Factorization Algebras in Quantum Field Theory

Description

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 this second volume, the authors 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. Along with a systematic reworking of the Batalin–Vilkovisky formalism via derived geometry and factorization algebras, this book offers concrete examples from physics, ranging from angular momentum and Virasoro symmetries to a five-dimensional gauge theory. Dedication Contents Contents of Volume 1 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 THE NOETHER THEOREM 11 Introduction to the Noether Theorems 12 The Noether Theorem in Classical Field Theory 13 The Noether 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