Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 16th 2014

    I am beginning to give the entry FQFT a comprehensive Exposition and Introduction section.

    So far I have filled some genuine content into the first subsection Quantum mechanics in Schrödinger picture.

    But I have to quit now. This isn’t even proof-read yet. So don’t look at it unless you feel more in editing-mood than in pure-reading-mood.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 18th 2014
    • (edited Nov 18th 2014)

    I have been further editing, but I will run out of time.

    Today I am giving a talk, on request, to introduce the description of TQFT via n-functors on n-dimensional cobordisms. This is to an audience of mathematical physicists but with no real background in category theory or homotopy theory, so to get anywhere in one hour, I need some strategy.

    My strategy is to explain in 1/2 of the talk the 1-dimensional case in detail and to explain in the next 1/4th of the talk the main results of the 2-dimensional case, so that in the last remaining 1/4th of the talk the statement of the full cobordism hypothesis falling from the sky will at least make some intuitive sense.

    So I start with

    motivating all the monoidal 1-category structure from textbook qantum mechanics

    then discuss

    with the aim to indicate elements of a concrete construction and at the same time introduce some basic ideas of homotopy theory that need to be alluded to later on.

    From that the Atiyah-axioms for 2d TQFT are evident and so I’ll show some of the usual 2d Yoga along a string physics storyline in

    That will leave just a handful of minutes at the end to say something about the actual topic,

    (and that section hardly exists yet as actual typed notes at the moment, will have to see how far I get).

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 18th 2019

    added pointer to

    • Stephan Stolz, Topology and Field Theories, Contemporary Mathematics 613, American Mathematical Society 2014 (ams:conm-613)

    diff, v66, current

    • CommentRowNumber4.
    • CommentAuthorDmitri Pavlov
    • CommentTimeOct 17th 2019

    Corrected to arXiv.

    diff, v67, current

    • CommentRowNumber5.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJan 13th 2021

    Added references.

    diff, v70, current

    • CommentRowNumber6.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJan 13th 2021

    Should this be renamed to “functorial field theory”? The formalism is not inherently quantum, and the title should probably not be abbreviated.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJan 13th 2021

    Sure, please do.

    • CommentRowNumber8.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJan 13th 2021

    Adjusted the title.

    diff, v71, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeJan 31st 2021

    I have added pointer to

    (I see that the list of references in this entry leaves much room for imrpovement, concerning all of: completeness, organization, commentary and formatting.)

    diff, v72, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeNov 2nd 2021

    added pointer to today’s

    diff, v76, current

    • CommentRowNumber11.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 6th 2022



    The term functorial quantum field theory appears to originate around June 2008 in

    At some point later, the adjective “quantum” was dropped because the formalism also encodes classical and prequantum field theories.

    diff, v77, current

    • CommentRowNumber12.
    • CommentAuthorGuest
    • CommentTimeJul 7th 2022
    the article still refers to this concept as "functorial quantum field theory" even though the title is just "functorial field theory".
Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)