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This question is taken from this Physics Stack Exchange question by "Dimension10 (page creator)" with it's answer given by "Lubos Motl".







QuestionEdit

I was watching Nima's very popular talk (download if you're using chrome) (also mirrored at youtube here about the "Amplitudihedron", which has suddenly become very popular recently.

He talks all about how the Amplitudihedron computes the same result for the scattering amplitudes as ordinary peturbation theory in a simple and elegant way, but I fail to understand how one actually computes the Amplitudihedron for a certain scattering process anyway?

As per the recent TRF posts about Amplitudihedrons and why they don't wear diapers, I can understand that one may calculate the scattering amplitudes by simply taking the volume of the Amplitudihedrons (ignoring constants, I guess), but how does one actually calculate the amplituhedron?

I'm especially stunned by the image (looks like a sort of a concrete example, don't know how they constructed the amplituhedron):

Amplitudihedron

To summarise my question, how does one actually figure out, or construct, the amplituhedron based on the specific scattzering process?

Dimension10 \left(\right. Talk  \cdot Edits \left. \right) 06:40, November 8, 2013 (UTC)

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AnswersEdit

Answer 1Edit

Wait for the paper. It's a geometric object in some space whose dimension depends on the number of external particles, number of loops, and number of "helicity flips". The volume form, the integrand, is a simple form roughly scaling like 1/x where x is the distance from a face, and the faces are given by inequalities of the type "determinants of a submatrix are zero". These inequalities depend on the external momenta and/or twistor variables, sort of linearly or simply. The scattering amplitude is the single simple integral of the volume form over the polytope.

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