Knots and Quantum Gravity: (1 Oxford Lecture Series in Mathematics and Its Applications)

In the mid-1980's, Abhay Ashtekar discovered a reformulation of general relativity in terms of what are now called the "new variables". This led to a rapid series of developments, and in 1990 Carlo Rovelli and Lee Smolin published a paper entitled "Loop representation of quantum general relativity", in which, among other things, it was shown that there is a space of solutions to the constraint equations of quantum gravity consisting of link invariants. The discovery of relations between quantum gravity and the theory of knots and links came as quite a surprise, since the topics had been regarded as quite remote from each other. This volume is the proceedings of a workshop held in 1993 at the University of California at Riverside. The purpose of the workshop was to bring together researchers in knot theory and quantum gravity and form more bridges between the two subjects. Most of the talks were given by researchers whose work has significance for both subjects. This volume contains expository papers as well as new results, and should serve as a guide for mathematicians and physicists seeking to understand this rapidly developing area of research.

Table of Contents:
Renate Loll: The Loop Formulation of Gauge Theory and Gravity Abhay Ashketar and Jerry Lewandowski: Representation Theory of Analytic Holonomy: C*-algebras Rodolfo Gambini and Jorge Pullin: The Gauss Linking Number in Quantum Gravity Louis H. Kauffman: Vassiliev Invariants and the Loop States in Quantum Gravity Steven Carlip: Geometric Structures and Loop Variables in (2+1)- Dimensional Gravity Dana S. Fine: From Chern-Simons to WZW via Path Integrals Louis Crane: Topological Field theory as the Key to Quantum Gravity John C. Baez: Strings, Loops, Knots and Gauge Fields Paolo Cotta-Ramusino and Maurizio Martellini: BF Theories and 2-knots J. Scott Carter and Masahico Saito: Knotted Surfaces, Braid Movies, and Beyond

Review :
`....it may be effectively used as a bridge for a researcher from one field to discover ties to another.' Class. Quantum Grav., No. 12, 1995 `This book is, however, best treated as a reference. Because of the breadth of topics addressed and the emphasis on connections and relationships, it may be effectively used as a bridge for a researcher from one field to discover ties to another.' Class. Quantum Grav., No. 12, 1995 `John Baez has put together an extremely interesting and timely book which brings into focus a bubbling emerging subject...The volume communicates the atmosphere of excitement and enthusiasm in the field. I heartily recommend this book to everybody working in the search for the next step [in] our understanding of the physical world at the fundamental level.' General Relativity and Gravitation, Vol. 27, No. 1, 1995