Talk:Amplituhedron

From Wikipedia, the free encyclopedia
Jump to: navigation, search
          This article is of interest to the following WikiProjects:
WikiProject Physics (Rated Start-class, Mid-importance)
WikiProject icon This article is within the scope of WikiProject Physics, a collaborative effort to improve the coverage of Physics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Start-Class article Start  This article has been rated as Start-Class on the project's quality scale.
 Mid  This article has been rated as Mid-importance on the project's importance scale.
 
WikiProject Mathematics (Rated Start-class, Mid-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
Start Class
Mid Importance
 Field: Mathematical physics

Usage and explanation of the terms Scattering amplitude, Scattering patterns[edit]

We should resolve several questions about the usage and explanation of the terms Scattering amplitude and Scattering patterns.

I've posted about this to Wikiproject Physics here (http://en.wikipedia.org/wiki/Wikipedia_talk:WikiProject_Physics#Amplituhedron.2C_Scattering_amplitude.2C_Scattering_patterns)

Thanks - 186.221.170.80 (talk) 20:26, 19 September 2013 (UTC)

It seems like an obvious next step for quantum mechanics to begin to treat mathematics as having the same eleven dimensions as physics. Where the authors speak of making educated guesses their mathematics might allow that rather than precision and irrational numbers there are values that have variable probabilities according to where and how they are vibrating on the membrane.It sounds like a somewhat libertarian philosophy that if you had no laws you would have no crimes...12.187.94.20 (talk) 09:50, 20 September 2013 (UTC)

Supercalifragilistic[edit]

I love this article! There were almost 2 or three words which I have understood! ;-) [No, it's not a problem, it's an extreme topic.] --grin 06:59, 20 September 2013 (UTC)

It's not you, the article makes no attempt to explain anything. Miguel (talk) 10:42, 22 September 2013 (UTC)
Alien technology. They are letting it out a little bit at a time and making it look like humans discovered it so we won't panic. “This is completely new and very much simpler than anything that has been done before.” No duh.

M-theory?[edit]

I see no perceptible relationship to M-theory, and invite someone to explain the relationship before restoring the "See also" link to M-theory. As it is, this link seems more confusing than enlightening. 81.155.213.195 (talk) 18:45, 20 September 2013 (UTC)

I can see superficial connections between this stuff and well-known facts about angular momentum, group representations, topological quantum field theries, and the like. I cannot comment on M theory. Miguel (talk) 10:41, 22 September 2013 (UTC)

Helpful blog?[edit]

The Amplituhedron and Other Excellently Silly Words 4 gravitons and a grad student, The trials and tribulations of four gravitons and a grad student

Why this article?[edit]

Am I correct in assuming that this article was written as a response to this popular piece?

- Miguel (talk) 10:38, 22 September 2013 (UTC)
And a bunch of other coverage in the mainstream media, thus giving it WP:N. The hype level of that article is a bit high, but the backgrounds of the authors, the venues in which the research has been presented, and the generally favourable reception by respectable physics bloggers and by leading physicists such as Ed Witten attest that this is serious. and potentially important, research. This article is a bit wooly at the moment, and needs kicking into shape by experienced editors with relevant knowledge, but that's in progress. -- The Anome (talk) 07:59, 23 September 2013 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── As mentioned on the wikiproject, I think this should be merged as a subset of the N=4 SYM article. What do other people think? AHusain (talk) 04:59, 5 October 2013 (UTC)

This article: N = 4 supersymmetric Yang–Mills theory? Lentower (talk) 06:16, 5 October 2013 (UTC)
Which Wikiproject? (And a link to that discussion please!) Lentower (talk) 06:16, 5 October 2013 (UTC)
Why do think this merger should happen in a few sentences or paragraphs? Lentower (talk) 06:16, 5 October 2013 (UTC)
Right now this article has a fundamental problem in that we have reliable pop sci articles about the reception of the amplituhedron, but the sources about the amplituhedron technique itself are all primary and unpublished. I don't doubt that they will get published in some form, but right now, it is [[WP:TOOSOON] for some of this material. I could see keeping this flawed article as a standalone in anticipation of eventual publication, but the flaws make me think that a merge to N = 4 supersymmetric Yang–Mills theory, where the amplituhedron is already mentioned, may be a better place for it. Of course, with no prejudice to article recreation when we get reliable sources. --Mark viking (talk) 06:37, 5 October 2013 (UTC)

Grassmannian as an infinite dimensional space?[edit]

The article refers to the Grassmannian as an infinite dimensional space, but then links to the Wikipedia article that only defines a Grassmannian in terms of finite dimensional spaces. Will there be any attempt made to reconcile the two articles? Penguian (talk) 07:52, 23 September 2013 (UTC)

