Factorization Algebras in Quantum Field Theory
Volume 1
£110.00
Part of New Mathematical Monographs
 Authors:
 Kevin Costello, Perimeter Institute for Theoretical Physics, Waterloo, Ontario
 Owen Gwilliam, MaxPlanckInstitut für Mathematik, Bonn
 Date Published: December 2016
 availability: Available
 format: Hardback
 isbn: 9781107163102
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Factorization algebras are localtoglobal 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 ChernSimons 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.
Read more Systematically develops the localtoglobal structure of observables of quantum field theory
 Treats several examples in depth, including scalar field theory, chiral conformal field theory, current algebras and a topological gauge theory
 Includes an exposition of tools such as operads, cosheaves and homological algebra with topological vector spaces
Reviews & endorsements
'Because the subject of this book touches many advanced leading theories of quantum physics which utilize heavily mathematical machineries from a diverse range of mathematical topics, the background material needed for this book is immense. So it is very helpful and much appreciated that a 103page foursection appendix is included in this 387page book, to provide a very wellorganized and fairly detailed review of relevant mathematical background topics, including simplicial techniques, colored operads/multicategories and their algebras, differential graded (dg) Lie algebras and their cohomology, sheaves/cosheaves, formal Hodge theory, and 'convenient, differentiable, or bornological' topological vector spaces facilitating the homological algebra for infinitedimensional vector spaces.' Albert Sheu, Zentralblatt MATH
See more reviews'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 diﬀerential 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 ﬁeld theory will enjoy many pleasant moments with Costello and Gwilliam and will ﬁnd many sources of enlightenment … in their treatment of the subject.' Domenico Fiorenza, Mathematical Reviews
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×Product details
 Date Published: December 2016
 format: Hardback
 isbn: 9781107163102
 length: 398 pages
 dimensions: 229 x 152 x 25 mm
 weight: 0.75kg
 availability: Available
Table of Contents
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.
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