You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
John Baez (May 01 2024 at 20:20):Nima Arkani-Hamed is a famous theoretical physicist at the Institute for Advanced Studies. Someone wrote and told me that in 2022 he said
six months ago, if you said the word category theory to me, I would have laughed in your face and said useless formal nonsense, and yet it’s somehow turned into something very important in my intellectual life in the last six months or so
That's from 44:05 in this talk:
https://www.youtube.com/watch?v=GL77oOnrPzY
But I don't know why he got interested in category theory or whether he still is.
Chris Grossack (they/them) (May 02 2024 at 02:42):Around the 22 minute mark, the speaker mentions that if you compute something with these feynman diagram sums, and you use enough terms, everything seems to magically cancel out and give a simple answer.
Do you know what computation he's talking about, and if anyone has written more about this in a way that a lowly mathematician like me can understand?
John Baez (May 02 2024 at 07:43):I'm too lazy to watch the video and scan it for clues, but Arkani-Hamed is famous for summarizing Feynman diagram sums as integrals:
The amplituhedron is a space whose geometric structure conjecturally determines scattering amplitudes in a certain class of quantum field theories. When it was introduced in 2013 by Arkani-Hamed and Trnka, Quanta Magazine reported that “Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality…” Scattering amplitudes are the bread and butter of quantum field theory. In this short article, we will not get as far as challenging the notions of space and time, but we will give some explanation as to the nature and significance of the amplituhedron both in physics and mathematics—where it arises as a natural generalization of the subject of total positivity for Grassmannians.
The stuff about "challenging the notions of space and time" is basically hype, but you can read this summary article here.
John Baez (May 02 2024 at 07:47):I've never studied this stuff but the article says Arkani-Hamed expressed the sums of planar diagrams in a certain supersymmetric Yang-Mills theory as integrals over a certain subset of the Grassmannian of -planes in -space, called the "positive Grassmannian".
John Baez (May 02 2024 at 07:49):For many decades people have known that in the limit of gauge theories, the planar Feynman diagrams dominate the others (which can only be drawn on surfaces of higher genus). This led to a lot of work on the limit of gauge theories, and on trying to sum all the planar Feynman diagrams.
John Baez (May 02 2024 at 07:51):A lot of this can be understood by humble mathematicians who understand string diagrams. In week92 I tried to distill a bit of it to its essence:
[I'm sure most of you have lost interest in my "tale of n-categories", because it takes a fair amount of work to keep up with all the abstract concepts involved. However, we are now at a point where we can have some fun with what we've got, even if you haven't really followed all the previous stuff. So what follows is a rambling tour through monads, adjunctions, the 4-color theorem and the large-N limit of SU(N) gauge theory...
Chris Barrett (May 02 2024 at 13:19):Chris Grossack (they/them) said:
Around the 22 minute mark, the speaker mentions that if you compute something with these feynman diagram sums, and you use enough terms, everything seems to magically cancel out and give a simple answer.
Do you know what computation he's talking about, and if anyone has written more about this in a way that a lowly mathematician like me can understand?
I am certainly not an expert, but this paper on understanding Feynman diagrams via ZX-calculus and string diagrams may be relevant: https://arxiv.org/abs/2205.00466.