A Mathematical Introduction to String Theory

Variational Problems, Geometric and Probabilistic Methods

By: Sergio A. Albeverio, Sergio Scarlatti, Sylvie Paycha

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Paperback | 15 September 1997

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144 Pages

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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.

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' ... 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

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Applied Mathematics Science Physics Nuclear Physics Probability & Statistics

Introduction	p. 1
The two-dimensional Plateau problem	p. 7
Topological and metric structures on the space of mappings and metrics	p. 11
ILH-structures	p. 17
Harmonic maps and global structures	p. 21
Cauchy-Riemann operators	p. 31
Zeta-function and heat-kernel determinants of an operator	p. 36
The Faddeev-Popov procedure	p. 41
The Faddeev-Popov map	p. 41
The Faddeev-Popov determinant: the case G=H	p. 44
The Faddeev-Popov determinant: the general case	p. 46
Determinant bundles	p. 48
Chern classes of determinant bundles	p. 59
Gaussian measures and random fields	p. 66
Functional quantization of the H[phis]egh-Krohn and Liouville models on a compact surface	p. 75
Small time asymptotics for heat-kernel regularized determinants	p. 85
Quantization by functional integrals	p. 92
The Polyakov measure	p. 96
Formal Lebesgue measures on Hilbert spaces	p. 101
The Gaussian integration on the space of embeddings	p. 106
The Faddeev-Popov procedure for bosonic strings	p. 109
The Polyakov measure in noncritical dimension and the Liouville measure	p. 113
The Polyakov measure in the critical dimension d=26	p. 117
Correlation functions	p. 122
References	p. 126
Index	p. 133
Table of Contents provided by Syndetics. All Rights Reserved.

A Mathematical Introduction to String Theory

Variational Problems, Geometric and Probabilistic Methods

At a Glance

Paperback

Industry Reviews

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How to return your order

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