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Factorization Algebras in Quantum Field Theory

Volume 1

$169.00 (C)

Part of New Mathematical Monographs

  • Authors:
  • Kevin Costello, Perimeter Institute for Theoretical Physics, Waterloo, Ontario
  • Owen Gwilliam, Max-Planck-Institut für Mathematik, Bonn
  • Date Published: December 2016
  • availability: Available
  • format: Hardback
  • isbn: 9781107163102

$ 169.00 (C)

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About the Authors
  • 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.

    • Systematically develops the local-to-global 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
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    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 103-page four-section appendix is included in this 387-page book, to provide a very well-organized 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 infinite-dimensional vector spaces.' Albert Sheu, Zentralblatt MATH

    '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

  • Authors

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

    Owen Gwilliam, Max-Planck-Institut für Mathematik, Bonn
    Owen Gwilliam is a postdoctoral fellow at the Max Planck Institute for Mathematics in Bonn.

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