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A Question about the associahedron/amplituhedron

  1. Aug 1, 2018 #1

    nrqed

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    If anyone here has worked on the associahedron and/or amplituhedron, I would like your input. I am focusing now on the paper by Nima Arkani-Hamed et al, "Scattering Forms and the Positive Geometry of Kinematics, Color an the Worldsheet".

    The key step to define the kinematic associahedron is to impose ##X_{ij} \geq 0## and also the impose the ##c_{ij} > 0 ##. They do this without giving any motivation at all. I know that it gives the correct answer in the end, but I wonder if there is any way to motivate these choices, from a physics point of view (or short of that, from a mathematical point of view). It would be nice to get some intuition about what leads to these choices, other than "because it gives the correct final answer".

    Thank you!
     
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  3. Aug 2, 2018 #2

    MathematicalPhysicist

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    How do they know what is the correct answer?
     
  4. Aug 2, 2018 #3

    nrqed

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    The scattering form restricted to the associahedron reproduces the correct amplitude. Or, alternatively, the volume of the dual associahedron gives the correct amplitude.
     
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