A Mathematical Introduction to String Theory Variational Problems, Geometric and Probabilistic Methods
Book contents
- Frontmatter
- Contents
- Preface
- Dedication
- I.0 Introduction
- Acknowledgements
- I.1 The two-dimensional Plateau problem
- I.2 Topological and metric structures on the space of mappings and metrics
- 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.7 Determinant bundles
- I.8 Chern classes of determinant bundles
- I.9 Gaussian measures and random fields
- I.10 Functional quantization of the Høegh-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
- II.5 The Faddeev–Popov procedure for bosonic strings
- II.6 The Polyakov measure in noncritical dimension and the Liouville measure
- II.7 The Polyakov measure in the critical dimension d=26
- II.8 Correlation functions
- References
- Index
I.4 - Cauchy–Riemann operators
Published online by Cambridge University Press: 01 June 2011
Book contents
- Frontmatter
- Contents
- Preface
- Dedication
- I.0 Introduction
- Acknowledgements
- I.1 The two-dimensional Plateau problem
- I.2 Topological and metric structures on the space of mappings and metrics
- 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.7 Determinant bundles
- I.8 Chern classes of determinant bundles
- I.9 Gaussian measures and random fields
- I.10 Functional quantization of the Høegh-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
- II.5 The Faddeev–Popov procedure for bosonic strings
- II.6 The Polyakov measure in noncritical dimension and the Liouville measure
- II.7 The Polyakov measure in the critical dimension d=26
- II.8 Correlation functions
- References
- Index
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- A Mathematical Introduction to String TheoryVariational Problems, Geometric and Probabilistic Methods, pp. 31 - 35Publisher: Cambridge University PressPrint publication year: 1997