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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.
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