A Mathematical Introduction to String Theory: Variational Problems, Geometric and Probabilistic Methods

by Sergio Albeverio, Jurgen Jost, Sylvie Paycha, Sergio Scarlatti

Overview

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.

Product Details

ISBN-13:	9780521556101
Publisher:	Cambridge University Press
Publication date:	07/17/1997
Series:	London Mathematical Society Lecture Note Series , #225
Edition description:	New Edition
Pages:	144
Product dimensions:	6.06(w) x 9.21(h) x 0.39(d)

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.

Editorial Reviews

' … a valuable addition … admirably lucid.' David Bailin, Contemporary Physics

' … 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

From the Publisher