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This title in other editions

Gauge Fields, Knots & Gravity

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Gauge Fields, Knots & Gravity Cover

 

Synopses & Reviews

Publisher Comments:


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.

Contents:
  • Electromagnetism:
  • Maxwell's Equations
  • Manifolds
  • Vector Fields
  • Differential Forms
  • Rewriting Maxwell's Equations
  • DeRham Theory in Electromagnetism
  • Gauge Fields:
  • Symmetry
  • Bundles and Connections
  • Curvature and the Yang-Mills Equation
  • Chern-Simons Theory
  • Link Invariants from Gauge Theory
  • Gravity:
  • Semi-Riemannian Geometry
  • Einstein's Equation
  • Lagrangians for General Relativity
  • The ADM Formalism
  • The New Variables

Product Details

ISBN:
9789810220341
Author:
John Baez and Javier P. Muniain
Publisher:
World Scientific Publishing Company
Author:
Muniain, Javier P.
Author:
Baez, John C.
Location:
Singapore
Subject:
Electromagnetism
Subject:
Waves & Wave Mechanics
Subject:
Quantum gravity
Subject:
Gauge fields (physics)
Subject:
Knot theory
Subject:
General relativity
Subject:
Gauge fields
Subject:
Physics-General
Copyright:
Edition Description:
Includes bibliographical references and index.
Series:
K & E Series on Knots and Everything
Series Volume:
Volume 4
Publication Date:
June 2006
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
480
Dimensions:
8.50x6.12x.96 in. 1.47 lbs.

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