Solitons and Instantons in High Energy Physics

Author: Erick J. Weinberg

Publisher: Cambridge University Press

ISBN: 0521114632

Category: Science

Page: 326

View: 6654

Overview of classical solutions and their consequences in quantum field theory, high energy physics and cosmology for graduates and researchers.
Read More

Author: Albert S. Schwarz

Publisher: Springer Science & Business Media

ISBN: 366202943X

Category: Mathematics

Page: 276

View: 1141

In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. It has many applications, first of all in quantum field theory, but increasingly also in other areas of physics. The main focus of this book is on the results of quantum field theory that are obtained by topological methods. Some aspects of the theory of condensed matter are also discussed. Part I is an introduction to quantum field theory: it discusses the basic Lagrangians used in the theory of elementary particles. Part II is devoted to the applications of topology to quantum field theory. Part III covers the necessary mathematical background in summary form. The book is aimed at physicists interested in applications of topology to physics and at mathematicians wishing to familiarize themselves with quantum field theory and the mathematical methods used in this field. It is accessible to graduate students in physics and mathematics.
Read More

Author: Valery Rubakov

Publisher: Princeton University Press

ISBN: 9781400825097

Category: Science

Page: 456

View: 9259

Based on a highly regarded lecture course at Moscow State University, this is a clear and systematic introduction to gauge field theory. It is unique in providing the means to master gauge field theory prior to the advanced study of quantum mechanics. Though gauge field theory is typically included in courses on quantum field theory, many of its ideas and results can be understood at the classical or semi-classical level. Accordingly, this book is organized so that its early chapters require no special knowledge of quantum mechanics. Aspects of gauge field theory relying on quantum mechanics are introduced only later and in a graduated fashion--making the text ideal for students studying gauge field theory and quantum mechanics simultaneously. The book begins with the basic concepts on which gauge field theory is built. It introduces gauge-invariant Lagrangians and describes the spectra of linear perturbations, including perturbations above nontrivial ground states. The second part focuses on the construction and interpretation of classical solutions that exist entirely due to the nonlinearity of field equations: solitons, bounces, instantons, and sphalerons. The third section considers some of the interesting effects that appear due to interactions of fermions with topological scalar and gauge fields. Mathematical digressions and numerous problems are included throughout. An appendix sketches the role of instantons as saddle points of Euclidean functional integral and related topics. Perfectly suited as an advanced undergraduate or beginning graduate text, this book is an excellent starting point for anyone seeking to understand gauge fields.
Read More

Author: Voja Radovanovic

Publisher: Springer Science & Business Media

ISBN: 9783540770145

Category: Science

Page: 243

View: 3280

The Problem Book in Quantum Field Theory contains about 200 problems with solutions or hints that help students to improve their understanding and develop skills necessary for pursuing the subject. It deals with the Klein-Gordon and Dirac equations, classical field theory, canonical quantization of scalar, Dirac and electromagnetic fields, the processes in the lowest order of perturbation theory, renormalization and regularization. The solutions are presented in a systematic and complete manner. The material covered and the level of exposition make the book appropriate for graduate and undergraduate students in physics, as well as for teachers and researchers.
Read More

Author: Andreas Knauf

Publisher: Springer-Verlag

ISBN: 3662557762

Category: Science

Page: 652

View: 1365

Als Grenztheorie der Quantenmechanik besitzt die klassische Dynamik einen großen Formenreichtum – vom gut berechenbaren bis zum chaotischen Verhalten. Ausgehend von interessanten Beispielen wird in dem Band nicht nur eine gelungene Auswahl grundlegender Themen vermittelt, sondern auch der Einstieg in viele aktuelle Forschungsgebiete im Bereich der klassischen Mechanik. Didaktisch geschickt aufgebaut und mit hilfreichen Anhängen versehen, werden lediglich Kenntnisse der Grundvorlesungen in Mathematik vorausgesetzt. Mit über 100 Aufgaben und Lösungen.
Read More

Field Theoretical Approach and Related Topics

Author: Zyun Francis Ezawa

Publisher: World Scientific

ISBN: 9812700323

Category: Science

Page: 706

View: 5276

A pedagogical and self-contained discussion on monolayer and bilayer quantum Hall systems is given in this volume in a field-theoretical framework, with an introduction to quantum field theory, anyon physics and Chem-Simons gauge theory.
Read More

Author: L Mangiarotti,G Sardanashvily

Publisher: World Scientific

ISBN: 9814501409

Category: Science

Page: 516

View: 5274

Geometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models in field theory and mechanics. This book is an encyclopaedia of modern geometric methods in theoretical physics. It collects together the basic mathematical facts about various types of connections, and provides a detailed exposition of relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental fields. The authors have tried to give all the necessary mathematical background, thus making the book self-contained. This book should be useful to graduate students, physicists and mathematicians who are interested in the issue of deep interrelations between theoretical physics and geometry. keywords:Lagrangian Field Theory;Hamiltonian Field Theory;Classical Mechanics;BRST Formalism;Topological Field Theories;Non-Commutative Geometry;Theoretical Physics;Mathematical Physics;Fibre Bundle;Connection;Jet Manifold;Gauge Theory;Gravitation;Theory;Quantum Field;Geometric Quantization;Supergeometry;BRST;Theory “this book certainly offers a valuable supplement to the existing literature on the impact of connection theory on theoretical physics.” Mathematical Reviews
Read More

