Synopses & Reviews
Classical string theory is concerned with the propagation of classical one-dimensional curves, i.e. "strings", and has connections to the calculus of variations, minimal surfaces and harmonic maps. The quantization of string theory gives rise to problems in different areas, according to the method used. The representation theory of Lie, Kac-Moody and Virasoro algebras has been used for such quantization. In this book, the authors give an introduction to global analytic and probabilistic aspects of string theory, bringing together and making explicit the necessary mathematical tools. Researchers with an interest in string theory, in either mathematics or theoretical physics, will find this a stimulating volume.
Review
' ... a valuable addition ... admirably lucid.' David Bailin, Contemporary Physics
Review
' ... it is admirable how the authors managed to introduce such a quantity of material in 85 pages ... a good introduction to contemporary research in the field.' European Mathematical Society
Synopsis
This book deals with the mathematical aspects of string theory.
Synopsis
This introduction to global analytic and probabilistic aspects of string theory brings together and makes explicit the necessary mathematical tools. Researchers with an interest in string theory, in either mathematics or theoretical physics, will find it a stimulating volume.
Description
Includes bibliographical references (p. 126-132) and index.
Table of Contents
Part I. 1. Introduction; 2. Topological and metric structures; 3. Harmonic maps and global structures; 4. Cauchy Riemann operators; 5. Zeta function and heat kernel determinants; 6. The Faddeev-Popov procedure; 7. Determinant bundles; 8. Chern classes of determinant bundles; 9. Gaussian meaures and random fields; 10. Functional quantization of the Høegh-Krohn and Liouville model on a compact surface; 11. Small time asymptotics for heat-kernel regularized determinants; Part II. 1. Quantization by functional integrals; 2. The Polyakov measure; 3. Formal Lebesgue measures; 4. Gaussian integration; 5. The Faddeev-Popov procedure for bosonic strings; 6. The Polyakov measure in non-critical dimension; 7. The Polyakov measure in critical dimension d=26; 8. Correlation functions.