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Questions tagged [amplituhedron]

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

A geometric object whose volume is related to scattering amplitudes.

30 questions
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What is the actual significance of the amplituhedron?

The news that physicists have discovered a geometrical object that simplifies a lot our models of quantum physics has recently became viral. For an outsider like me, it is difficult to actually understand the significance of this finding. Is it…
MaiaVictor
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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 about how the amplituhedron computes the same result…
Abhimanyu Pallavi Sudhir
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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 Amplituhedron? Most QFTs are not integrable. Does Nima…
Bubble
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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 triangle in $CP_2$, can be expressed, using dual…
Trimok
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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 interactions). I would like to get more details on…
Yair
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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 Jaroslav Trnka in the amplituhedron 1 and later it was…
vengaq
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What is the meaning of the $d\log$ integrations in the on-shell/Grassmannian representation of ${\cal N}=4$ 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 $d\log(\alpha)$ integrations. Any on-shell diagram is associated with a "differential form" (see 6.1 of…
giulio bullsaver
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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 \begin{equation} A_3(1^{h_1}2^{h_2}3^{h_3}) = c\langle…
MathZilla
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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 \begin{equation} A_n[1^- 2^- 3^+\cdots n^+] = \frac{\langle 12\rangle^4}{\langle…
MathZilla
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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 $$\frac{dx(b-a)}{(b-x)(x-a)}$$ My question is: Why do…
MZperX
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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 define it? I find the quest to geometrize anything…
LowFieldTheory
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Are new discoveries in quantum physics (e.g. Amplituhedron) supporting one of the classical QM interpretations?

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 are these discoveries making new path for new…
Ripe90
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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 space. The Fourier transformation is given…
MathZilla
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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 am already close to the full solution.) Consider the…
MathZilla
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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 [...] in various references (Jaroslav Trnka, 2014; page…
Petermailpan
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