Gauge Fields, Knots And Gravity
Gauge Fields, Knots And Gravity

Author: John C Baez

Publisher: World Scientific Publishing Company

Published: 1994-10-24

Total Pages: 481

ISBN-13: 9813103248

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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.

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.

Gauge Fields, Knots, and Gravity
Gauge Fields, Knots, and Gravity

Author: John C. Baez

Publisher: World Scientific Publishing Company Incorporated

Published: 1994

Total Pages: 465

ISBN-13: 9789810220341

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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.

Gauge Theory and Variational Principles
Gauge Theory and Variational Principles

Author: David Bleecker

Publisher: Courier Corporation

Published: 2005-12-10

Total Pages: 202

ISBN-13: 0486445461

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This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas. Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field equation. Additional topics include free Dirac electron fields; interactions; calculus on frame bundle; and unification of gauge fields and gravitation. The text concludes with references, a selected bibliography, an index of notation, and a general index.

Differential Geometry, Gauge Theories, and Gravity
Differential Geometry, Gauge Theories, and Gravity

Author: M. Göckeler

Publisher: Cambridge University Press

Published: 1989-07-28

Total Pages: 248

ISBN-13: 9780521378215

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Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced using digital technology. This technology has enabled Cambridge to keep the book in print for specialists and students when traditional methods of reprinting would not have been feasible. While the new digital cover differs from the original, the text content is identical to that of previous printings.

Loops, Knots, Gauge Theories
Loops, Knots, Gauge Theories

Author: Rodolfo Gambini

Publisher: Cambridge University Press

Published: 2023-01-31

Total Pages: 341

ISBN-13: 1009290193

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This volume provides a self-contained introduction to applications of loop representations in particle physics and quantum gravity, in order to explore the gauge invariant quantization of Yang-Mills theories and gravity. First published in 1996, this title has been reissued as an Open Access publication on Cambridge Core.

Discrete Gauge Theory
Discrete Gauge Theory

Author: Robert Oeckl

Publisher: Imperial College Press

Published: 2005

Total Pages: 218

ISBN-13: 1860947379

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This book provides an introduction to topological quantum field theory as well as discrete gauge theory with quantum groups. In contrast to much of the existing literature, the present approach is at the same time intuitive and mathematically rigorous, making extensive use of suitable diagrammatic methods. It provides a highly unified description of lattice gauge theory, topological quantum field theory and models of quantum (super)gravity. The reader is thus in a unique position to understand the relations between these subjects as well as the underlying groundwork.

Gravitation and Gauge Symmetries
Gravitation and Gauge Symmetries

Author: M Blagojevic

Publisher: CRC Press

Published: 2001-10-25

Total Pages: 522

ISBN-13: 142003426X

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In the course of the development of electromagnetic, weak and strong interactions, the concept of (internal) gauge invariance grew up and established itself as an unavoidable dynamical principle in particle physics. It is less known that the principle of equivalence, and the basic dynamical properties of the gravitational interaction can also be ex