Author: R. J. Rivers

Publisher: Cambridge University Press

ISBN: 9780521368704

Category: Science

Page: 339

View: 4875

The applications of functional integral methods introduced in this text for solving a range of problems in quantum field theory will prove useful for students and researchers in theoretical physics and quantum field theory.
Read More

Author: Poul Henrik Damgaard,Jerzy Jurkiewicz

Publisher: Springer Science & Business Media

ISBN: 0306470756

Category: Science

Page: 364

View: 6958

Quantum field theory is one of most central constructions in 20th century th- retical physics, and it continues to develop rapidly in many different directions. The aim of the workshop “New Developments in Quantum Field Theory”, which was held in Zakopane, Poland, June 14-20, 1997, was to capture a broad selection of the most recent advances in this field. The conference was sponsored by the Scientific and - vironmental Affairs Division of NATO, as part of the Advanced Research Workshop series. This book contains the proceedings of that meeting. Major topics covered at the workshop include quantized theories of gravity, string theory, conformal field theory, cosmology, field theory approaches to critical phenomena and the renormalization group, matrix models, and field theory techniques applied to the theory of turbulence. One common theme at the conference was the use of large-Nmatrix models to obtain exact results in a variety of different disciplines. For example, it has been known for several years that by taking a suitable double-scaling limit, certain string theories (or two-dimensional quantum gravity coupled to matter) can be re-obtained from the large-Nexpansion of matrix models. There continues to be a large activity in this area of research, which was well reflected by talks given at our workshop. Remarkably, large- Nmatrix models have very recently – just a few months before our meeting – been shown to have yet another deep relation to string theory.
Read More

From Spin Systems to 2-dimensional Gravity

Author: E. Br‚zin,Spenta R. Wadia

Publisher: World Scientific

ISBN: 9789810204563

Category: Science

Page: 1130

View: 302

This book contains an edited comprehensive collection of reprints on the subject of the large N limit as applied to a wide spectrum of problems in quantum field theory and statistical mechanics. The topics include (1) Spin Systems; (2) Large N Limit of Gauge Theories; (3) Two-Dimensional QCD; (4) Exact Results on Planar Perturbation Series and the Nature of the 1/N Series; (5) Schwinger-Dyson Equations Approach; (6) QCD Phenomenological Lagrangians and the Large N Limit; (7) Other Approaches to Large N: Eguchi-Kawai Model, Collective Fields and Numerical Methods; (8) Matrix Models; (9) Two-Dimensional Gravity and String Theory.
Read More

Author: R. S. Ward,Raymond O. Wells, Jr

Publisher: Cambridge University Press

ISBN: 9780521422680

Category: Mathematics

Page: 520

View: 4925

This book deals with the twistor treatment of certain linear and non-linear partial differential equations. The description in terms of twistors involves algebraic and differential geometry, algebraic topology and results in a new perspective on the properties of space and time. The authors firstly develop the mathematical background, then go on to discuss Yang-Mills fields and gravitational fields in classical language, and in the final part a number of field-theoretic problems are solved. Issued here for the first time in paperback, this self-contained volume should be of use to graduate mathematicians and physicists and research workers in theoretical physics, relativity, and cosmology.
Read More

Author: Wolfgang Krull

Publisher: Springer-Verlag

ISBN: 3642870333

Category: Mathematics

Page: 160

View: 9259

Read More

Author: Daniel S. Freed,Karen K. Uhlenbeck,American Mathematical Society,Institute for Advanced Study (Princeton, N.J.)

Publisher: American Mathematical Soc.

ISBN: 9780821886830

Category: Science

Page: 459

View: 796

The first title in a new series, this book explores topics from classical and quantum mechanics and field theory. The material is presented at a level between that of a textbook and research papers making it ideal for graduate students. The book provides an entree into a field that promises to remain exciting and important for years to come.
Read More