The Grassmannian Gr(k, V) comprises all the k-spaces through a point in V-dimensional space. Making V = ∞ (infinity) is perfectly meaningful and consistent with the Grassmannian article. Unfortunately I do not know if it the correct Grassmannian in the present context. If it is, and assuming also that k is finite, then my understanding is that the amplituhedron will not have a closed boundary and I do not understand how an interior volume can be defined. Equally, if k = ∞ - 2 then the volume must be infinite, which is not what we get, so that must be wrong. — Cheers, Steelpillow (Talk) 12:51, 23 September 2013 (UTC)
The finite one applies here. AHusain (talk) 02:12, 24 September 2013 (UTC)
Thanks. I have edited the lead accordingly. — Cheers, Steelpillow (Talk) 09:18, 24 September 2013 (UTC)

Image request[edit]

As pointed out above, this article is a bit too close to OR w/o published research. Yet, there is a request for images. While the popular articles use either a hand drawn image of tetrahedral segments or the artist rendering (not yet public domain AFAIK), I always offer my images to WP (see examples below). I have created a tool that can project high-dimensional geometry into 2 & 3D and calculate the surface and volume through tetrahedral meshing (the technique suggested by Nima Arkani-Hamed for getting the scattering amplitudes of positive Grassmannians). I can also change the vertex shape, color, size based on their particle identities. I will upload more, suggestions of style/technique based on the physics are welcome.

Amplituhedron-0c.png
7-simplex orthogonal projection to 3D
Amplituhedron-0b.png
7-simplex to 3D with camera perspective showing hints of its 2D Petrie projection

Jgmoxness (talk) 13:58, 4 December 2013 (UTC)

I have seen next to nothing published on the conditions which any image must meet. Other than being a polytope in n dimensions, is there anything else that has been said about the geometrical form of the amplituhedron? I would assume that it is convex, but is that assumption justified? Must its facets necessarily be simplices? Must it, or can it, itself be a simplex, and under what circumstances? Does an amplituhedron in general show metric symmetries? Without references to this kind of information or a peer-reviewed and freely-licensed image, I don't think we can attempt anything that would be acceptable. The images shown above appear to me to stray too far into WP:OR territory (BTW, aren't they of a 7-simplex, an n-simplex in general having n + 1 vertices?) — Cheers, Steelpillow (Talk) 18:51, 4 December 2013 (UTC)
As I too inferred, I agree and can't answer your valid questions. My offer to produce and donate the image based on the answers still stands...
But if you read what seems to be the latest published/peer reviewed article on the topic, ref [2] of the article arXiv:1212.5605, it seems that there are several other types of images of interest. One is basically a type of G+(2,4) positive Grassmannian Hasse diagram seen on page 64. The other type are the "positroid" diagrams from J. Bourjaily's Mathematica code (publicly available at arxiv.org/1212.6974v1) which I used to quickly produce this image (but it is not quite as symmetric as the one on the last page of that paper).
Amplituhedron-0a.jpg
Jgmoxness (talk) 02:09, 5 December 2013 (UTC)
Yes, there can be no objection in principle to shell diagrams or Hasse diagrams, I had assumed you just meant geometrical polytopes. I'm not convinced that a Hasse diagram in the present article would explain very much unless there is a need to discuss its role, though I personally would find a brief discussion of shell diagrams useful. — Cheers, Steelpillow (Talk) 10:16, 5 December 2013 (UTC)

Geometric properties[edit]

What are some of the basic geometric properties of this shape? Is it regular? Schlaffi symbol? Others properties? In what system and geometry (there are a few mentions of spaces, but I really just want the details spelled out to me all in one go)? Actually, how does one determine how many dimensions it is (4?)? (I am not even sure if these questions make sense, especially in a general case, but I thought that I would ask.) 99.72.108.134 (talk) 08:01, 8 December 2013 (UTC)

In geometry, one may distinguish topological properties of a general form from the metric sizing of specific features. From what I have seen (that I can understand): the kind of topological space may vary, though being a Grassmannian it will be some type of compact, smooth manifold. So, for example, I read that at least one Grassmannian is a projective space, while none can be a simple-minded Euclidean space of our schooldays because that is not compact. The number of dimensions is basically the number of particles involved in the chosen scattering interaction to be modelled, but I don't know if it is exactly the same number or one or two higher. As to the metric properties, one might naively assume that they depend on the nature of the particular interaction and so would vary from one amplituhedron to another. Is there any symmetry in there? I have seen nothing on this and I suspect that it will be an important question for future research, as any systematic symmetry would point the way to an underlying principle. To the point of regularity and the accompanying Schläfli symbol? I would doubt that except as an arbitrarily-occurring special case of no significance, but who can say. Is an amplituhedron necessarily convex? I don't know myself, but that should be a relatively trivial and well-known fact for any competent theorist reading this (please?). The speculative nature of this reply means that I can add none of it to the article, but hoping it helps you a little. — Cheers, Steelpillow (Talk) 11:26, 8 December 2013 (UTC)

New paper[edit]

The Amplituhedron Nima Arkani-Hamed, Jaroslav Trnka, Submitted on 6 Dec 2013

Awesome, Tom. Many thanks for this and well spotted. It is answering a lot of questions for me. And it looks like there are more answers in there for people who actually understand this stuff, too! — Cheers, Steelpillow (Talk) 10:21, 12 December 2013 (UTC)