String Path Integral Realization of Vertex Operator Algebras.

Intro -- Table of Contents -- Introduction -- Chapter I. Vertex Operator Algebras -- Section 1. Fock Spaces -- 1-A. Fock spaces -- 1-B. Double Fock Spaces -- Section 2. Vertex Operators -- 2-A. Vertex Operators -- 2-B. Neutral Vertex Operators -- Section 3. Representations -- 3-A. Vertex Operator Algebras -- 3-B. Virasoro Algebra -- 3-C. Affine Kac-Moody Lie Algebras -- Chapter II. Geometric Realization of Vertex Operator Algebras -- Section 4. Functional Realization of Fock Spaces -- 4-A. Gaussian Measures -- 4-B. Functional Realization of Fock Spaces -- Section 5. Function Spaces on Riemann Surfaces -- 5-A. General Theory -- 5-B. Examples -- Section 6. Geometric Realization of Vertex Operators -- 6-A. Gaussian Integrals over Harmonic Functions -- 6-B. String Path Integrals on Disks with Holes -- 6-C. Geometric Realization of Vertex Operators -- Chapter III. Analytic Realization of Vertex Operator Algebras -- Section 7. Zeta-Regularization -- 7-A. Zeta-Regularized Infinite Products -- 7-B. Zeta-Regularized Determinant of Laplacian and Conformal Anomaly -- Section 8. Zeta-Regularized Determinants on Cylinders and Elliptic Curves -- 8-A. Zeta-Regularized Determinants on Elliptic Curves -- 8-B. Zeta-Regularized Determinants on Cylinders -- 8-C. Sewing of Determinants on Cylinders -- Section 9. String Path Integrals over Cylinders and Elliptic Curves -- 9-A. String Path Integrals on Elliptic Curves -- 9-B. String Path Integrals on Cylinders -- 9-C. Analytic Realization of Vertex Operators -- 9-D. Sewing of String Path Integrals on Cylinders -- Appendix -- Section A. Poisson Summation Formula -- References.

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