# Questions tagged [amplituhedron]

A geometric object whose volume is conjectured to be related to scattering amplitudes. It is used mostly in string theory.

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### 3-Particle Kinematics and Parity of Operators

Recall that if the momentum of scattering amplitudes is taken to be complex and from little group scaling that the 3-particle interaction for massless particles of any spin is given as ...
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### "Fourier Transformation" of angle spinors to twistor variables

This relates to the derivation of equation (5.15) if Elvang and Huang's textbook. The idea is to transform the spinor helicity variables we are using, $(|i\rangle_{\dot{a}},[j|^a)$ to go into twistor ...
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### N=4 Supersymmetric Ward identity

(This question pertains to exercise 4.13 of Elvang and Huang's textbook (which used to be lecture notes). This is not for a class, just to learn some new tools for work). Consider the expansion of the ...
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### Scalar QED amplitudes with BCFW Recursion Relation

(This question comes from exercise 3.5 of Elvang's and Huang's "Scattering amplitudes in Gauge Theory and Gravity" book. This is not for a class, this is to learn a new technique; albeit I ...
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### Complex BCFW-shift of Parke-Taylor amplitude

(This question stems from problem 3.3 of Elvang's and Huang's "Scattering Amplitudes in Gauge Theory and Gravity" book). Consider the Parke-Taylor amplitude given as A_n[1^- ...
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### Every possible QFT from positive geometry?

Physicist Nima Arkani-Hamed has taken an interesting approach to understand fundamental physics based on geometry (specifically, positive geometry constructions). This started with his work with ...
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### Why does the amplitude not increase the speed of the sound wave?

The way I see it,if there's a set up A which has 5 particles and another set up B which also has 5 particles,and assuming everything else is same in these set up,like distance between particles etc,if ...
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### Positive geometry and log singularities

In order to define a positive geometry it is a requirement that has to be a logarithmic singularities on the boundaries, for example for an interval (endpoints $a$ and $b$) the canonical form is \...
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### Kinematics of Scattering Amplitudes in $\left(2, 2\right)$ Signature within the Amplituhedron

I am just working my way through the concepts of Amplituhedron and often stumble across the phrase [...] in $\left(2,2\right)$ signature $\lambda$, $\tilde{\lambda}$ are real and independent [...] ...
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### Differential forms in projective space

I am currently reading some paper about the Amplituhedron, and it is using projective geometric way to present amplitudes. How can we define forms in projective space to measure volume for a polytope?
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### Question about an NHMV amplitude (in the book by Elvang et al) and its representation by plabic graphs

I am looking at the NMHV amplitude with six particles with three positive helicities (particles 1,3,5). This amplitude is given in Eq.(10.1), which is [3,1,6,5,4]+[3,2,1,6,5]+[3,2,1,5,4] My question ...
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### Questions about the plabic graphs in the amplituhedron program

I am reading the book by Arkani-Hamed et al. I see how one can get the permutation from a plabic graph, and I see how different plabic graphs can be shown to be equivalent through moves. But I don't ...
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### Ordering ambiguity in the spinor helicity formalism of scattering amplitudes

I am following Nima's course on "Quantum mechanics and spacetime, total positivity and motives", and I wonder if there's a direct way to understand the ordering ambiguity when we are summing ...
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### Veneziano amplitude in quantum field theory

It is well-known, that Veneziano amplitude is the string scattering amplitude for the scattering of four open bosonic strings in their tachyon states. Are some QFT models, in which amplitude is ...
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### How to derive a formula involves a delta function? [closed]

I watched the video: Geometry of scattering amplitudes of lectures by Nima Arkani-Hamed. At 3:00:00, he derived the following equation: \begin{align} & \int \frac{dc_1}{c_1} \cdots \frac{dc_5}{c_5}...
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### What are the equations and constraints defining an/the Amplituhedron?

No doubt we've all read quite a bit about amplituhedra in recent years, the best thing since sliced bread apparently for obtaining scattering amplitudes. But finding on the web formal definitions of ...
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### Amplituhedron without SUSY

I was reading around about the Amplituhedron (there are many topics on this SE or in other places for discussions outside this), and I was wondering, is supersymmetry required to make it work or to ...
1 vote
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### How to prove that the scattering amlitude of bi-adjoint scalar field theory admits a Cachazo-He-Yuan (CHY) representation?

How to prove that the scattering amlitude of bi-adjoint scalar field theory admits a Cachazo-He-Yuan (CHY) representation?
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### Other spaces like Fourier space

Are there any other spaces like Fourier space in which one can more physical information than configuration space? In a summer school about scattering amplitudes, someone told me that this relation ...
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### Can elementary particles be abstractly represented as polytopes or geometric functions?

In Quantum Field Theory, elementary particles are represented like localized oscillations (localized transverse spherical standing waves) of their underlying fields, or superpositions of their normal ...
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### Is the Amplituhedron somehow equivalent to the S-matrix theory?

Amplituhedra are a family of spaces with the property that co-dimension one boundary of an Amplituhedron are the product of "smaller" Amplituhedra. In addition they are given a volume form that has a ...
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### Are new discoveries in quantum physics (e.g. Amplituhedron) supporting one of the classical QM interpretations? [closed]

Are new discoveries in quantum physics (e.g. Amplituhedron, Higgs boson) supporting one of the classical QM interpretations? For example Copenhagen, Everett many worlds or Penrose interpretations. Or ...
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### What is the meaning of the dlog integrations in the on-shell/grassmannian representation of N=4 SYM scattering amplitudes?

After reading part of this paper by Nima Arkani-Hamed, http://arxiv.org/abs/1212.5605, I cannot understand what is the precise meaning of the $dlog(\alpha)$ integrations. Any on-shell diagram is ...
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### Notation for Propability Amplitudes

I've recently stumbled upon a certain piece of notation that doesn't quite seem clear to me. When discussing the amplituhedron, my teacher mentioned the relation between the volume and the amplitude ...
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### Relation between canonical forms and volume of polytopes

Références: Ref $1$: Henriette Elvang, Yu-tin Huang: Scattering Amplitudes Ref $2$: Jaroslav Trnka: The Amplituhedron [For simplicity, the notations of the $2$ refs have been merged] The area of a ...
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### What happens to the amplituhedron in a non-peturbative context?

The Amplituhedron has recently been popular; it supposedly encodes perturbative scattering amplitudes in a simple, geometric fashion. What happens to it in a non-perturbative context? Is there ...
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### What is known on violations of unitarity or locality?

Recently the amplituhedron become a hot topic. I realized that two of the central pillars that QFT is based on, unitarity and locality, are no longer playing an important part (due to gravitational ...
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### How does one actually compute the amplituhedron?

I was watching Nima's very popular talk (download if you're using chrome) (also mirrored at youtube here) about the "Amplituhedron", which has suddenly become very popular recently. He talks all ...
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### Is integrability necessary for the Amplituhedron?

It is well known that there exist mappings between operators in N = 4 Super Yang–Mills and spin chain states making the theory Bethe Ansatz integrable. Is integrability a necessity for the ...
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