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nLab > Latest Changes: functorial field theory

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  1.  
    • 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 xxx.lanl.gov 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

    Added:

    Terminology

    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".

  13. Added references to 2D construction of smooth FFTs.

    S. Bunk

    diff, v79, current

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeJul 27th 2023

    Thanks.

    I have moved this out of the block of references on 1d QFT (now here)

    and added the DOI-links:

    diff, v80, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeAug 3rd 2023
    • (edited Aug 3rd 2023)

    added pointer to today’s

    Since this may essentially be the third existing article on the relation between functorial quantum field theory (axiomatizing the Schrödinger picture of quantum field theory) and algebraic quantum field theory (axiomatizing the Heisenberg picture) it may be time to reference this more systematically, so I am creating now an !include-entry:

    diff, v81, current

    • CommentRowNumber16.
    • CommentAuthorperezl.alonso
    • CommentTimeApr 24th 2024

    pointer

    • Lorenzo Riva. Higher categories of push-pull spans, I: Construction and applications (2024). (arXiv:2404.14597).

    diff, v83, current

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeApr 24th 2024
    • (edited Apr 24th 2024)

    This would more canonically be listed at extended functorial field theory and Rozansky-Witten theory – I have added the pointers.

    diff, v84, current

1 to 17 of 17

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