Question about plabic graphs in the amplituhedron approach

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SUMMARY

This discussion centers on the use of plabic graphs within the amplituhedron framework, specifically addressing the determination of physicality and the parameter "k" related to negative helicities. The participant seeks clarification on whether the value of "k" can be derived from the permutation associated with a graph by counting the values mapped above "n." The conversation highlights the need for references, particularly the seminal work "Grassmannian Geometry of Scattering Amplitudes" by Akani-Hamed et al., to provide context and understanding of these concepts.

PREREQUISITES
  • Understanding of plabic graphs in the context of the amplituhedron.
  • Familiarity with permutations and their application in mathematical graph theory.
  • Knowledge of negative helicities in particle physics.
  • Awareness of the foundational text "Grassmannian Geometry of Scattering Amplitudes."
NEXT STEPS
  • Research the properties and applications of plabic graphs in the amplituhedron framework.
  • Study the concept of negative helicities and their significance in scattering amplitudes.
  • Examine the mathematical underpinnings of permutations in graph theory.
  • Read "Grassmannian Geometry of Scattering Amplitudes" by Akani-Hamed et al. for comprehensive insights.
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Researchers, physicists, and mathematicians interested in advanced topics in scattering amplitudes, particularly those exploring the intersections of graph theory and theoretical physics.

nrqed
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I have a few questions on these graphs. For example if there is a way to tell directly from a complicated graph if it is "physical" in the sense that it describes an actual process. I have also questions on the building of graphs using BCFW bridges, on determining the value of the parameter "k" directly from the permutation associated to a graph, etc.

I won't type all my questions yet, I will wait to see if someone is familiar with these questions first.

But one question is this: I think that the value of "k" (=number of negative helicities) can be obtained directly from the permutation by counting how many of the values are mapped by the permutation to a value above n. Is that correct? I have not seen this stated explicitly like this or proved anywhere.

Thanks!
 
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nrqed said:
I have a few questions on these graphs.

What graphs? What are you talking about?

A reference would help.
 
PeterDonis said:
What graphs? What are you talking about?

A reference would help.
I meant the graphs mentioned in the title of my post: the plabic graphs in the amplituhedron program.
 
nrqed said:
I meant the graphs mentioned in the title of my post: the plabic graphs in the amplituhedron program.

Which doesn't help, since I have no idea what "the amplituhedron program" is, much less what "the plabic graph" in it are. Even if I did, I would have no idea what version of those things you are talking about. That's why you need to give a reference.
 
PeterDonis said:
Which doesn't help, since I have no idea what "the amplituhedron program" is, much less what "the plabic graph" in it are. Even if I did, I would have no idea what version of those things you are talking about. That's why you need to give a reference.

If someone asks a question about Feynman diagrams and someone replies "what diagrams? What are you talking about?", it is probably a sign that the person cannot help with the question.

I wonder how you know that if you knew about plabic graphs as used for the amplituhedron, you would still not know what I am talking about. That's quite amazing to me :-)

If you need a specific reference, you can of course look for example at the "bible" on the topic, "Grassmannian Geometry of Scattering Amplitudes" by Akani-Hamed et al.
 
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