Factorization Algebras in Quantum Field Theory
Factorization algebras are local-to-global objects that play a role in classical and quantum field theory that is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In the first volume of this set, the authors develop the theory of factorization algebras in depth, with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern–Simons theory. In the second volume, they show how factorization algebras arise from interacting field theories, both classical and quantum, and how they encode essential information such as operator product expansions, Noether currents, and anomalies.
1139071754
Factorization Algebras in Quantum Field Theory
Factorization algebras are local-to-global objects that play a role in classical and quantum field theory that is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In the first volume of this set, the authors develop the theory of factorization algebras in depth, with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern–Simons theory. In the second volume, they show how factorization algebras arise from interacting field theories, both classical and quantum, and how they encode essential information such as operator product expansions, Noether currents, and anomalies.
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Factorization Algebras in Quantum Field Theory

Factorization Algebras in Quantum Field Theory

Factorization Algebras in Quantum Field Theory

Factorization Algebras in Quantum Field Theory

Overview

Factorization algebras are local-to-global objects that play a role in classical and quantum field theory that is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In the first volume of this set, the authors develop the theory of factorization algebras in depth, with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern–Simons theory. In the second volume, they show how factorization algebras arise from interacting field theories, both classical and quantum, and how they encode essential information such as operator product expansions, Noether currents, and anomalies.

Product Details

ISBN-13: 9781009006163
Publisher: Cambridge University Press
Publication date: 02/29/2024
Series: New Mathematical Monographs
Pages: 818
Product dimensions: 6.10(w) x 9.25(h) x 2.20(d)

About the Author

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).

Owen Gwilliam is Assistant Professor in the Department of Mathematics and Statistics at the University of Massachusetts, Amherst.

Table of Contents

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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