{"id":1403,"date":"2013-11-10T16:00:32","date_gmt":"2013-11-10T23:00:32","guid":{"rendered":"http:\/\/theoryofeverything.org\/MyToE\/?p=1403"},"modified":"2013-11-10T16:00:32","modified_gmt":"2013-11-10T23:00:32","slug":"more-amplituhedron-capability-projected-hull-surface-area-and-volume","status":"publish","type":"post","link":"http:\/\/theoryofeverything.org\/theToE\/2013\/11\/10\/more-amplituhedron-capability-projected-hull-surface-area-and-volume\/","title":{"rendered":"More amplituhedron capability (projected hull surface area and volume)"},"content":{"rendered":"

Getting more capability built into ToE_Demonstration.nb<\/a> 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…<\/p>\n

A few more pics of Positive Grassmannian Amplituhedrons…
\n\"amplituhedron-0b\"<\/a><\/p>\n

\"amplituhedron-0c\"<\/a>
\nThis last diagram is obtained using the following amplituhedron0.m<\/a> as input to the ToE_Demonstration.nb<\/a> (when using fully licensed Mathematica) as shown below:
\n* This is an auto generated list from ToE_Demonstration.nb *)
\nnew := {
\nartPrint=True;
\nscale=0.1;
\ncylR=0.018;
\nrange=2.;
\npt={-0.3, 0.0, 0.6};
\nfavorite=1;
\nshowAxes=False;
\nshowEdges=True;
\nshowPolySurfaces=True;
\neColorPos=False;
\ndimTrim=5;
\nds=6;
\npListName=”First8″;
\ndsName=”nSimplex”;
\np3D=” 3D”;
\nedgeVals={{Sqrt[11\/2], 8}, {Sqrt[9\/2 – Sqrt[2]], 4}, {Sqrt[9\/2 + Sqrt[2]], 4}};
\n};new;<\/p>\n

Positroid Diagrams:
\n\"amplituhedron-0a\"<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

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 … Continue reading More amplituhedron capability (projected hull surface area and volume)<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[28,16],"class_list":["post-1403","post","type-post","status-publish","format-standard","hentry","category-physics","tag-amplituhedron","tag-physics"],"aioseo_notices":[],"_links":{"self":[{"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/1403","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/comments?post=1403"}],"version-history":[{"count":0,"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/1403\/revisions"}],"wp:attachment":[{"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=1403"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=1403"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=1403"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}