Fundamental Problems Of Gauge Field Theory

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Fundamental Problems Of Gauge Field Theory

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Author : G. Velo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

Fundamental Problems Of Gauge Field Theory written by G. Velo 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 2013-11-11 with Mathematics categories.

The sixth Ettore Majorana International School of Mathematical Physics was held at the Centro della Cultura Scientifica Erice, Sicily, 1-14 July 1985. The present volume collects lecture notes on the ses sion which was devoted to Fundamental Problems of Gauge Field Theory. The School was a NATO Advanced Study Institute sponsored by the Italian Ministry of Public Education, the Italian Ministry of Scientific and Technological Research and the Regional Sicilian Government. As a result of the experimental and theoretical developments of the last two decades, gauge field theory, in one form or another, now pro vides the standard language for the description of Nature; QCD and the standard model of the electroweak interactions illustrate this point. It is a basic task of mathematical physics to provide a solid foundation for these developments by putting the theory in a physically transparent and mathematically rigorous form. The lectures and seminars of the school concentrated on the many unsolved problems which arise here, and on the general ideas and methods which have been proposed for their solution. In particular, we mention the use of rigorous renormalization group methods to obtain control over the continuum limit of lattice gauge field theories, the explora tion of the extraordinary enigmatic connections between Kac-Moody Virasoro algebras and string theory, and the systematic use of the theory of local algebras and indefinite metric spaces to classify the charged C* states in gauge field theories.

Fundamental Problems In Quantum Field Theory

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Author : Takehisa Fujita
language : en
Publisher: Bentham Science Publishers
Release Date : 2013-08-07

Fundamental Problems In Quantum Field Theory written by Takehisa Fujita and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-07 with Science categories.

Quantum physics is based on four fundamental interactions of electromagnetic, weak, gravitational and strong forces. All the interactions are expressed in terms of fermion and boson fields which can describe the quantum states of electrons, nucleons and photons in atoms or nuclei. Correct behaviors of these particles can now be described by the basic field theory terminology, and this textbook explains, for the first time, quantum field theory in a unifying method. At present, modern quantum theory is at a critical junction between different theories, and this textbook presents a clear description of fundamental quantum fields with a sound theoretical framework. No exotic theoretical concepts such as general relativity nor spontaneous symmetry breaking nor quantum anomaly are adopted in this textbook, and indeed all the observed physical quantities can be well understood within the standard field theory framework without introducing any non-physical particles or fields. From this textbook, readers will be guided through a concrete future direction of quantum field theory and will learn how the motion of electrons in any kind of material can be understood in terms of fields or state vectors. Readers will also learn about application of basic field theory in quantum chemistry, quantum biology and so on. Fundamental Problems in Quantum Field Theory is a handy resource for undergraduate and graduate students as well as supervisors involved in advanced courses in quantum physics.

Progress In Gauge Field Theory

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Author : G. 't Hooft
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Progress In Gauge Field Theory written by G. 't 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.

The importance of gauge theory for elementary particle physics is by now firmly established. Recent experiments have yielded convincing evidence for the existence of intermediate bosons, the carriers of the electroweak gauge force, as well as for the presence of gluons, the carriers of the strong gauge force, in hadronic interactions. For the gauge theory of strong interactions, however, a number of important theoretical problems remain to be definitely resolved. They include the quark confinement problem, the quantitative study of the hadron mass spectrum as well as the role of topology in quantum gauge field theory. These problems require for their solution the development and application of non-perturbative methods in quantum gauge field theory. These problems, and their non-perturbative analysis, formed the central interest of the 1983 Cargese summer institute on "Progress in Gauge Field Theory. " In this sense it was a natural sequel to the 1919 Cargese summer institute on "Recent Developments in Gauge Theories. " Lattice gauge theory provides a systematic framework for the investigation of non-perturbative quantum effects. Accordingly, a large number of lectures dealt with lattice gauge theory. Following a systematic introduction to the subject, the renormalization group method was developed both as a rigorous tool for fundamental questions, and in the block-spin formulation, the computations by Monte Carlo programs. A detailed analysis was presented of the problems encountered in computer simulations. Results obtained by this method on the mass spectrum were reviewed.

Chaos And Gauge Field Theory

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Author : T S Biró
language : en
Publisher: World Scientific
Release Date : 1995-03-07

Chaos And Gauge Field Theory written by T S Biró and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-07 with Science categories.