A Reprint Volume from Physics Reports

Author: J L Gervais,M Jacob

Publisher: World Scientific

ISBN: 9814518891

Category: Science

Page: 522

View: 7983

Contents: Extended Systems in Field Theory :Introduction (J-L Gervais and A Neveu)Vortices and Quark Confinement in Non-Abelian Gauge Theories (S Mandelstam)Magnetic and Electric Confinement of Quarks (Y Nambu)Examples of Four-Dimensional Soliton Solutions and Abnormal Nuclear States (T D Lee)Classical Solution in the Massive Thirring Model (S-J Chang)Semiclassical Quantization Methods in Field Theory (A Neveu)The Quantum Theory of Solitons and Other Non-Linear Classical Waves (R Jackiw)Collective Coordinate Method for Quantization of Extended Systems (J-L Gervais, A Jevicki and B Sakita)Quantum Expansion of Soliton Solutions (N H Christ)Hartree-Type Approximation Applied to a ϕ4 Field Theory (S-J Chang)Soliton Operators for the Quantized Sine–Gordon Equation (S Mandelstam)Classical Aspects and Fluctuation-Behaviour of Two Dimensional Models in Statistical Mechanics and Many Body Physics (B Schroer)Quarks on a Lattice, or, the Colored String Model (K G Wilson)New Ideas about Confinement (L Susskind and J Kogut)Gauge Fields on a Lattice (C Itzykson)Non-Perturbative Aspects in Quantum Field Theory:Self-Dual Solutions to Euclidean Yang–Mills Equations (E Corrigan)An Introduction to the Twistor Programme (J Madore, J L Richard and R Stora)Collective Coordinates with Non-Trivial Dynamics (J-L Gervais)A Theory of the Strong Interactions (D J Gross)Magneticmonopoles (D Olive)Dynamical and Topological Considerations on Quark Confinement (F Englert and P Windey)Difficulties in Fixing the Gauge in Non-Abelian Gauge Theories (S Sciuto)Indeterminate-Mass Particles (B M Mccoy and T T Wu)Duality for Discrete Lattice Gauge Fields (C Itzykson)Large Order Estimates in Perturbation Theory (J Zinn-Justin)The Borel Transform and the Renormalization Group (G Parisi)Planar Diagrams (E Brezin)Exact S-Matrices and Form Factors in 1 + 1 Dimensional Field Theoretic Models with Soliton Behaviour (M Karowski)Topology and Higher Symmetries of the Two-Dimensional Nonlinear σ Model (A D'adda, M Luscher and P Di Vecchia)Two-Dimensional Yang–Mills Theory in the Leading 1/N Expansion (T T Wu)Superfluidity and the Two-Dimensional XY Model' (D R Nelson)Bosonized Fermions in Three Dimensions (A Luther)Symmetry and Topology Concepts for Spin Glasses and Other Glasses (G Toulouse)Common Trends in Particle and Condensed Matter Physics:Introduction to Localization(D J Thouless)Conductivity Scaling and Localization(E Abrahams)Disordered Electronic System as a Model of Interacting Matrices(F Wegner)Status Report on Spin Glasses (Not Included in this Report)(S Kirkpatrick)Mean Field Theory for Spin Glasses(G Parisi)The Random Energy Model(B Derrida)Towards a Mean Field Theory of Spin Glasses: the Tap Route Revisited (C De Dominicis)On the Connection Between Spin Glasses and Gauge Field Theories(G Toulouse, J Vannimenus)Monte Carlo Simulations of Lattice Gauge Theories(C Rebbi)Large Dimension Expansions and Transition Patterns in Lattice Gauge Theories(J-M Drouffe)Progress in Lattice Gauge Theory(J B Kogut)Phase Structure of the Z(2) Gauge and Matter Theory(D Horn)General Introduction to Confinement(S Mandelstam)A Simple Picture of the Weak-to-Strong Coupling Transition in Quantum Chromodynamics(C G Callan Jr.)Quantum Fluctuations in a Multiinstanton Background(B A Berg)Some Comments on the Crossover Between Strong and Weak Coupling in Su(2) Pure Yang–Mills Theory(J Frohlich)String Dynamics in QCD (J-L Gervais, A Neveu)Dual Models and Strings: The Critical Dimension(C B Thorn: )Duality and Finite Size Effects in Six Vertex Models(C.B. Thorn: )Scaling at a Bifurcation Point(M Nauenberg, D Scalapino)Some Implications of a Cosmological Phase Transition(T W B Kibble) Readership: Graduate students and researchers in particle physics andcondensed matter physics.
Read More

Author: George Sterman

Publisher: Cambridge University Press

ISBN: 9780521311328

Category: Science

Page: 572

View: 5756

This is a systematic presentation of Quantum Field Theory from first principles, emphasizing both theoretical concepts and experimental applications. Starting from introductory quantum and classical mechanics, this book develops the quantum field theories that make up the "Standard Model" of elementary processes. It derives the basic techniques and theorems that underly theory and experiment, including those that are the subject of theoretical development. Special attention is also given to the derivations of cross sections relevant to current high-energy experiments and to perturbative quantum chromodynamics, with examples drawn from electron-positron annihilation, deeply inelastic scattering and hadron-hadron scattering. The first half of the book introduces the basic ideas of field theory. The discussion of mathematical issues is everywhere pedagogical and self contained. Topics include the role of internal symmetry and relativistic invariance, the path integral, gauge theories and spontaneous symmetry breaking, and cross sections in the Standard Model and the parton model. The material of this half is sufficient for an understanding of the Standard Model and its basic experimental consequences. The second half of the book deals with perturbative field theory beyond the lowest-order approximation. The issues of renormalization and unitarity, the renormalization group and asymptotic freedom, infrared divergences in quantum electrodynamics and infrared safety in quantum chromodynamics, jets, the perturbative basis of factorization at high energy and the operator product expansion are discussed. Exercises are included for each chapter, and several appendices complement the text.
Read More