Skip to content
Register Sign in Wishlist

Factorization Algebras in Quantum Field Theory

Volume 2

Part of New Mathematical Monographs

  • Authors:
  • Kevin Costello, Perimeter Institute for Theoretical Physics, Waterloo, Ontario
  • Owen Gwilliam, University of Massachusetts, Amherst
  • Date Published: September 2021
  • availability: Available
  • format: Hardback
  • isbn: 9781107163157

Hardback

Add to wishlist

Other available formats:
eBook


Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • Factorization algebras are local-to-global objects that play a role in classical and quantum field theory that 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 second volume, the authors show how factorization algebras arise from interacting field theories, both classical and quantum, and how they encode essential information such as operator product expansions, Noether currents, and anomalies. Along with a systematic reworking of the Batalin–Vilkovisky formalism via derived geometry and factorization algebras, this book offers concrete examples from physics, ranging from angular momentum and Virasoro symmetries to a five-dimensional gauge theory.

    • Systematically develops the local-to-global structure of observables of a quantum field theory
    • Examines several different examples: scalar field theories, holomorphic field theories, current algebras, and topological field theories
    • Revisits and generalizes Noether's theorem as a statement about factorization algebras, including a quantized version of the theorem
    Read more

    Reviews & endorsements

    'The central achievement of the book is in its development of a formalism that leads to classical and quantum versions of Noether's theorem, itself a familiar topic in physics, using the language of factorization algebras … Institutions employing mathematicians and theoretical physicists actively working in this area should acquire the book … Recommended.' M. C. Ogilvie, Choice Connect

    '… perfectly suitable for self-study by an interested scholar with little to almost no previous exposure to factorization algebras, or for use as a reference text for a lecture series on the subject.' Domenico Fiorenza, MathSciNet

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: September 2021
    • format: Hardback
    • isbn: 9781107163157
    • length: 380 pages
    • dimensions: 235 x 157 x 30 mm
    • weight: 0.78kg
    • availability: Available
  • Table of Contents

    1. Introduction and overview
    Part I. Classical Field Theory:
    2. Introduction to classical field theory
    3. Elliptic moduli problems
    4. The classical Batalin–Vilkovisky formalism
    5. The observables of a classical field theory
    Part II. Quantum Field Theory:
    6. Introduction to quantum field theory
    7. Effective field theories and Batalin–Vilkovisky quantization
    8. The observables of a quantum field theory
    9. Further aspects of quantum observables
    10. Operator product expansions, with examples
    Part III. A Factorization Enhancement of Noether's Theorem:
    11. Introduction to Noether's theorems
    12. Noether's theorem in classical field theory
    13. Noether's theorem in quantum field theory
    14. Examples of the Noether theorems
    Appendix A. Background
    Appendix B. Functions on spaces of sections
    Appendix C. A formal Darboux lemma
    References
    Index.

  • Authors

    Kevin Costello, Perimeter Institute for Theoretical Physics, Waterloo, Ontario
    Kevin Costello is Krembil William Rowan Hamilton Chair in Theoretical Physics at the Perimeter Institute for Theoretical Physics, Waterloo, Canada. He is an honorary member of the Royal Irish Academy and a Fellow of the Royal Society. He has won several awards, including the Berwick Prize of the London Mathematical Society (2017) and the Eisenbud Prize of the American Mathematical Society (2020).

    Owen Gwilliam, University of Massachusetts, Amherst
    Owen Gwilliam is Assistant Professor in the Department of Mathematics and Statistics at the University of Massachusetts, Amherst.

Related Books

also by this author

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon
×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×