Gauge Fields Knots And Gravity

Author : John Baez,Javier P Muniain
Publisher : World Scientific Publishing Company
Page : 480 pages
File Size : 50,5 Mb
Release : 1994-10-24
Category : Science
ISBN : 9789813103245

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Gauge Fields, Knots and Gravity by John Baez,Javier P Muniain Pdf

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.

Author : Rodolfo Gambini,Jorge Pullin
Publisher : Cambridge University Press
Page : 341 pages
File Size : 50,6 Mb
Release : 2023-01-31
Category : Science
ISBN : 9781009290197

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Loops, Knots, Gauge Theories by Rodolfo Gambini,Jorge Pullin Pdf

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.

Author : John C. Baez
Publisher : Unknown
Page : 0 pages
File Size : 52,5 Mb
Release : 1994
Category : Electromagnetism
ISBN : OCLC:1341897748

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Gauge Fields, Knots, and Gravity by John C. Baez Pdf

Author : M. Göckeler,T. Schücker
Publisher : Cambridge University Press
Page : 248 pages
File Size : 40,5 Mb
Release : 1989-07-28
Category : Mathematics
ISBN : 0521378214

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Differential Geometry, Gauge Theories, and Gravity by M. Göckeler,T. Schücker Pdf

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.

Author : Eckehard W. Mielke
Publisher : Springer
Page : 377 pages
File Size : 55,9 Mb
Release : 2017-01-22
Category : Science
ISBN : 9783319297347

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Geometrodynamics of Gauge Fields by Eckehard W. Mielke Pdf

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.

Author : Carlo Rovelli
Publisher : Cambridge University Press
Page : 175 pages
File Size : 43,5 Mb
Release : 2021-09-09
Category : Science
ISBN : 9781316516072

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General Relativity: The Essentials by Carlo Rovelli Pdf

A straightforward introduction to General Relativity, explaining the physical, philosophical and mathematical ideas it is built on.

Author : Stephen Wolfram
Publisher : Wolfram Media
Page : 0 pages
File Size : 44,7 Mb
Release : 2020
Category : Science
ISBN : 1579550355

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A Project to Find the Fundamental Theory of Physics by Stephen Wolfram Pdf

The Wolfram Physics Project is a bold effort to find the fundamental theory of physics. It combines new ideas with the latest research in physics, mathematics and computation in the push to achieve this ultimate goal of science. Written with Stephen Wolfram's characteristic expository flair, this book provides a unique opportunity to learn about a historic initiative in science right as it is happening. A Project to Find the Fundamental Theory of Physics includes an accessible introduction to the project as well as core technical exposition and rich, never-before-seen visualizations.

Author : Kerson Huang
Publisher : World Scientific
Page : 372 pages
File Size : 53,9 Mb
Release : 1992
Category : Science
ISBN : 9810206593

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Quarks, Leptons & Gauge Fields by Kerson Huang Pdf

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.

Author : Charles Nash,Siddhartha Sen
Publisher : Courier Corporation
Page : 302 pages
File Size : 42,8 Mb
Release : 2013-08-16
Category : Mathematics
ISBN : 9780486318363

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Topology and Geometry for Physicists by Charles Nash,Siddhartha Sen Pdf

Written by physicists for physics students, this text assumes no detailed background in topology or geometry. Topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory. 1983 edition.

Author : John C. Baez,Irving E. Segal,Zhengfang Zhou
Publisher : Princeton University Press
Page : 310 pages
File Size : 47,8 Mb
Release : 2014-07-14
Category : Science
ISBN : 9781400862504

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Introduction to Algebraic and Constructive Quantum Field Theory by John C. Baez,Irving E. Segal,Zhengfang Zhou Pdf

The authors present a rigorous treatment of the first principles of the algebraic and analytic core of quantum field theory. Their aim is to correlate modern mathematical theory with the explanation of the observed process of particle production and of particle-wave duality that heuristic quantum field theory provides. Many topics are treated here in book form for the first time, from the origins of complex structures to the quantization of tachyons and domains of dependence for quantized wave equations. This work begins with a comprehensive analysis, in a universal format, of the structure and characterization of free fields, which is illustrated by applications to specific fields. Nonlinear local functions of both free fields (or Wick products) and interacting fields are established mathematically in a way that is consistent with the basic physical constraints and practice. Among other topics discussed are functional integration, Fourier transforms in Hilbert space, and implementability of canonical transformations. The authors address readers interested in fundamental mathematical physics and who have at least the training of an entering graduate student. A series of lexicons connects the mathematical development with the underlying physical motivation or interpretation. The examples and problems illustrate the theory and relate it to the scientific literature. Originally published in 1992. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : Robert Oeckl
Publisher : Imperial College Press
Page : 218 pages
File Size : 42,6 Mb
Release : 2005
Category : Science
ISBN : 9781860947377

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Discrete Gauge Theory by Robert Oeckl Pdf

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.

Author : David Bleecker
Publisher : Courier Corporation
Page : 253 pages
File Size : 40,9 Mb
Release : 2013-01-18
Category : Science
ISBN : 9780486151878

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Gauge Theory and Variational Principles by David Bleecker Pdf

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.

Author : Steven Carlip,Steven Jonathan Carlip
Publisher : Cambridge University Press
Page : 296 pages
File Size : 41,9 Mb
Release : 2003-12-04
Category : Science
ISBN : 0521545889

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Quantum Gravity in 2+1 Dimensions by Steven Carlip,Steven Jonathan Carlip Pdf

The first comprehensive survey of (2+1)-dimensional quantum gravity - for graduate students and researchers.

Author : Mark J.D. Hamilton
Publisher : Springer
Page : 658 pages
File Size : 44,5 Mb
Release : 2017-12-06
Category : Mathematics
ISBN : 9783319684390

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Mathematical Gauge Theory by Mark J.D. Hamilton Pdf

The Standard Model is the foundation of modern particle and high energy physics. This book explains the mathematical background behind the Standard Model, translating ideas from physics into a mathematical language and vice versa. The first part of the book covers the mathematical theory of Lie groups and Lie algebras, fibre bundles, connections, curvature and spinors. The second part then gives a detailed exposition of how these concepts are applied in physics, concerning topics such as the Lagrangians of gauge and matter fields, spontaneous symmetry breaking, the Higgs boson and mass generation of gauge bosons and fermions. The book also contains a chapter on advanced and modern topics in particle physics, such as neutrino masses, CP violation and Grand Unification. This carefully written textbook is aimed at graduate students of mathematics and physics. It contains numerous examples and more than 150 exercises, making it suitable for self-study and use alongside lecture courses. Only a basic knowledge of differentiable manifolds and special relativity is required, summarized in the appendix.

Author : Gregory L. Naber
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 53,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475727425

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Topology, Geometry, and Gauge Fields by Gregory L. Naber Pdf

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.