Amplituhedron: newly discovered mathematical object

[Physics Monkey]

I have no idea :), but why not tensor networks for scattering amplitudes?

 

[atyy]

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.

 

[Physics Monkey]

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.

 

[atyy]

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".

 

[Physics Monkey]

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.

 

[.Scott]

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?

 

[MathematicalPhysicist]

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?

 

[Myslius]

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.

 

[lpetrich]

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.