conference
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Author : Keith A Olive
language : en
Publisher: World Scientific
Release Date : 2002-12-16
Continuous Advances In Qcd 2002 Arkadyfest Honoring The 60th Birthday Of Arkady Vainshtein Proceedings Of The Conference written by Keith A Olive and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-16 with Science categories.
The symposium and workshop “Continuous Advances in QCD / Arkadyfest” 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.
Introduction To Quantum Mechanics
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Author : H. J. W. Mller-Kirsten
language : en
Publisher: World Scientific
Release Date : 2006
Introduction To Quantum Mechanics written by H. J. W. Mller-Kirsten and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Science categories.
After a consideration of basic quantum mechanics, this introduction aims at a side by side treatment of fundamental applications of the Schrdinger 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 Schrdinger 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.