Variational problems, geometric and probabilistic methods

Editors: S. Albeverio, J. Jost, S. Paycha, and S. Scarlatti

Number 225 in London Mathematical Society Lecture Note Series.
Cambridge Univ. Press, 1997. London Math. Soc.

Part I

0 Introduction

1 The two-dimensional Plateau problem

2 Topological and metric structures on the space of mappings and metrics
Appendix to 2: ILH-structures

3 Harmonic maps and global structures

4 Cauchy-Riemann operators

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

6 The Faddeev-Popov procedure

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

7 Determinant bundles

8 Chern classes of determinant bundles

9 Gaussian measures and random fields

10 Functional quantization of the Høegh-Krohn and Liouville models 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 on Hilbert spaces

4 The Gaussian integration on the space of embeddings

5 The Faddeev-Popov procedure for bosonic strings

6 The Polyakov measure in noncritical dimension and the Liouville measure

7 The Polyakov measure in the critical dimension d=26

8 Correlation functions