I loved this lecture by Nina Arkani-Hamed. He has a nice way of presenting things as a story.
After he gets rolling here, he explains how particle physicists could discover some famous shapes called "associahedra" just by keeping track of the poles in the scattering matrix. Since I know associahedra from category theory and topology, this is astounding!
He also keeps prerequisites to a minimum. Well, okay: if you don't have a physics PhD don't watch this. You need to know the Feynman rules, and how Feynman diagrams have poles when the energy-momentum of a virtual particle is 'on shell' - i.e., takes a value that a real particle can have.
It also helps to have seen how Feynman diagrams for gauge bosons look like they're made of ribbons. But this shows up only at first.
What I don't love is how he covers up some of his assumptions. He's talking about a spin-0 field Φ of mass m that takes values in the Lie algebra su(n), with a cubic self-interaction
tr(Φ³)
This is not like our universe! When he sets m=0 this theory would apply to nonexistent 'spin-zero gluons'.
More importantly, he only considers planar, tree-shaped Feynman diagrams! This restriction kicks in naturally only when we consider the limit n → ∞. Things simplify a lot then.
So, while this is the best talk I've heard in a long time, there's a bit of salesmanship involved here. And by the time the pop science media get ahold of his work, they say stuff like "physicists have discovered a jewel-shaped geometric object that challenges the notion that space and time are fundamental constituents of nature". 🤢
But still, a great talk.
https://www.youtube.com/watch?v=lJwn4R3PeNc
John Carlos Baez
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2024-10-17 00:58:26 UTC
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"content": "I loved this lecture by Nina Arkani-Hamed. He has a nice way of presenting things as a story. \n\nAfter he gets rolling here, he explains how particle physicists could discover some famous shapes called \"associahedra\" just by keeping track of the poles in the scattering matrix. Since I know associahedra from category theory and topology, this is astounding! \n\nHe also keeps prerequisites to a minimum. Well, okay: if you don't have a physics PhD don't watch this. You need to know the Feynman rules, and how Feynman diagrams have poles when the energy-momentum of a virtual particle is 'on shell' - i.e., takes a value that a real particle can have. \n\nIt also helps to have seen how Feynman diagrams for gauge bosons look like they're made of ribbons. But this shows up only at first.\n\nWhat I don't love is how he covers up some of his assumptions. He's talking about a spin-0 field Φ of mass m that takes values in the Lie algebra su(n), with a cubic self-interaction\n\ntr(Φ³)\n \nThis is not like our universe! When he sets m=0 this theory would apply to nonexistent 'spin-zero gluons'.\n\nMore importantly, he only considers planar, tree-shaped Feynman diagrams! This restriction kicks in naturally only when we consider the limit n → ∞. Things simplify a lot then.\n\nSo, while this is the best talk I've heard in a long time, there's a bit of salesmanship involved here. And by the time the pop science media get ahold of his work, they say stuff like \"physicists have discovered a jewel-shaped geometric object that challenges the notion that space and time are fundamental constituents of nature\". 🤢 \n\nBut still, a great talk.\n\nhttps://www.youtube.com/watch?v=lJwn4R3PeNc",
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