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Amplituhedron: newly discovered mathematical object

  1. Sep 18, 2013 #1


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    Is this anything to get excited about? I have no idea what it's about.

    https://www.simonsfoundation.org/wp-content/uploads/2013/09/amplutihedron_span.jpg [Broken]

    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Sep 18, 2013 #2
    It's beautiful and very exciting!
  4. Sep 18, 2013 #3


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    It must exist because it is so beautiful! :approve:
  5. Sep 18, 2013 #4
    I guess the next question is "where did this structure come from in the first place?"
  6. Sep 18, 2013 #5


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    This is amazing! Great article link, thanks.
  7. Sep 18, 2013 #6
    You can watch Arkani Hamed give a talk at the SUSY 2013 conference about the Ampllituhedron and how their research led them to its discovery here. It's pretty involved as far as having an in-depth understanding of particle physics and QFT, but it's engaging regardless.

    It's a pretty fantastic discovery, that all of the information about scattering amplitudes can be encoded in one geometric object, with no reference to space or time, locality or unitarity (which come out as emergent properties of the geometry). Granted, keep in mind that this model is built on maximally supersymmetric Yang-Mills Theory, and it will take a lot of work to generalize it to more complex QFTs (especially since we have found no evidence to support SUSY), but it looks pretty promising just in the beauty of the theory.
  8. Sep 18, 2013 #7


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    Don't know what it is , but it's beautiful.
  9. Sep 18, 2013 #8
  10. Sep 18, 2013 #9


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    Why isn't he wearing socks?
  11. Sep 18, 2013 #10
    He's copying Albert.
  12. Sep 19, 2013 #11


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    What a wannabe. But Albert would be pleased if he got rid of unitarity.
  13. Sep 19, 2013 #12
    I hate to be disagreeable but I feel I must add some sense of sensibility to this dog and pony show.

    That picture does nothing for me. It's just some rainbow curvy-looking thing that appears to be missing a piece. Is the actual object a higher-dimensional object and if so then what is the picture representing and I bet a dollar the colors are really not part of the object but just added to make it look pretty.

    I request a better explanation of what exactly the geometric object is, and a better illustration of what exactly it looks like. Hold the pretty colors please.
  14. Sep 19, 2013 #13
    Last edited by a moderator: May 6, 2017
  15. Sep 19, 2013 #14
    Ok Enigman. Thank you. That is in my opinion much, much better and I can actually see what it looks like in 3D although a nice 3D model that I could rotate would be better. And I did read the link above but I guess I missed that diagram. Sorry.

    Also, while we're at it, I don't think it would be too hard to actually create a 3D model of that figure in Mathematica that we could rotate and if so, then we could say, "hey, anybody if you want more than a pretty flat picture of what's happening, PF's got it cus' we know what's happening." So I say we move this thread to the Math and Science software forum and ask someone to do that. No I don't want to do it because I do that stuff all the time and would like someone else to.

    Thank you.
    Last edited: Sep 19, 2013
  16. Sep 19, 2013 #15
    There's so many ways to look at that thing...
  17. Sep 19, 2013 #16
    Oh guys don't you see, don't you see? Someone here has a marvelous opportunity to contribute to humanity. What I would like is for someone to create a Wolfram Demonstration Project that not only draws the amplituhedron accurately in 3D, (with colors if you want) but also gives the user the opportunity to adjust the dimensions of each face interactively (if that is an allowable transformation). And that person would, I suggest, be the first person in the world to write a very nice 3D demonstration on this wonderful, newly created mathematical object.

    Just sayin' that's all. :)

    Haven't checked the demonstration project but I doubt seriously it's already in there.
    Last edited: Sep 19, 2013
  18. Sep 19, 2013 #17
    How can it be a mathematical object?
  19. Sep 19, 2013 #18
    Lemme' ask you this hameed, you code? I mean am I the only one in PF that actually likes coding in Mathematica for fun? Keep in mind who ever does this can never be forgotten even in death cus' all we have to do is google them and bam! There it is: first person in the world to create a nice 3D realistic, interactive image of the amplituhedron.

    But that's ok, that's alright, no big deal if no one is interested. I got plenty other stuff to do.
  20. Sep 19, 2013 #19
    No I don't code but I will start learning how to do so when I start collage but I still don't get your point, are you trying to draw this shape using coding in mathematica?
  21. Sep 19, 2013 #20


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    I doubt that you can accurately represent that thing in just 3 dimensions. Feel free to prove me wrong ;).
  22. Sep 19, 2013 #21


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    It would just look silly. Like describing a cow with a single point.

    However, we can take 3D cross sections. That's where the steak is:

    https://www.simonsfoundation.org/wp-content/uploads/2013/09/amplituhedron-drawing_web-271x300.jpg [Broken]
    Last edited by a moderator: May 6, 2017
  23. Sep 19, 2013 #22
    The actual object itself would prepresent every possible particle interaction, and is infinite dimensional. The hand-drawn geometric object with the subtitle "8-gluon particle interaction" is actually only one face of a 4-dimensional object which fully describes the 8-gluon interaction. The 3-D face describes one possible permutation, so to speak, of the possible ways that 8 gluons can interact, as written underneath [1- 2+ 3+ 4+ 5+ 6+ 7- 8-].
  24. Sep 19, 2013 #23
    Yes hameed, just a nice 3D plot of that hand-drawn figure posted above. It's not rocket science guys. Jesus, why you guys trying to make it so complicated?
  25. Sep 19, 2013 #24


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    Epps, ¿moved to General Discussion?
  26. Sep 19, 2013 #25
    So this is just a re-formulation of an existing theory, which its self is just a toy-model.

    So it simplifies and already over-simplified theory?

    I don't see the excitement.
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