FCLoopFindSubtopologies[topo]
finds all scalefull subtopologies of the FCTopology topo
.
Each subtopology receives a marker that specifies the topology from which it was derived. The symbol denoting the marker is specified via the option SubtopologyMarker
. Setting it to False
will disable the inclusion of the markers
See also
Overview, FCTopology, FCLoopFindTopologies, FCLoopFindTopologyMappings, SubtopologyMarker.
Examples
res = FCLoopFindSubtopologies[FCTopology[TRI, {SFAD[{{p1, 0}, {0, 1}, 1}],
SFAD[{{p2, 0}, {0, 1}, 1}], SFAD[{{p1 + Q1, 0}, {0, 1}, 1}], SFAD[{{p1 + p2 + Q1, 0},
{0, 1}, 1}], SFAD[{{-p1 + Q2, 0}, {0, 1}, 1}], SFAD[{{-p1 - p2 + Q2, 0}, {0, 1}, 1}]},
{p1, p2}, {Q1, Q2}, {}, {}]];
19
Show the first three subtopologies of this 2-loop self-energy topology
{FCTopology(TRI,{(p12+iη)1,(p22+iη)1,((p1+Q1)2+iη)1,((p1+p2+Q1)2+iη)1,((Q2−p1)2+iη)1,((−p1−p2+Q2)2+iη)1},{p1,p2},{Q1,Q2},{},{}),FCTopology(TRIR1,{(p22+iη)1,((p1+Q1)2+iη)1,((p1+p2+Q1)2+iη)1,((Q2−p1)2+iη)1,((−p1−p2+Q2)2+iη)1},{p1,p2},{Q1,Q2},{},{FCGV(SubtopologyOf)→TRI}),FCTopology(TRIR2,{(p12+iη)1,((p1+Q1)2+iη)1,((p1+p2+Q1)2+iη)1,((Q2−p1)2+iη)1,((−p1−p2+Q2)2+iη)1},{p1,p2},{Q1,Q2},{},{FCGV(SubtopologyOf)→TRI})}
res = FCLoopFindSubtopologies[FCTopology[topo1, {SFAD[{{p3, 0}, {0, 1}, 1}],
SFAD[{{p2, 0}, {0, 1}, 1}], SFAD[{{p1, 0}, {0, 1}, 1}],
SFAD[{{p2 + p3, 0}, {0, 1}, 1}], SFAD[{{p2 - Q, 0}, {0, 1}, 1}],
SFAD[{{p1 - Q, 0}, {0, 1}, 1}], SFAD[{{p2 + p3 - Q, 0}, {0, 1}, 1}],
SFAD[{{p1 + p3 - Q, 0}, {0, 1}, 1}], SFAD[{{p1 + p2 + p3 - Q, 0},
{0, 1}, 1}]}, {p1, p2, p3}, {Q}, {}, {}], FCE -> True];
36
Show the first three subtopologies of this 3-loop self-energy topology
{FCTopology(topo1,{(p32+iη)1,(p22+iη)1,(p12+iη)1,((p2+p3)2+iη)1,((p2−Q)2+iη)1,((p1−Q)2+iη)1,((p2+p3−Q)2+iη)1,((p1+p3−Q)2+iη)1,((p1+p2+p3−Q)2+iη)1},{p1,p2,p3},{Q},{},{}),FCTopology(topo1R1,{(p22+iη)1,(p12+iη)1,((p2+p3)2+iη)1,((p2−Q)2+iη)1,((p1−Q)2+iη)1,((p2+p3−Q)2+iη)1,((p1+p3−Q)2+iη)1,((p1+p2+p3−Q)2+iη)1},{p1,p2,p3},{Q},{},{FCGV(SubtopologyOf)→topo1}),FCTopology(topo1R2,{(p32+iη)1,(p12+iη)1,((p2+p3)2+iη)1,((p2−Q)2+iη)1,((p1−Q)2+iη)1,((p2+p3−Q)2+iη)1,((p1+p3−Q)2+iη)1,((p1+p2+p3−Q)2+iη)1},{p1,p2,p3},{Q},{},{FCGV(SubtopologyOf)→topo1})}