**Factorization Algebras in Quantum Field Theory: Volume 1 First Edition by Kevin Costello, ISBN-13: 978-1107163102**

[PDF eBook eTextbook]

- Publisher: Cambridge University Press; 1st edition (December 1, 2016)
- Language: English
- 398 pages
- ISBN-10: 1107163102
- ISBN-13: 978-1107163102

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.

Ideal for researchers and graduates in mathematics and physics, this volume develops factorization algebras while highlighting examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory. This first volume also includes expositions of the relevant background in homological algebra, sheaves and functional analysis.

**Kevin Costello** is the Krembil Foundation William Rowan Hamilton Chair in Theoretical Physics at the Perimeter Institute in Waterloo, Ontario.

**Owen Gwilliam** is a postdoctoral fellow at the Max Planck Institute for Mathematics in Bonn.

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