GAUGE FIELDS, KNOTS AND GRAVITY (Paperback)

Javier P. Muniain

ISBN 10: 9810220340 / ISBN 13: 9789810220341

Published by World Scientific Publishing Co Pte Ltd, Singapore, 1994

About this Item

Paperback. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9789810220341

Bibliographic Details

• Title: GAUGE FIELDS, KNOTS AND GRAVITY (Paperback)
• Publisher: World Scientific Publishing Co Pte Ltd, Singapore
• Publication Date: 1994
• Language: English
• ISBN 10: 9810220340
• ISBN 13: 9789810220341
• Binding: Paperback
• Condition: new

About this title

Synopsis

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.

Reviews

"The book is clearly written and should be accessible to readers who have a good undergraduate preparation in mathematics or physics. Each part of the book ends with a list of references that will enable the reader to pursue the material presented in greater detail."