Gauge Fields, Knots And Gravity Paperback

John C Baez

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.

9810220340

9789810220341

English

World Scientific Publishing Co Pte Ltd

01 Oct 1994

480

John Carlos Baez born on June 12, 1961 is an American mathematical physicist and a professor of mathematics at the University of California, Riverside (UCR) in Riverside, California. He is known for his work on spin foams in loop quantum gravity.For some time, his research had focused on applications of higher categories to physics and other things. Baez is also known to science fans as the author of This Week's Finds in Mathematical Physics,an irregular column on the internet featuring mathematical exposition and criticism. He started This Week's Finds in 1993 for the Usenet community, and it now has a following in its new form, the blog

Javier P. Muniain