内容

目次

Volume 1: 1. Introduction; Part I. Prefactorization Algebras: 2. From Gaussian Measures to Factorization Algebras; 3. Prefactorization Algebras and Basic Examples; Part II. First Examples of Field Theories: 4. Free Field Theories; 5. Holomorphic Field Theories and Vertex Algebras; Part III. Factorization Algebras: 6. Factorization Algebras - Definitions and Constructions; 7. Formal Aspects of Factorization Algebras; 8. Factorization Algebras - Examples; Appendix A. Background; Appendix B. Functional Analysis; Appendix C. Homological Algebra in Differentiable Vector Spaces; Appendix D. The Atiyah-Bott Lemma; References; Index; Volume 2: 1. Introduction and Overview; Part I. Classical Field Theory: 2. Introduction to Classical Field Theory; 3. Elliptic Moduli Problems; 4. The Classical Batalin-Vilkovisky Formalism; 5. The Observables of a Classical Field Theory; Part II. Quantum Field Theory: 6. Introduction to Quantum Field Theory; 7. Effective Field Theories and Batalin-Vilkovisky Quantization; 8. The Observables of a Quantum Field Theory; 9. Further Aspects of Quantum Observables; 10. Operator Product Expansions, with Examples; Part III. A Factorization Enhancement of Noether's Theorem: 11. Introduction to Noether's Theorems; 12. Noether's Theorem in Classical Field Theory; 13. Noether's Theorem in Quantum Field Theory; 14. Examples of the Noether Theorems; Appendix A. Background; Appendix B. Functions on Spaces of Sections; Appendix C. A Formal Darboux Lemma; References; Index.