Factorization Algebras in Quantum Field Theory: Volume 2

This second volume shows how factorization algebras arise from interacting field theories, both classical and quantum.

Kevin Costello (Author), Owen Gwilliam (Author)

9781107163157, Cambridge University Press

Hardback, published 23 September 2021

380 pages
23.5 x 15.7 x 3 cm, 0.78 kg

'The central achievement of the book is in its development of a formalism that leads to classical and quantum versions of Noether's theorem, itself a familiar topic in physics, using the language of factorization algebras … Institutions employing mathematicians and theoretical physicists actively working in this area should acquire the book … Recommended.' M. C. Ogilvie, Choice Connect

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.

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.

Subject Areas: Quantum physics [quantum mechanics & quantum field theory PHQ], Topology [PBP], Geometry [PBM], Algebra [PBF]