Classical Theory of Gauge Fields

Classical Theory of Gauge Fields

Author: Valery Rubakov

Publisher: Princeton University Press

Published: 2009-02-09

Total Pages: 456

ISBN-13: 1400825091

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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.


Book Synopsis Classical Theory of Gauge Fields by : Valery Rubakov

Download or read book Classical Theory of Gauge Fields written by Valery Rubakov and published by Princeton University Press. This book was released on 2009-02-09 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Theory of Gauge Fields in Four Dimensions

The Theory of Gauge Fields in Four Dimensions

Author: H. Blaine Lawson

Publisher: American Mathematical Soc.

Published: 1985

Total Pages: 112

ISBN-13: 0821807080

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Presents an examination of the work of Simon Donaldson. This book offers foundation work in gauge theory (Uhlenbeck, Taubes, Atiyah, Hitchin, Singer, et al.) which underlies Donaldson's work. It is suitable for geometric topologists and differential geometers.


Book Synopsis The Theory of Gauge Fields in Four Dimensions by : H. Blaine Lawson

Download or read book The Theory of Gauge Fields in Four Dimensions written by H. Blaine Lawson and published by American Mathematical Soc.. This book was released on 1985 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an examination of the work of Simon Donaldson. This book offers foundation work in gauge theory (Uhlenbeck, Taubes, Atiyah, Hitchin, Singer, et al.) which underlies Donaldson's work. It is suitable for geometric topologists and differential geometers.

Gauge Fields and Strings

Gauge Fields and Strings

Author: A. M. Polyakov

Publisher: Routledge

Published: 2018-05-02

Total Pages: 312

ISBN-13: 1351446096

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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.


Book Synopsis Gauge Fields and Strings by : A. M. Polyakov

Download or read book Gauge Fields and Strings written by A. M. Polyakov and published by Routledge. This book was released on 2018-05-02 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Gauge Field Theories

Gauge Field Theories

Author: Mike Guidry

Publisher: John Wiley & Sons

Published: 2008-07-11

Total Pages: 620

ISBN-13: 3527617361

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Acquaints readers with the main concepts and literature of elementary particle physics and quantum field theory. In particular, the book is concerned with the elaboration of gauge field theories in nuclear physics; the possibility of creating fundamental new states of matter such as an extended quark-gluon plasma in ultra-relativistic heavy ion collisions; and the relation of gauge theories to the creation and evolution of the universe. Divided into three parts, it opens with an introduction to the general principles of relativistic quantum field theory followed by the essential ingredients of gauge fields for weak and electromagnetic interactions, quantum chromodynamics and strong interactions. The third part is concerned with the interface between modern elementary particle physics and "applied disciplines" such as nuclear physics, astrophysics and cosmology. Includes references and numerous exercises.


Book Synopsis Gauge Field Theories by : Mike Guidry

Download or read book Gauge Field Theories written by Mike Guidry and published by John Wiley & Sons. This book was released on 2008-07-11 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acquaints readers with the main concepts and literature of elementary particle physics and quantum field theory. In particular, the book is concerned with the elaboration of gauge field theories in nuclear physics; the possibility of creating fundamental new states of matter such as an extended quark-gluon plasma in ultra-relativistic heavy ion collisions; and the relation of gauge theories to the creation and evolution of the universe. Divided into three parts, it opens with an introduction to the general principles of relativistic quantum field theory followed by the essential ingredients of gauge fields for weak and electromagnetic interactions, quantum chromodynamics and strong interactions. The third part is concerned with the interface between modern elementary particle physics and "applied disciplines" such as nuclear physics, astrophysics and cosmology. Includes references and numerous exercises.

Gauge Field Theories

Gauge Field Theories

Author: Paul H. Frampton

Publisher: John Wiley & Sons

Published: 2008-09-08

Total Pages: 353

ISBN-13: 3527623361

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The first edition of this necessary reading for cosmologists and particle astrophysicists was quickly adopted by universities and other institutions of higher learning around the world. And with the data and references updated throughout, this third edition continues to be an ideal reference on the subject. The tried-and-tested logical structuring of the material on gauge invariance, quantization, and renormalization has been retained, while the chapters on electroweak interactions and model building have been revised. Completely new is the chapter on conformality. As in the past, Frampton emphasizes formalism rather than experiments and provides sufficient detail for readers wishing to do their own calculations or pursue theoretical physics research.


Book Synopsis Gauge Field Theories by : Paul H. Frampton

Download or read book Gauge Field Theories written by Paul H. Frampton and published by John Wiley & Sons. This book was released on 2008-09-08 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this necessary reading for cosmologists and particle astrophysicists was quickly adopted by universities and other institutions of higher learning around the world. And with the data and references updated throughout, this third edition continues to be an ideal reference on the subject. The tried-and-tested logical structuring of the material on gauge invariance, quantization, and renormalization has been retained, while the chapters on electroweak interactions and model building have been revised. Completely new is the chapter on conformality. As in the past, Frampton emphasizes formalism rather than experiments and provides sufficient detail for readers wishing to do their own calculations or pursue theoretical physics research.

