Factorization Algebras in Quantum Field Theory: Volume 1

Nonfiction, Science & Nature, Mathematics, Topology, Science
Cover of the book Factorization Algebras in Quantum Field Theory: Volume 1 by Kevin Costello, Owen Gwilliam, Cambridge University Press
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Author: Kevin Costello, Owen Gwilliam ISBN: 9781316732090
Publisher: Cambridge University Press Publication: December 15, 2016
Imprint: Cambridge University Press Language: English
Author: Kevin Costello, Owen Gwilliam
ISBN: 9781316732090
Publisher: Cambridge University Press
Publication: December 15, 2016
Imprint: Cambridge University Press
Language: English

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.

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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.

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