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Topics in Quantum Geometry of Riemann Surfaces: Two-Dimensional Quantum Gravity

Leon Takhtajan

Abstract

Lectures given at International School of Physics ``Enrico Fermi'', Varenna, Villa Monastero, June 28-July 7 1994

Topics in Quantum Geometry of Riemann Surfaces: Two-Dimensional Quantum Gravity

Abstract

Lectures given at International School of Physics ``Enrico Fermi'', Varenna, Villa Monastero, June 28-July 7 1994

Paper Structure

This paper contains 17 sections, 186 equations.

Table of Contents

  1. Beginning Concepts
  2. Introduction
  3. Quantization of the Hyperbolic Geometry
  4. Conformal Symmetry
  5. Operator Product Expansion
  6. Conformal Ward Identities
  7. Friedan-Shenker Modular Geometry
  8. Expectation Value and Correlation Functions
  9. Expectation Value $<X>$
  10. Generating Functional $Z(\mu, \bar{\mu};X)$
  11. Examples
  12. Ward Identities and Modular Geometry
  13. Semi-classical Approximation
  14. One-loop Approximation
  15. Elements of the Teichmüller Theory
  16. ...and 2 more sections