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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.
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).
added pointer to
Should this be renamed to “functorial field theory”? The formalism is not inherently quantum, and the title should probably not be abbreviated.
Sure, please do.
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.)
added pointer to today’s
Added:
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.
Thanks.
I have moved this out of the block of references on 1d QFT (now here)
and added the DOI-links:
Severin Bunk, Konrad Waldorf, Transgression of D-branes, Adv. Theor. Math. Phys. 25 5 (2021) 1095-1198 [[arXiv:1808.04894] (https://arxiv.org/abs/arXiv:1808.04894), doi:10.4310/ATMP.2021.v25.n5.a1]
Severin Bunk, Konrad Waldorf, Smooth functorial field theories from B-fields and D-branes, J. Homot. Rel. Struc. 16 1 (2021) 75-153 [doi:10.1007/s40062-020-00272-2, [arXiv:1911.09990] (https://arxiv.org/abs/arXiv:1911.09990)]
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:
pointer
This would more canonically be listed at extended functorial field theory and Rozansky-Witten theory – I have added the pointers.
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