Kevin Costello is Krembil William Rowan Hamilton Chair in Theoretical Physics at the Perimeter Institute for Theoretical Physics, Waterloo, Canada. He is an honorary member of the Royal Irish Academy and a Fellow of the Royal Society. He has won several awards, including the Berwick Prize of the London Mathematical Society (2017) and the Eisenbud Prize of the American Mathematical Society (2020).
Inhaltsangabe
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.
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.
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