This book introduces a rapidly growing new research area — the study of dynamical properties of elementary fields. The methods used in this field range from algebraic topology to parallel computer programming. The main aim of this research is to understand the behavior of elementary particles and fields under extreme circumstances, first of all at high temperature and energy density generated in the largest accelerators of the world and supposed to be present in the early evolution of our Universe shortly after the Big Bang. In particular, chaos is rediscovered in a new appearance in these studies: in gauge theories the well-known divergence of initially adjacent phase space trajectories leads over into a quasi-thermal distribution of energy with a saturated average distance of different field configurations. This particular behavior is due to the compactness of the gauge group. Generally this book is divided into two main parts: the first part mainly deals with the “classical” discovery of chaos in gauge field theory while the second part presents methods and research achievements in recent years. One chapter is devoted entirely to the presentation and discussion of computational problems. The major theme, returning again and again throughout the book, is of course the phenomenon with a thousand faces — chaos itself. This book is intended to be a research book which introduces the reader to a new research field, presenting the basic new ideas in detail but just briefly touching on the problems of other related fields, like perturbative or lattice gauge theory, or dissipative chaos. The terminology of these related fields are, however, used. Exercises are also included in this book. They deepen the reader's understanding of special issues and at the same time offer more information on related problems. For the convenience of the fast reader, solutions are presented right after the problems. Contents:IntroductionChaotic DynamicsChaos in Gauge TheoryTopological Field TheoriesLattice Gauge TheoryHamiltonian Lattice Gauge TheoryComputing SU(2) Gauge TheoryChaos in Lattice Gauge TheoryApplications and ExtensionsBeyond the Classical TheoryChaos and Confinement Readership: Nonlinear scientists, high energy physicists, mathematicians and engineers. keywords:Non-Abelian Gauge Fields;Periodic Orbits;Lyapunov Exponents;Classical and Quantum Yang–Mills Mechanics;Higgs Mechanism;Self-Thermalization via Chaos;Chaos and Confinement;Quark-Gluon Plasma;Lattice Gauge Theory;Monte Carlo Methods;Physics;Field Theory;Chaos;Gauge;Lattice;Thermalization;Entropy;Computing “This book is a good place to approach the research area of chaos applied to gauge field theories.” Mathematical Reviews

Introduction To Gauge Field Theories

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Author : M. Chaichian
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Introduction To Gauge Field Theories written by M. Chaichian 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.

In recent years, gauge fields have attracted much attention in elementary par ticle physics. The reason is that great progress has been achieved in solving a number of important problems of field theory and elementary particle physics by means of the quantum theory of gauge fields. This refers, in particular, to constructing unified gauge models and theory of strong interactions between the elementary particles. This book expounds the fundamentals of the quantum theory of gauge fields and its application for constructing unified gauge models and the theory of strong interactions. In writing the book, the authors' aim was three-fold: firstly, to outline the basic ideas underlying the unified gauge models and the theory of strong inter actions; secondly, to discuss the major unified gauge models, the theory of strong interactions and their experimental implications; and, thirdly, to acquaint the reader with a rather special mathematical approach (path-in tegral method) which has proved to be well suited for constructing the quantum theory of gauge fields. Gauge fields are a vigorously developing area. In this book, we have select ed for presentation the more or less traditional and commonly accepted mate rial. There also exist a number of different approaches which are presently being developed. The most important of them are touched upon in the Conclusion.

Quantum Field Theory Iii Gauge Theory

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Author : Eberhard Zeidler
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-17

Quantum Field Theory Iii Gauge Theory written by Eberhard Zeidler 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 2011-08-17 with Mathematics categories.

In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).

Recent Developments In Gauge Theories

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Author : G. 't Hooft
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Recent Developments In Gauge Theories written by G. 't 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 2013-03-09 with Science categories.

Almost all theories of fundamental interactions are nowadays based on the gauge concept. Starting with the historical example of quantum electrodynamics, we have been led to the successful unified gauge theory of weak and electromagnetic interactions, and finally to a non abelian gauge theory of strong interactions with the notion of permanently confined quarks. The. early theoretical work on gauge theories was devoted to proofs of renormalizability, investigation of short distance behaviour, the discovery of asymptotic freedom, etc . . , aspects which were accessible to tools extrapolated from renormalised perturbation theory. The second phase of the subject is concerned with the problem of quark confinement which necessitates a non-perturbative understanding of gauge theories. This phase has so far been marked by the introduc tion of ideas from geometry, topology and statistical mechanics in particular the theory of phase transitions. The 1979 Cargese Institute on "Recent Developments on Gauge Theories" was devoted to a thorough discussion of these non-perturbative, global aspects of non-abelian gauge theories. In the lectures and seminars reproduced in this volume the reader wilf find detailed reports on most of the important developments of recent times on non perturbative gauge fields by some of the leading experts and innovators in this field. Aside from lectures on gauge fields proper, there were lectures on gauge field concepts in condensed matter physics and lectures by mathematicians on global aspects of the calculus of variations, its relation to geometry and topology, and related topics.

Gauge Theories As A Problem Of Constructive Quantum Field Theory And Statistical Mechanics

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Author : Erhard Seiler
language : en
Publisher: Springer
Release Date : 1982

Gauge Theories As A Problem Of Constructive Quantum Field Theory And Statistical Mechanics written by Erhard Seiler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Science categories.

Gauge Theories Of Fundamental Interactions

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Author : Marek Pawłowski
language : en
Publisher: World Scientific Publishing Company
Release Date : 1990

Gauge Theories Of Fundamental Interactions written by Marek Pawłowski and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Science categories.

The 23 review lectures in this volume were presented by prominent specialists in the field. The scope is wide: major trends in gauge field theory and its applications are covered. A considerable part of the articles contain previously unpublished results.

Gauge Fields And Strings

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Author : Polyakov
language : en
Publisher: Routledge
Release Date : 2018-05-02

Gauge Fields And Strings written by Polyakov and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-02 with Mathematics categories.

Based on his own work, the author synthesizes the most promising approaches and ideals in field theory today. He presents such subjects as statistical mechanics, quantum field theory and their interrelation, continuous global symmetry, non-Abelian gauge fields, instantons and the quantam theory of loops, and quantum strings and random surfaces. This book is aimed at postgraduate students studying field theory and statistical mechanics, and for research workers in continuous global theory.