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.
Rezensionen / Stimmen
'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 '... perfectly suitable for self-study by an interested scholar with little to almost no previous exposure to factorization algebras, or for use as a reference text for a lecture series on the subject.' Domenico Fiorenza, MathSciNet
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Verlagsort
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Maße
Höhe: 235 mm
Breite: 157 mm
Dicke: 29 mm
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ISBN-13
978-1-107-16315-7 (9781107163157)
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Schweitzer Klassifikation
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.
Autor*in
University of Massachusetts, Amherst
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.
