Factorization Algebras in Quantum Field Theory: Volume 1

This first volume develops factorization algebras with a focus upon examples exhibiting their use in field theory, which will be useful for researchers and graduates.

Kevin Costello (Author), Owen Gwilliam (Author)

9781107163102, Cambridge University Press

Hardback, published 15 December 2016

398 pages
22.9 x 15.2 x 2.5 cm, 0.75 kg

'It is a truth universally acknowledged that one cannot make two independent measurements at the very same place and very same time. In this book full of wit, Costello and Gwilliam show what can actually be done by taking this common lore seriously. … Reading this book requires minimal prerequisites: essentially only the basic notions of topology, of di?erential geometry, of homological algebra and of category theory will be needed, while all other background material … is provided in the four appendices that take up about one third of the book. Yet some familiarity with the subject is needed to really appreciate it. The reader who has even occasionally been close to the interface between algebraic topology, derived geometry and quantum ?eld theory will enjoy many pleasant moments with Costello and Gwilliam and will ?nd many sources of enlightenment … in their treatment of the subject.' Domenico Fiorenza, Mathematical Reviews

Factorization algebras are local-to-global objects that play a role in classical and quantum field theory which 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 first volume, the authors develop the theory of factorization algebras in depth, but 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. Expositions of the relevant background in homological algebra, sheaves and functional analysis are also included, thus making this book ideal for researchers and graduates working at the interface between mathematics and physics.

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.

Subject Areas: Mathematical physics [PHU], Quantum physics [quantum mechanics & quantum field theory PHQ], Topology [PBP], Functional analysis & transforms [PBKF], Algebra [PBF], Mathematical foundations [PBC]