Quarks, Leptons & Gauge Fields

Quarks, Leptons & Gauge Fields

Author: Kerson Huang

Publisher: World Scientific

Published: 1992

Total Pages: 372

ISBN-13: 9789810206598

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This is perhaps the most up-to-date book on Modern Elementary Particle Physics. The main content is an introduction to Yang-Mills fields, and the Standard Model of Particle Physics. A concise introduction to quarks is provided, with a discussion of the representations of SU(3).The Standard Model is presented in detail, including such topics as the Kobayashi-Maskawa matrix, chiral symmetry breaking, and the ?-vacuum. Theoretical topics of a more general nature include path integrals, topological solitons, renormalization group, effective potentials, the axial anomaly, and lattice gauge theory.This second edition, which has been expanded, incorporates the following new subjects: Wilson's renormalization scheme, and its relation to perturbative renormalization; pitfalls in quantizing gauge fields, such as the Gribov ambiguity; the lattice as a consistent regularization; Monte Carlo methods of solution; and the issues, folklores, and scenarios of quark confinement. More than a quarter of the book comprise of new materials.This book may be used as a text for a one-semester course on advanced quantum field theory, or reference book for particle physicists.


Book Synopsis Quarks, Leptons & Gauge Fields by : Kerson Huang

Download or read book Quarks, Leptons & Gauge Fields written by Kerson Huang and published by World Scientific. This book was released on 1992 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is perhaps the most up-to-date book on Modern Elementary Particle Physics. The main content is an introduction to Yang-Mills fields, and the Standard Model of Particle Physics. A concise introduction to quarks is provided, with a discussion of the representations of SU(3).The Standard Model is presented in detail, including such topics as the Kobayashi-Maskawa matrix, chiral symmetry breaking, and the ?-vacuum. Theoretical topics of a more general nature include path integrals, topological solitons, renormalization group, effective potentials, the axial anomaly, and lattice gauge theory.This second edition, which has been expanded, incorporates the following new subjects: Wilson's renormalization scheme, and its relation to perturbative renormalization; pitfalls in quantizing gauge fields, such as the Gribov ambiguity; the lattice as a consistent regularization; Monte Carlo methods of solution; and the issues, folklores, and scenarios of quark confinement. More than a quarter of the book comprise of new materials.This book may be used as a text for a one-semester course on advanced quantum field theory, or reference book for particle physicists.

Topology, Geometry, and Gauge Fields

Topology, Geometry, and Gauge Fields

Author: Gregory L. Naber

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 410

ISBN-13: 1475727429

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Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.


Book Synopsis Topology, Geometry, and Gauge Fields by : Gregory L. Naber

Download or read book Topology, Geometry, and Gauge Fields written by Gregory L. Naber and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.

Geometrodynamics of Gauge Fields

Geometrodynamics of Gauge Fields

Author: Eckehard W. Mielke

Publisher: Springer

Published: 2017-01-22

Total Pages: 377

ISBN-13: 3319297341

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This monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed. Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter type gauge theory in the spirit of Yang-Mills, some new progress in its topological form is presented. After symmetry breaking, Einstein’s standard general relativity with cosmological constant emerges as a classical background. The geometrical structure of BRST quantization with non-propagating topological ghosts is developed in some detail.


Book Synopsis Geometrodynamics of Gauge Fields by : Eckehard W. Mielke

Download or read book Geometrodynamics of Gauge Fields written by Eckehard W. Mielke and published by Springer. This book was released on 2017-01-22 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed. Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter type gauge theory in the spirit of Yang-Mills, some new progress in its topological form is presented. After symmetry breaking, Einstein’s standard general relativity with cosmological constant emerges as a classical background. The geometrical structure of BRST quantization with non-propagating topological ghosts is developed in some detail.

Gauge Fields, Knots, and Gravity

Gauge Fields, Knots, and Gravity

Author: Associate Professor Department of Mathematics John C Baez

Publisher: World Scientific Publishing Company Incorporated

Published: 1994

Total Pages: 465

ISBN-13: 9789810217297

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This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.


Book Synopsis Gauge Fields, Knots, and Gravity by : Associate Professor Department of Mathematics John C Baez

Download or read book Gauge Fields, Knots, and Gravity written by Associate Professor Department of Mathematics John C Baez and published by World Scientific Publishing Company Incorporated. This book was released on 1994 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.

Gauge Field Theory and Complex Geometry

Gauge Field Theory and Complex Geometry

Author: Yuri I. Manin

Publisher: Springer Science & Business Media

Published: 1997-05-20

Total Pages: 368

ISBN-13: 9783540613787

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From the reviews: "... focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distinguished contributor to the field" (Contemporary Physics )"the book provides a large amount of background for current research across a spectrum of field. ... requires effort to read but it is worthwhile and rewarding" (New Zealand Math. Soc. Newsletter) " The contents are highly technical and the pace of the exposition is quite fast. Manin is an outstanding mathematician, and writer as well, perfectly at ease in the most abstract and complex situation. With such a guide the reader will be generously rewarded!" (Physicalia) This new edition includes an Appendix on developments of the last 10 years, by S. Merkulov.


Book Synopsis Gauge Field Theory and Complex Geometry by : Yuri I. Manin

Download or read book Gauge Field Theory and Complex Geometry written by Yuri I. Manin and published by Springer Science & Business Media. This book was released on 1997-05-20 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "... focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distinguished contributor to the field" (Contemporary Physics )"the book provides a large amount of background for current research across a spectrum of field. ... requires effort to read but it is worthwhile and rewarding" (New Zealand Math. Soc. Newsletter) " The contents are highly technical and the pace of the exposition is quite fast. Manin is an outstanding mathematician, and writer as well, perfectly at ease in the most abstract and complex situation. With such a guide the reader will be generously rewarded!" (Physicalia) This new edition includes an Appendix on developments of the last 10 years, by S. Merkulov.