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E-raamat: Mathematical Introduction to String Theory: Variational Problems, Geometric and Probabilistic Methods

(Université Louis Pasteur, Strasbourg), (Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig), (Ruhr-Universität, Bochum, Germany), (Università degli Studi di Roma 'Tor Vergata')
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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.

This book deals with the mathematical aspects of string theory.

Arvustused

' 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

Muu info

This book deals with the mathematical aspects of string theory.
I.0 Introduction
1(6)
I.1 The two-dimensional Plateau problem
7(4)
I.2 Topological and metric structures on the space of mappings and metrics
11(10)
Appendix to I.2: ILH-structures
17(4)
I.3 Harmonic maps and global structures
21(10)
I.4 Cauchy-Riemann operators
31(5)
I.5 Zeta-function and heat-kernel determinants of an operator
36(5)
I.6 The Faddeev-Popov procedure
41(7)
I.6.1 The Faddeev-Popov map
41(3)
I.6.2 The Faddeev-Popov determinant: the case G=H
44(2)
I.6.3 The Faddeev-Popov determinant: the general case
46(2)
I.7 Determinant bundles
48(11)
I.8 Chern classes of determinant bundles
59(7)
I.9 Gaussian measures and random fields
66(9)
I.10 Functional quantization of the Hoegh-Krohn and Liouville models on a compact surface
75(10)
I.11 Small time asymptotics for heat-kernel regularized determinants
85(7)
II.1 Quantization by functional integrals
92(4)
II.2 The Polyakov measure
96(5)
II.3 Formal Lebesgue measures on Hilbert spaces
101(5)
II.4 The Gaussian integration on the space of embeddings
106(3)
II.5 The Faddeev-Popov procedure for bosonic strings
109(4)
II.6 The Polyakov measure in noncritical dimension and the Liouville measure
113(4)
II.7 The Polyakov measure in the critical dimension d=26
117(5)
II.8 Correlation functions
122(4)
References 126(7)
Index 133