A mathematical introduction to string theory : variational problems, geometric and probabilistic methods / Sergio Albeverio [and others].

Format:

Book

Author/Creator:

Albeverio, Sergio, author.

Contributor:

London Mathematical Society, issuing body.

Series:

London Mathematical Society lecture note series ; 225.

London Mathematical Society lecture note series ; 225

Language:

English

Subjects (All):

String models--Mathematics.

String models.

Mathematical physics.

Physical Description:

1 online resource (viii, 135 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1997.

Language Note:

English

Summary:

Classical string theory is concerned with the propagation of classical 1-dimensional curves 'strings', and the theory 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 have been used for such quantization. In this lecture note the authors give an introduction to certain global analytic and probabilistic aspects of string theory. It is their intention to bring together, and make explicit the necessary mathematical tools. Researchers with an interest in string theory, in either mathematics or theoretical physics, will find this a stimulating volume.

Contents:

I.0. Introduction

I.1. The two-dimensional Plateau problem

I.2. Topological and metric structures on the space of mappings and metrics

Appendix to I.2. ILH-structures

I.3. Harmonic maps and global structures

I.4. Cauchy-Riemann operators

I.5. Zeta-function and heat-kernel determinants of an operator

I.6. The Faddeev-Popov procedure. I.6.1. The Faddeev-Popov map. I.6.2. The Faddeev-Popov determinant: the case G=H. I.6.3. The Faddeev-Popov determinant: the general case

I.7. Determinant bundles

I.8. Chern classes of determinant bundles

I.9. Gaussian measures and random fields

I.10. Functional quantization of the Hoegh-Krohn and Liouville models on a compact surface

I.11. Small time asymptotics for heat-kernel regularized determinants

II. 1. Quantization by functional integrals

II. 2. The Polyakov measure

II. 3. Formal Lebesgue measures on Hilbert spaces

II. 4. The Gaussian integration on the space of embeddings.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-139-88667-3

1-107-36729-8

1-107-37187-2

1-107-36238-5

1-107-36900-2

1-299-40493-6

1-107-36483-3

0-511-60079-8