# Tag Archives: Amplituhedron

# More amplituhedron capability (projected hull surface area and volume)

Getting more capability built into ToE_Demonstration.nb where it can now calculate the scattering amplitude by calculating the volume of the projected hull of selected edges in the n-Simplex Amplituhedron (based on a theory by Nima Arkani-Hamed, with some Mathematica code from J. Bourjaily for the positroid diagram). Of course, there is still much work to get this wrapped up…

A few more pics of Positive Grassmannian Amplituhedrons…

This last diagram is obtained using the following amplituhedron0.m as input to the ToE_Demonstration.nb (when using fully licensed Mathematica) as shown below:

* This is an auto generated list from ToE_Demonstration.nb *)

new := {

artPrint=True;

scale=0.1;

cylR=0.018;

range=2.;

pt={-0.3, 0.0, 0.6};

favorite=1;

showAxes=False;

showEdges=True;

showPolySurfaces=True;

eColorPos=False;

dimTrim=5;

ds=6;

pListName=”First8″;

dsName=”nSimplex”;

p3D=” 3D”;

edgeVals={{Sqrt[11/2], 8}, {Sqrt[9/2 – Sqrt[2]], 4}, {Sqrt[9/2 + Sqrt[2]], 4}};

};new;

# Amplituhedron Visualizations!

Playing around trying to visualize the latest in the theoretical high energy particle physics (HEP/TH) determining how particle masses might be predicted from geometric principles (based on a theory by Nima Arkani-Hamed, with some Mathematica code from J. Bourjaily for the positroid diagram).

Positive Grassmannian Amplituhedrons

Compare this Mathematica(l) basis to the artistic representation by Andy Gilmore