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• 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.

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

• Stephan Stolz, Topology and Field Theories, Contemporary Mathematics 613, American Mathematical Society 2014 (ams:conm-613)
• CommentRowNumber4.
• CommentAuthorDmitri Pavlov
• CommentTimeOct 17th 2019

Corrected xxx.lanl.gov to arXiv.

• CommentRowNumber5.
• CommentAuthorDmitri Pavlov
• CommentTimeJan 13th 2021

• 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

• CommentRowNumber8.
• CommentAuthorDmitri Pavlov
• CommentTimeJan 13th 2021

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeJan 31st 2021

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

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeNov 2nd 2021

• CommentRowNumber11.
• CommentAuthorDmitri Pavlov
• CommentTimeJul 6th 2022

### 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.

• 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".