Amplituhedron: newly discovered mathematical object

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Discussion Overview

The discussion revolves around the amplituhedron, a newly discovered mathematical object related to particle interactions and quantum physics. Participants express varying levels of excitement and skepticism about its implications, beauty, and the nature of its representation.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants express excitement about the beauty of the amplituhedron and its potential significance in understanding particle interactions.
  • Others question the origins of the structure and seek clarification on its geometric representation and higher-dimensional nature.
  • A participant suggests that the information about scattering amplitudes can be encoded in the amplituhedron without reference to space or time, but acknowledges the challenges in generalizing this model.
  • Concerns are raised about the aesthetic representation of the amplituhedron, with requests for clearer illustrations and explanations of its geometric properties.
  • Some participants propose creating a 3D interactive model of the amplituhedron to better visualize its structure.
  • There are doubts about the ability to accurately represent the amplituhedron in three dimensions, with suggestions that it may only be a simplification of a more complex object.
  • One participant argues that the amplituhedron may simply be a re-formulation of existing theories and expresses skepticism about its novelty and excitement.
  • Another participant references a talk by Arkani-Hamed, discussing the relationship between the amplituhedron and permutations in a mathematical context.

Areas of Agreement / Disagreement

Participants exhibit a mix of enthusiasm and skepticism regarding the amplituhedron, with no clear consensus on its significance or the adequacy of its representations. Multiple competing views remain about its implications and the nature of the object itself.

Contextual Notes

Some participants highlight the dependence on specific theoretical frameworks, such as maximally supersymmetric Yang-Mills Theory, and the unresolved nature of certain mathematical steps related to the amplituhedron's properties.

  • #61
I have no idea :), but why not tensor networks for scattering amplitudes?
 
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  • #62
It'd be neat. I have to understand more what they are doing. I'd kind of assumed it doesn't generalize beyond such a high symmetric theory, unlike AdS/CFT. But maybe that's wrong.
 
  • #63
I have a similar feeling. In fact, in the case of AdS/CFT I do think it generalizes as you know, but here I'm not so sure.
 
  • #64
Physics Monkey said:
I have no idea :), but why not tensor networks for scattering amplitudes?

Like http://arxiv.org/abs/0907.0151 and http://arxiv.org/abs/1209.3304 ?

But I'm not sure if Arkani-Hamed and collaborators mean amplitude in the same way, I remember it's just the integrand or something like that. But conceptually it seems like it should be related to the normal meaning of "amplitude".
 
  • #65
Yes, I think they focus on the integrand of the multi-loop scatting amplitude. It still has to integrated over internal momenta (which I think are "on shell" but have been complexified). I'm not exactly sure what the full procedure is.

But if they're somehow considering twistors or something similar, perhaps we can build a twistor tensor network so that the sum over the internal variables is like a sum over loop momenta.
 
  • #66
MathematicalPhysicist said:
How do you know that it's finite?
As I understand it, the number of dimensions you need for the "gem" is proportional to the number of particles involved in the interaction. So how many particles are there in the universe? Or more precisely, what is the cardinality of particles in the universe?
 
  • #67
.Scott said:
As I understand it, the number of dimensions you need for the "gem" is proportional to the number of particles involved in the interaction. So how many particles are there in the universe? Or more precisely, what is the cardinality of particles in the universe?

How do you know that there's a finite number of particles in the universe?
 
  • #68
jackmell said:
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.

I can do that and i would love to do that :) Just a couple of days of coding, that's the easy part. The hardest part is to understand Amplituhedron's geometrical properties and how it actually works.
 
  • #69
jackmell said:
Lemme' ask you this hameed, you code? I mean am I the only one in PF that actually likes coding in Mathematica for fun? ...
I do also.

However, I don't see what's so special about the amplituhedron. It looks like it could be a good graphical method, like Young diagrams, but I think that it may be too early to say.
 

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